Statistical Analysis Subject

umairchill5

MAT10251Workbooks2018.zip

Home >Mathematics homework help >Statistics homework help >Statistical Analysis Subject

MAT10251 Workbooks 2018/~$Multiple Regression 2 Independent Variables Workbook.xlsx

MAT10251 Workbooks 2018/~$Simple Linear Regression Workbook.xlsx

MAT10251 Workbooks 2018/Boxplot Workbook.xlsx

DATA

Festival Expenditure
Amount Spent $
1119
615
971
553
343
502
928
1005
993
408
725
763

Boxplot

Festival Expenditure

343 343 343 0.5 1 1.5 502 502 502 0.5 1 1.5 744 744 744 0.5 1 1.5 993 993 993 0.5 1 1.5 1119 1119 1119 0.5 1 1.5 343 1119 1 1 502 993 0.5 0.5 502 993 1.5 1.5 Amount Spent $

Five-Number Summary

Five-Number Summary
Minimum	343.00
First quartile	502.00
Median	744.00
Third quartile	993.00
Maximum	1119.00

PLOT_DATA

Five-Number Summary
Minimum	343.00		Value	Plot
First quartile	502.00		343	0.5
Median	744.00		343	1
Third quartile	993.00		343	1.5
Maximum	1119.00		502	0.5
			502	1
			502	1.5
			744	0.5
			744	1
			744	1.5
			993	0.5
			993	1
			993	1.5
			1119	0.5
			1119	1
			1119	1.5
			343	1
			1119	1
			502	0.5
			993	0.5
			502	1.5
			993	1.5
Quartile Calculations (Book Rules)
	Initial first quartile rank	3.25
		Rule 3 applies
	use rank:	3
	value of rank:	502
	first quartile:	502
	Initial third quartile rank	9.75
		Rule 3 applies
	use rank:	10
	value of rank:	993
	third quartile:	993

PLOT_SUMMARY

Five-Number Summary
Minimum	343.00	Value	Plot
First quartile	502.00	343	0.5
Median	744.00	343	1
Third quartile	993.00	343	1.5
Maximum	1119.00	502	0.5
		502	1
		502	1.5
		744	0.5
		744	1
		744	1.5
		993	0.5
		993	1
		993	1.5
		1119	0.5
		1119	1
		1119	1.5
		343	1
		1119	1
		502	0.5
		993	0.5
		502	1.5
		993	1.5

Boxplot

343 343 343 0.5 1 1.5 502 502 502 0.5 1 1.5 744 744 744 0.5 1 1.5 993 993 993 0.5 1 1.5 1119 1119 1119 0.5 1 1.5 343 1119 1 1 502 993 0.5 0.5 502 993 1.5 1.5

PLOT_DATA_FORMULAS

Five-Number Summary
Minimum	343.00		Value	Plot
First quartile	502.00		343	0.5
Median	744.00		343	1
Third quartile	993.00		343	1.5
Maximum	1119.00		502	0.5
			502	1
			502	1.5
			744	0.5
			744	1
			744	1.5
			993	0.5
			993	1
			993	1.5
			1119	0.5
			1119	1
			1119	1.5
			343	1
			1119	1
			502	0.5
			993	0.5
			502	1.5
			993	1.5
Quartile Calculations (Book Rules)
	Initial first quartile rank	3.25
		Rule 3 applies
	use rank:	3
	value of rank:	502
	first quartile:	502
	Initial third quartile rank	9.75
		Rule 3 applies
	use rank:	10
	value of rank:	993
	third quartile:	993

Boxplot

343 343 343 0.5 1 1.5 502 502 502 0.5 1 1.5 744 744 744 0.5 1 1.5 993 993 993 0.5 1 1.5 1119 1119 1119 0.5 1 1.5 343 1119 1 1 502 993 0.5 0.5 502 993 1.5 1.5

PLOT_FORMULAS

Five-Number Summary
Minimum	343.00	Value	Plot
First quartile	502.00	343	0.5
Median	744.00	343	1
Third quartile	993.00	343	1.5
Maximum	1119.00	502	0.5
		502	1
		502	1.5
		744	0.5
		744	1
		744	1.5
		993	0.5
		993	1
		993	1.5
		1119	0.5
		1119	1
		1119	1.5
		343	1
		1119	1
		502	0.5
		993	0.5
		502	1.5
		993	1.5

Boxplot

343 343 343 0.5 1 1.5 502 502 502 0.5 1 1.5 744 744 744 0.5 1 1.5 993 993 993 0.5 1 1.5 1119 1119 1119 0.5 1 1.5 343 1119 1 1 502 993 0.5 0.5 502 993 1.5 1.5

MAT10251 Workbooks 2018/CIE Proportion Workbook.xlsx

COMPUTE

Confidence Interval: Proportion
Data
Sample Size	100
Number of Successes	10
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.1
Z Value	-1.9600
Standard Error of the Proportion	0.03
Interval Half Width	0.0588
Confidence Interval
Interval Lower Limit	0.0412
Interval Upper Limit	0.1588

COMPUTE_FORMULAS

Confidence Interval: Proportion
Data
Sample Size	100
Number of Successes	10
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.1
Z Value	-1.9600
Standard Error of the Proportion	0.03
Interval Half Width	0.0588
Confidence Interval
Interval Lower Limit	0.0412
Interval Upper Limit	0.1588

COMPUTE_OLDER

Confidence Interval: Proportion
Data
Sample Size	100
Number of Successes	10
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.1
Z Value	-1.9600
Standard Error of the Proportion	0.03
Interval Half Width	0.0588
Confidence Interval
Interval Lower Limit	0.0412
Interval Upper Limit	0.1588

COMPUTE_OLDER_FORMULAS

Confidence Interval: Proportion
Data
Sample Size	100
Number of Successes	10
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.1
Z Value	-1.9600
Standard Error of the Proportion	0.03
Interval Half Width	0.0588
Confidence Interval
Interval Lower Limit	0.0412
Interval Upper Limit	0.1588

MAT10251 Workbooks 2018/CIE Sigma Known Workbook.xlsx

DATA

Exam Mark
47.80
38.10
57.20
42.45
68.25
79.35
18.30
50.65
47.60
52.00
51.65
67.80
71.30
55.75
55.45
76.40
59.80
76.15
86.20
86.35
64.55
87.10
83.45
57.65
79.90
51.65
53.80
18.75
51.05
52.15

COMPUTE POP SD

Confidence Estimate for the Mean
Data
Population Standard Deviation	17.90022
Sample Mean	59.62
Sample Size	30
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.2681180928
Z Value	-1.9600
Interval Half Width	6.4054
Confidence Interval
Interval Lower Limit	53.2146
Interval Upper Limit	66.0254

COMPUTE SAMPLE SD

Confidence Estimate for the Mean
Data
Sample Standard Deviation	17.9002196095
Sample Mean	59.62
Sample Size	30
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.2681180215
Z Value	-1.9600
Interval Half Width	6.4054
Confidence Interval
Interval Lower Limit	53.2146
Interval Upper Limit	66.0254

COMPUTE STATISTICS

Confidence Estimate for the Mean
Data
Population/Sample Standard Deviation	17.9002196095
Sample Mean	59.62
Sample Size	30
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.2681180215
Z Value	-1.9600
Interval Half Width	6.4054
Confidence Interval
Interval Lower Limit	53.2146
Interval Upper Limit	66.0254

COMPUTE_FORMULAS

Confidence Estimate for the Mean
Data
Population Standard Deviation	17.9002
Sample Mean	59.62
Sample Size	30
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.2681144413
Z Value	-1.9600
Interval Half Width	6.4054
Confidence Interval
Interval Lower Limit	53.2146
Interval Upper Limit	66.0254

COMPUTE_OLDER

Confidence Estimate for the Mean
Data
Population Standard Deviation	17.9002
Sample Mean	59.62
Sample Size	30
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.2681144413
Z Value	-1.9600
Interval Half Width	6.4054
Confidence Interval
Interval Lower Limit	53.2146
Interval Upper Limit	66.0254

COMPUTE_OLDER_FORMULAS

Confidence Estimate for the Mean
Data
Population Standard Deviation	17.9002
Sample Mean	59.62
Sample Size	30
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.2681144413
Z Value	-1.9600
Interval Half Width	6.4054
Confidence Interval
Interval Lower Limit	53.2146
Interval Upper Limit	66.0254

MAT10251 Workbooks 2018/CIE Sigma Unknown Workbook.xlsx

DATA

Exam Mark
47.80
38.10
57.20
42.45
68.25
79.35
18.30
50.65
47.60
52.00
51.65
67.80
71.30
55.75
55.45
76.40
59.80
76.15
86.20
86.35
64.55
87.10
83.45
57.65
79.90
51.65
53.80
18.75
51.05
52.15

COMPUTE

Confidence Estimate for the Mean
Data
Sample Standard Deviation	17.9002196095
Sample Mean	59.62
Sample Size	30
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.2681
Degrees of Freedom	29
t Value	2.0452
Interval Half Width	6.6841
Confidence Interval
Interval Lower Limit	52.94
Interval Upper Limit	66.30

COMPUTE_STATISTICS

Confidence Estimate for the Mean
Data
Sample Standard Deviation	17.9002196095
Sample Mean	59.62
Sample Size	30
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.2681
Degrees of Freedom	29
t Value	2.0452
Interval Half Width	6.6841
Confidence Interval
Interval Lower Limit	52.94
Interval Upper Limit	66.30

COMPUTE_FORMULAS

Confidence Estimate for the Mean
Data
Sample Standard Deviation	17.9002196095
Sample Mean	59.62
Sample Size	30
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.2681
Degrees of Freedom	29
t Value	2.0452
Interval Half Width	6.6841
Confidence Interval
Interval Lower Limit	52.94
Interval Upper Limit	66.30

COMPUTE_OLDER

Confidence Estimate for the Mean
Data
Sample Standard Deviation	17.9002196095
Sample Mean	59.62
Sample Size	30
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.2681
Degrees of Freedom	29
t Value	2.0452
Interval Half Width	6.6841
Confidence Interval
Interval Lower Limit	52.94
Interval Upper Limit	66.30

COMPUTE_OLDER_FORMULAS

Confidence Estimate for the Mean
Data
Sample Standard Deviation	17.9002196095
Sample Mean	59.62
Sample Size	30
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.2681
Degrees of Freedom	29
t Value	2.0452
Interval Half Width	6.6841
Confidence Interval
Interval Lower Limit	52.94
Interval Upper Limit	66.30

MAT10251 Workbooks 2018/Descriptive Statistics Workbook.xlsx

DATA

Get-Ready Time
39
29
43
52
39
44
40
31
44
35

Descriptive_Summary

Descriptive Summary
	Get-Ready Time
Mean	39.6
Median	39.5
Mode	39
Minimum	29
Maximum	52
Range	23
Variance	45.8222
Standard Deviation	6.7692
Coeff. of Variation	17.09%
Skewness	0.0858
Kurtosis	0.1375
Count	10
Standard Error	2.1406

ZScores

Get-Ready Time	Z Score
39	-0.09
29	-1.57
43	0.50
52	1.83
39	-0.09
44	0.65
40	0.06
31	-1.27
44	0.65
35	-0.68

Descriptive_Summary_FORMULAS

Descriptive Summary
	Get-Ready Time
Mean	39.6
Median	39.5
Mode	39
Minimum	29
Maximum	52
Range	23
Variance	45.8222
Standard Deviation	6.7692
Coeff. of Variation	17.09%
Skewness	0.0858
Kurtosis	0.1375
Count	10
Standard Error	2.1406

Descriptive_Summary_OLDER

Descriptive Summary
	Get-Ready Time
Mean	39.6
Median	39.5
Mode	39
Minimum	29
Maximum	52
Range	23
Variance	45.8222
Standard Deviation	6.7692
Coeff. of Variation	17.09%
Skewness	0.0858
Kurtosis	0.1375
Count	10
Standard Error	2.1406

Descriptive_Summary_OLD_FORMUL

Descriptive Summary
	Get-Ready Time
Mean	39.6
Median	39.5
Mode	39
Minimum	29
Maximum	52
Range	23
Variance	45.8222
Standard Deviation	6.7692
Coeff. of Variation	17.09%
Skewness	0.0858
Kurtosis	0.1375
Count	10
Standard Error	2.1406

MAT10251 Workbooks 2018/Exponential Smoothing Workbook.xlsx

Chart1

Sales (Yi) 1 2 3 4 5 6 7 8 9 10 11 23 40 25 27 32 48 33 37 37 50 40 0.2 1 2 3 4 5 6 7 8 9 10 11 23 26.400000000000002 26.120000000000005 26.296000000000006 27.436800000000005 31.549440000000008 31.839552000000008 32.871641600000011 33.69731328000001 36.95785062400001 37.566280499200005 0.25 1 2 3 4 5 6 7 8 9 10 11 23 27.25 26.6875 26.765625 28.07421875 33.0556640625 33.041748046875 34.03131103515625 34.773483276367188 38.580112457275391 38.935084342956543 Time Period (i)

Sales (Yi)

COMPUTE

		W	W	Add or delete rows rows 5 to 10
Time Period (i)	Sales (Yi)	0.2	0.25	then copy formulas from row 4 in columns C and D
1	23	23.00	23.00
2	40	26.40	27.25
3	25	26.12	26.69
4	27	26.30	26.77
5	32	27.44	28.07
6	48	31.55	33.06
7	33	31.84	33.04
8	37	32.87	34.03
9	37	33.70	34.77
10	50	36.96	38.58
11	40	37.57	38.94

MAT10251 Workbooks 2018/Histogram Workbook Use When Have Zero in Data.xlsx

Data

Suburban Restaurant
Price of Main Meal $	Bin Values	Midpoint Values	Minimum	23
37	19.999	$17.50	Maximum	55
37	24.999	$22.50	Range	32
29	29.999	$27.50
38	34.999	$32.50
37	39.999	$37.50
38	44.999	$42.50
39	49.999	$47.50
29	54.999	$52.50
36	59.999	$57.50
38	64.999	$62.50
44	69.999	$67.50
27	74.999	$72.50
24	79.999	$77.50
34	84.999	$82.50
44	89.999	$87.50
23
30
32
25
29
43
31
26
34
23
41
32
30
28
33
26
51
26
48
39
55
24
38
31
30
51
30
27
38
26
28
33
38
32
25

Histogram and Frequency

Bins	Midpoints	Frequency
19.999	$17.50	0
24.999	$22.50	4
29.999	$27.50	13
34.999	$32.50	13
39.999	$37.50	12
44.999	$42.50	4
49.999	$47.50	1
54.999	$52.50	2
59.999	$57.50	1
64.999	$62.50	0
69.999	$67.50	0
74.999	$72.50	0
79.999	$77.50	0
84.999	$82.50	0
89.999	$87.50	0

Suburban Restaurant

Frequency 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5 77.5 82.5 87.5 0 4 13 13 12 4 1 2 1 0 0 0 0 0 0 Price of Main Meal $

Frequency

MAT10251 Workbooks 2018/Histogram Workbook.xlsx

Data

Suburban Restaurant
Price of Main Meal $	Bin Values	Midpoint Values	Minimum	23
37	9.999	$7.50	Maximum	55
37	14.999	$12.50	Range	32
29	19.999	$17.50
38	24.999	$22.50
37	29.999	$27.50
38	34.999	$32.50
39	39.999	$37.50
29	44.999	$42.50
36	49.999	$47.50
38	54.999	$52.50
44	59.999	$57.50
27	64.999	$62.50
24
34
44
23
30
32
25
29
43
31
26
34
23
41
32
30
28
33
26
51
26
48
39
55
24
38
31
30
51
30
27
38
26
28
33
38
32
25

Histogram

Suburban Restaurant

Frequency 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 0 0 4 13 13 12 4 1 2 1 0 Price of Main Meal $

Frequency

Bins	Midpoints	Frequency
9.999	$7.50	0
14.999	$12.50	0
19.999	$17.50	0
24.999	$22.50	4
29.999	$27.50	13
34.999	$32.50	13
39.999	$37.50	12
44.999	$42.50	4
49.999	$47.50	1
54.999	$52.50	2
59.999	$57.50	1
64.999	$62.50	0
0	$0.00	0
0	$0.00	0
0	$0.00	0
0	$0.00	0
0	$0.00	0
0	$0.00	0
0	$0.00	0
0	$0.00	0

MAT10251 Workbooks 2018/Moving Averages Workbook.xlsx

Chart1

Unemp 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 258 263 315 247 222 236 317 288 279 288 231 228 219 MA 3-Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 #N/A 278.66666666666669 275 261.33333333333331 235 258.33333333333331 280.33333333333331 302.5 279 259.5 249 226 #N/A MA 5-Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 #N/A #N/A 261 256.60000000000002 267.39999999999998 262 268.39999999999998 281.60000000000002 280.60000000000002 262.8 249 #N/A #N/A MA 7-Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 #N/A #N/A #N/A 265.42857142857144 269.71428571428572 272 268.14285714285717 265.85714285714283 266.71428571428572 264.28571428571428 #N/A #N/A #N/A Year

Unemp

COMPUTE

Year	Unemp	MA 3-Year	MA 5-Year	MA 7-Year	Add or delete rows at row 10
1995	258	ERROR:#N/A	ERROR:#N/A	ERROR:#N/A	then copy formulas in row 5 down columns C, D and E
1996	263	278.67	ERROR:#N/A	ERROR:#N/A
1997	315	275.00	261.00	ERROR:#N/A
1998	247	261.33	256.60	265.43
1999	222	235.00	267.40	269.71
2000	236	258.33	262.00	272.00
2001	317	280.33	268.40	268.14
2002	288	302.50	281.60	265.86
2003	279	279.00	280.60	266.71
2004	288	259.50	262.80	264.29
2005	231	249.00	249.00	ERROR:#N/A
2006	228	226.00	ERROR:#N/A	ERROR:#N/A
2007	219	ERROR:#N/A	ERROR:#N/A	ERROR:#N/A

MAT10251 Workbooks 2018/Multiple Regression 2 Independent Variables Workbook.xlsx

MRData

Dependent variable		Independent variables		Add or delete middle rows.
Bars		Price	Promotion	Rows 4 to 35
4141	1	59	200	Copy 1's in column B
3842	1	59	200
3056	1	59	200
3519	1	59	200
4226	1	59	400
4630	1	59	400
3507	1	59	400
3754	1	59	400
5000	1	59	600
5120	1	59	600
4011	1	59	600
5015	1	59	600
1916	1	79	200
675	1	79	200
3636	1	79	200
3224	1	79	200
2295	1	79	400
2730	1	79	400
2618	1	79	400
4421	1	79	400
4113	1	79	600
3746	1	79	600
3532	1	79	600
3825	1	79	600
1096	1	99	200
761	1	99	200
2088	1	99	200
820	1	99	200
2114	1	99	400
1882	1	99	400
2159	1	99	400
1602	1	99	400
3354	1	99	600
2927	1	99	600

RESIDUALS

Observation	Price	Promotion	Predicted	Bars	Residuals
1	59	200	3420.3095238095	4141	720.6904761905
2	59	200	3420.3095238095	3842	421.6904761905
3	59	200	3420.3095238095	3056	-364.3095238095
4	59	200	3420.3095238095	3519	98.6904761905
5	59	400	4142.9211309524	4226	83.0788690476
6	59	400	4142.9211309524	4630	487.0788690476
7	59	400	4142.9211309524	3507	-635.9211309524
8	59	400	4142.9211309524	3754	-388.9211309524
9	59	600	4865.5327380952	5000	134.4672619048
10	59	600	4865.5327380952	5120	254.4672619048
11	59	600	4865.5327380952	4011	-854.5327380952
12	59	600	4865.5327380952	5015	149.4672619048
13	79	200	2355.962797619	1916	-439.962797619
14	79	200	2355.962797619	675	-1680.962797619
15	79	200	2355.962797619	3636	1280.037202381
16	79	200	2355.962797619	3224	868.037202381
17	79	400	3078.5744047619	2295	-783.5744047619
18	79	400	3078.5744047619	2730	-348.5744047619
19	79	400	3078.5744047619	2618	-460.5744047619
20	79	400	3078.5744047619	4421	1342.4255952381
21	79	600	3801.1860119048	4113	311.8139880952
22	79	600	3801.1860119048	3746	-55.1860119048
23	79	600	3801.1860119048	3532	-269.1860119048
24	79	600	3801.1860119048	3825	23.8139880952
25	99	200	1291.6160714286	1096	-195.6160714286
26	99	200	1291.6160714286	761	-530.6160714286
27	99	200	1291.6160714286	2088	796.3839285714
28	99	200	1291.6160714286	820	-471.6160714286
29	99	400	2014.2276785714	2114	99.7723214286
30	99	400	2014.2276785714	1882	-132.2276785714
31	99	400	2014.2276785714	2159	144.7723214286
32	99	400	2014.2276785714	1602	-412.2276785714
33	99	600	2736.8392857143	3354	617.1607142857
34	99	600	2736.8392857143	2927	190.1607142857

COMPUTE

Multiple Regression									Calculations
									b2, b1, b0 intercepts	3.6131	-53.2173	5837.5208
Regression Statistics									b2, b1, b0 Standard Error	0.6852	6.8522	628.1502
Multiple R	0.8705								R Square, Standard Error	0.7577	638.0653	ERROR:#N/A
R Square	0.7577								F, Residual df	48.4771	31	ERROR:#N/A
Adjusted R Square	0.7421								Regression SS, Residual SS	39472730.7730217	12620946.6681548	ERROR:#N/A
Standard Error	638.0653
Observations	34								Confidence level	95%
									t Critical Value	2.0395
ANOVA									Half Width b0	1281.1208
	df	SS	MS	F	Significance F				Half Width b1	13.9752
Regression	2	39472730.7730	19736365.3865	48.4771	0.0000				Half Width b2	1.3975
Residual	31	12620946.6682	407127.3119
Total	33	52093677.4412
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95%	Upper 95%
Intercept	5837.5208	628.1502	9.2932	0.0000	4556.3999	7118.6416	4556.3999	7118.6416
Price	-53.2173	6.8522	-7.7664	0.0000	-67.1925	-39.2421	-67.1925	-39.2421
Promotion	3.6131	0.6852	5.2728	0.0000	2.2155	5.0106	2.2155	5.0106

CIEandPI

Confidence Interval Estimate and Prediction Interval
Data
Confidence Level	95%
	1
Price	79
Promotion	400
X'X	34	2646	13200
	2646	214674	1018800
	13200	1018800	6000000
Inverse of X'X	0.9692	-0.0094	-0.0005
	-0.0094	0.0001	0.0000
	-0.0005	0.0000	0.0000
X'G times Inverse of X'X	0.0121	0.0001	0.0000
[X'G times Inverse of X'X] times XG	0.0298
t Statistic	2.0395
Predicted Y (YHat)	3078.57
For Average Predicted Y (YHat)
Interval Half Width	224.50
Confidence Interval Lower Limit	2854.07
Confidence Interval Upper Limit	3303.08
For Individual Response Y
Interval Half Width	1320.57
Prediction Interval Lower Limit	1758.01
Prediction Interval Upper Limit	4399.14

MAT10251 Workbooks 2018/Multiple Regression 3 Independent Variables Workbook.xlsx

MRData

Dependent variable		Independent variables			Add or delete middle rows.
Price		Age	Kms (000)	State	Rows 4 to 126
25000	1	2	15	1	Copy 1's in column B
22000	1	3	29	0
14999	1	4	73	0
18950	1	4	45	1
15000	1	5	63	0
11500	1	6	91	0
16500	1	6	109	0
10000	1	6	83	1
11000	1	6	155	1
9000	1	7	110	0
11500	1	7	74	0
13500	1	7	69	1
10490	1	8	133	1
11500	1	8	130	0
10950	1	9	133	0
8500	1	9	151	0
9750	1	9	96	0
7500	1	10	190	0
4200	1	12	190	0
4300	1	12	190	1
8000	1	14	182	1
900	1	16	142	1
4300	1	17	209	0
3200	1	17	253	0
25000	1	2	15	1
22000	1	3	29	0
14999	1	4	73	0
18950	1	4	45	1
15000	1	5	63	0
11500	1	6	91	0
16500	1	6	109	0
10000	1	6	83	1
11000	1	6	155	1
9000	1	7	110	0
11500	1	7	74	0
13500	1	7	69	1
10490	1	8	133	1
11500	1	8	130	0
10950	1	9	133	0
8500	1	9	151	0
9750	1	9	96	0
7500	1	10	190	0
4200	1	12	190	0
4300	1	12	190	1
8000	1	14	182	1
900	1	16	142	1
4300	1	17	209	0
3200	1	17	253	0
25000	1	2	15	1
22000	1	3	29	0
14999	1	4	73	0
18950	1	4	45	1
15000	1	5	63	0
11500	1	6	91	0
16500	1	6	109	0
10000	1	6	83	1
11000	1	6	155	1
9000	1	7	110	0
11500	1	7	74	0
13500	1	7	69	1
10490	1	8	133	1
11500	1	8	130	0
10950	1	9	133	0
8500	1	9	151	0
9750	1	9	96	0
7500	1	10	190	0
4200	1	12	190	0
4300	1	12	190	1
8000	1	14	182	1
900	1	16	142	1
4300	1	17	209	0
3200	1	17	253	0
25000	1	2	15	1
22000	1	3	29	0
14999	1	4	73	0
18950	1	4	45	1
15000	1	5	63	0
11500	1	6	91	0
16500	1	6	109	0
10000	1	6	83	1
11000	1	6	155	1
9000	1	7	110	0
11500	1	7	74	0
13500	1	7	69	1
10490	1	8	133	1
11500	1	8	130	0
10950	1	9	133	0
8500	1	9	151	0
9750	1	9	96	0
7500	1	10	190	0
4200	1	12	190	0
4300	1	12	190	1
8000	1	14	182	1
900	1	16	142	1
4300	1	17	209	0
3200	1	17	253	0
25000	1	2	15	1
22000	1	3	29	0
14999	1	4	73	0
18950	1	4	45	1
15000	1	5	63	0
11500	1	6	91	0
16500	1	6	109	0
10000	1	6	83	1
11000	1	6	155	1
9000	1	7	110	0
11500	1	7	74	0
13500	1	7	69	1
10490	1	8	133	1
11500	1	8	130	0
10950	1	9	133	0
8500	1	9	151	0
9750	1	9	96	0
7500	1	10	190	0
4200	1	12	190	0
4300	1	12	190	1
8000	1	14	182	1
900	1	16	142	1
4300	1	17	209	0
3200	1	17	253	0
900	1	16	142	1
4300	1	17	209	0
3200	1	17	253	0
2500	1	18	289	1
550	1	20	220	0

COMPUTE

Multiple Regression									Calculations
									b2, b1, b0 intercepts	-42.7210	-28.2782	-818.6800	21415.024218839
Regression Statistics									b2, b1, b0 Standard Error	486.3240	7.7879	108.5081	575.430985714
Multiple R	0.8998								R Square, Standard Error	0.8096	2595.9684	ERROR:#N/A	ERROR:#N/A
R Square	0.8096								F, Residual df	171.4522	121	ERROR:#N/A	ERROR:#N/A
Adjusted R Square	0.8048								Regression SS, Residual SS	3466275351.3257	815425305.474305	ERROR:#N/A	ERROR:#N/A
Standard Error	2595.9684
Observations	125								Confidence level	95%
									t Critical Value	1.9798
ANOVA									Half Width b0	1139.2174
	df	SS	MS	F	Significance F				Half Width b1	214.8205
Regression	3	3466275351.3257	1155425117.1086	171.4522	0.0000				Half Width b2	15.4182
Residual	121	815425305.4743	6739052.1114						Half Width b3	962.8066655651
Total	124	4281700656.8000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95%	Upper 95%
Intercept	21415.0242	575.4310	37.2156	0.0000	20275.8068	22554.2416	20275.8068	22554.2416
Age	-818.6800	108.5081	-7.5449	0.0000	-1033.5005	-603.8595	-1033.5005	-603.8595
Kms (000)	-28.2782	7.7879	-3.6310	0.0004	-43.6963	-12.8600	-43.6963	-12.8600
State	-42.7210	486.3240	-0.0878	0.9301	-1005.5276	920.0857	-1005.5276	920.0857

CI and PI

Confidence Interval Estimate and Prediction Interval
Data
Confidence Level	95%
	1
Age	2
Kms (000)	50
State	0
X'X	125	1108	15688	47
	1108	12308	169533	409
	15688	169533	2456650	5501
	47	409	5501	47
Inverse of X'X	0.0491346	-0.0012895	-0.0001896	-0.0157255
	-0.0012895	0.0017471	-0.0001100	-0.0010385
	-0.0001896	-0.0001100	0.0000090	0.0000935
	-0.0157255	-0.0010385	0.0000935	0.0350956
X'G times Inverse of X'X	0.0371	-0.003295729	0.0000404132	-0.0131274565
[X'G times Inverse of X'X] times XG	0.0325
t Statistic	1.9798
Predicted Y (YHat)	18363.76
For Average Predicted Y (YHat)
Interval Half Width	926.61
Confidence Interval Lower Limit	17437.15
Confidence Interval Upper Limit	19290.37
For Individual Response Y
Interval Half Width	5222.27
Prediction Interval Lower Limit	13141.49
Prediction Interval Upper Limit	23586.02

MAT10251 Workbooks 2018/Multiple Regression 4 Independent Variables Workbook.xlsx

MRData

Dependent variable		Independent variables				Add or delete middle rows.
Y		var #1	var #2	var #3	var #4	Rows 4 to 51
4139	1	279	27	162.6	0	Copy 1's in column B
2381	1	267	29	152.4	0
3260	1	302	28	162.6	0
3260	1	281	25	152.4	0
3345	1	284	28	177.8	1
2580	1	292	19	154.9	0
3175	1	255	39	152.4	0
3260	1	316	29	162.6	0
3118	1	269	38	154.9	0
3317	1	277	34	167.6	0
4082	1	276	23	170.2	1
3856	1	268	30	160.0	1
3430	1	278	28	175.3	0
4678	1	282	29	167.6	0
3402	1	279	38	162.6	0
3544	1	280	30	165.1	1
3884	1	285	29	165.1	0
2835	1	288	28	154.9	1
3799	1	284	28	157.5	0
2495	1	262	20	165.1	1
3232	1	291	35	152.4	0
3005	1	289	28	170.2	1
3459	1	292	34	165.1	0
3856	1	261	24	165.1	0
3430	1	286	22	175.3	1
3175	1	282	26	165.1	0
3175	1	266	26	162.6	0
3487	1	314	22	154.9	1
3941	1	286	33	165.1	1
3544	1	290	36	149.9	0
3430	1	282	30	165.1	0
3572	1	299	21	152.4	0
3374	1	286	33	170.2	0
3232	1	277	19	160.0	0
3345	1	272	23	162.6	0
3600	1	295	36	165.1	0
3317	1	290	22	170.2	0
3884	1	277	41	165.1	0
3770	1	292	29	165.1	0
2835	1	264	28	152.4	1
4082	1	283	25	167.6	0
3289	1	273	33	167.6	1
2126	1	265	21	165.1	1
3912	1	286	28	172.7	0
2807	1	271	39	175.3	0
3345	1	293	21	160.0	0
2750	1	266	24	157.5	0
4139	1	319	28	167.6	0
2296	1	285	19	160.0	1
3118	1	321	28	167.6	0

COMPUTE

Multiple Regression							Calculations
							b4 through b0 intercepts	-212.4820	19.9323	16.4192	7.2099388177	-2330.9500260837
Regression Statistics							b4 through b0 Standard Error	159.0045	9.9773	12.3715	4.7946396152	2073.897840347
Multiple R	0.4469						R Square, Standard Error	0.1997	478.3271	ERROR:#N/A	ERROR:#N/A	ERROR:#N/A
R Square	0.1997						F, Residual df	2.8071	45	ERROR:#N/A	ERROR:#N/A	ERROR:#N/A
Adjusted R Square	0.1286						Regression SS, Residual SS	2569028.08100369	10295855.1389963	ERROR:#N/A	ERROR:#N/A	ERROR:#N/A
Standard Error	478.3271
Observations	50						Confidence level	95%
							t Critical Value	2.0141
ANOVA							Half Width b0	4177.0447
	df	SS	MS	F	Significance F		Half Width b1	9.6569
Regression	4	2569028.0810	642257.0203	2.8071	0.0366		Half Width b2	24.9175
Residual	45	10295855.1390	228796.7809				Half Width b3	20.0954
Total	49	12864883.2200					Half Width b4	320.2514
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-2330.9500	2073.8978	-1.1239	0.2670	-6507.9947	1846.0946
var #1	7.2099	4.7946	1.5037	0.1396	-2.4470	16.8668
var #2	16.4192	12.3715	1.3272	0.1911	-8.4983	41.3368
var #3	19.9323	9.9773	1.9978	0.0518	-0.1631	40.0277
var #4	-212.4820	159.0045	-1.3363	0.1882	-532.7334	107.7695

CIEandPI

Confidence Interval Estimate and Prediction Interval
Data
Confidence Level	90%
	1
var #1	2
var #2	50
var #3	1
var #4	0
X'X	50	14157	1413	8158.5	14
	14157	4018819	399685	2310317.9	3920
	1413	399685	41551	230582.5	365
	8158.5	2310317.9	230582.5	1333580.91	2303.7
	14	3920	365	2303.7	14
Inverse of X'X	18.7985698	-0.0265560382	-0.0247432329	-0.0645561662	-0.095070532
	-0.0265560	0.0001004759	0.0000355938	-0.0000187636	0.0005823442
	-0.0247432	0.0000355938	0.0006689553	-0.0000298359	0.0022458258
	-0.0645562	-0.0000187636	-0.0000298359	0.0004350913	-0.0010064467
	-0.0950705	0.0005823442	0.0022458258	-0.0010064467	0.1105016376
X'G times Inverse of X'X	17.4437	-0.0245941574	0.0087458833	-0.065650395	0.0173790015
[X'G times Inverse of X'X] times XG	17.7662
t Statistic	1.6794
Predicted Y (YHat)	-1475.64
For Average Predicted Y (YHat)
Interval Half Width	3385.97
Confidence Interval Lower Limit	-4861.61
Confidence Interval Upper Limit	1910.34
For Individual Response Y
Interval Half Width	3479.96
Prediction Interval Lower Limit	-4955.60
Prediction Interval Upper Limit	2004.32

MAT10251 Workbooks 2018/Multiple Regression 5 Independent Variables Workbook.xlsx

MRData

Dependent variable		Independent variables					Add or delete middle rows.
Y		var #1	var #2	var #3	var #4	var #5	Rows 4 to 51
4139	1	279	27	162.6	56.25	0	Copy 1's in column B
2381	1	267	29	152.4	43.09	0
3260	1	302	28	162.6	52.62	0
3260	1	281	25	152.4	42.64	0
3345	1	284	28	177.8	65.77	1
2580	1	292	19	154.9	56.70	0
3175	1	255	39	152.4	52.16	0
3260	1	316	29	162.6	49.90	0
3118	1	269	38	154.9	46.27	0
3317	1	277	34	167.6	63.50	0
4082	1	276	23	170.2	58.51	1
3856	1	268	30	160.0	59.87	1
3430	1	278	28	175.3	59.87	0
4678	1	282	29	167.6	65.77	0
3402	1	279	38	162.6	56.25	0
3544	1	280	30	165.1	58.97	1
3884	1	285	29	165.1	49.90	0
2835	1	288	28	154.9	48.99	1
3799	1	284	28	157.5	50.80	0
2495	1	262	20	165.1	53.52	1
3232	1	291	35	152.4	50.80	0
3005	1	289	28	170.2	54.43	1
3459	1	292	34	165.1	60.33	0
3856	1	261	24	165.1	49.90	0
3430	1	286	22	175.3	58.97	1
3175	1	282	26	165.1	55.34	0
3175	1	266	26	162.6	55.34	0
3487	1	314	22	154.9	54.88	1
3941	1	286	33	165.1	56.70	1
3544	1	290	36	149.9	47.63	0
3430	1	282	30	165.1	55.34	0
3572	1	299	21	152.4	51.71	0
3374	1	286	33	170.2	62.14	0
3232	1	277	19	160.0	48.53	0
3345	1	272	23	162.6	51.26	0
3600	1	295	36	165.1	65.77	0
3317	1	290	22	170.2	49.90	0
3884	1	277	41	165.1	57.15	0
3770	1	292	29	165.1	61.23	0
2835	1	264	28	152.4	50.35	1
4082	1	283	25	167.6	63.50	0
3289	1	273	33	167.6	58.97	1
2126	1	265	21	165.1	46.72	1
3912	1	286	28	172.7	54.43	0
2807	1	271	39	175.3	68.49	0
3345	1	293	21	160.0	46.72	0
2750	1	266	24	157.5	49.44	0
4139	1	319	28	167.6	65.77	0
2296	1	285	19	160.0	68.04	1
3118	1	321	28	167.6	81.65	0

COMPUTE

Multiple Regression							Calculations
							b5 through b0 intercepts	-210.1841	-1.3215	20.7005	16.7939167961	7.4311787039	-2456.360067457
Regression Statistics							b5 through b0 Standard Error	162.2591	12.5667	12.4560	13.0072820184	5.2850057685	2412.449165389
Multiple R	0.4471						R Square, Standard Error	0.1999	483.6713	ERROR:#N/A	ERROR:#N/A	ERROR:#N/A	ERROR:#N/A
R Square	0.1999						F, Residual df	2.1985	44	ERROR:#N/A	ERROR:#N/A	ERROR:#N/A	ERROR:#N/A
Adjusted R Square	0.1090						Regression SS, Residual SS	2571615.10610605	10293268.1138939	ERROR:#N/A	ERROR:#N/A	ERROR:#N/A	ERROR:#N/A
Standard Error	483.6713
Observations	50						Confidence level	95%
							t Critical Value	2.0154
ANOVA							Half Width b0	4861.9718
	df	SS	MS	F	Significance F		Half Width b1	10.6512
Regression	5	2571615.1061	514323.0212	2.1985	0.0715		Half Width b2	26.2145
Residual	44	10293268.1139	233937.9117				Half Width b3	25.1033
Total	49	12864883.2200					Half Width b4	25.3266
							Half Width b5	327.0117
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-2456.3601	2412.4492	-1.0182	0.3141	-7318.3319	2405.6118
var #1	7.4312	5.2850	1.4061	0.1667	-3.2201	18.0824
var #2	16.7939	13.0073	1.2911	0.2034	-9.4205	43.0084
var #3	20.7005	12.4560	1.6619	0.1036	-4.4028	45.8039
var #4	-1.3215	12.5667	-0.1052	0.9167	-26.6481	24.0051
var #5	-210.1841	162.2591	-1.2954	0.2020	-537.1958	116.8276

CIEandPI

Confidence Interval Estimate and Prediction Interval
Data
Confidence Level	95%
	1
var #1	2
var #2	50
var #3	1
var #4	2
var #5	0
X'X	50	14157	1413	8158.5	2792.78	14
	14157	4018819	399685	2310317.9	792488.45	3920
	1413	399685	41551	230582.5	79277.84	365
	8158.5	2310317.9	230582.5	1333580.91	457162.73	2303.7
	2792.78	792488.45	79277.84	457162.73	158739.1258	794.69
	14	3920	365	2303.7	794.69	14
Inverse of X'X	24.8780154	-0.0372809837	-0.0429069438	-0.1017967077	0.0640625376	-0.2064648572
	-0.0372810	0.0001193961	0.000067637	0.0000469336	-0.0001130148	0.0007788585
	-0.0429069	0.000067637	0.0007232235	0.0000814286	-0.0001914012	0.0025786414
	-0.1017967	0.0000469336	0.0000814286	0.0006632138	-0.0003924245	-0.0003240843
	0.0640625	-0.0001130148	-0.0001914012	-0.0003924245	0.000675063	-0.0011738246
	-0.2064649	0.0007788585	0.0025786414	-0.0003240843	-0.0011738246	0.1125427276
X'G times Inverse of X'X	22.6844	-0.0338394355	-0.0069118707	-0.097753044	0.0552241476	-0.0786468022
[X'G times Inverse of X'X] times XG	22.2839
t Statistic	2.0154
Predicted Y (YHat)	-1583.74
For Average Predicted Y (YHat)
Interval Half Width	4601.50
Confidence Interval Lower Limit	-6185.25
Confidence Interval Upper Limit	3017.76
For Individual Response Y
Interval Half Width	4703.62
Prediction Interval Lower Limit	-6287.36
Prediction Interval Upper Limit	3119.87

MAT10251 Workbooks 2018/Normal Workbook.xlsx

COMPUTE

Normal Probabilities
Common Data
Mean	7
Standard Deviation	2
Probability for X <=
X Value	3.5
Z Value	-1.75
P(X<=3.5)	0.0401
Probability for X >
X Value	9
Z Value	1
P(X>9)	0.1587
Probability for X<3.5 or X >9
P(X<3.5 or X >9)	0.1987
Probability for a Range
From X Value	5
To X Value	9
Z Value for 5	-1
Z Value for 9	1
P(X<=5)	0.1587
P(X<=9)	0.8413
P(5<=X<=9)	0.6827
Find X and Z Given a Cum. Pctage.
Cumulative Percentage	10.00%
Z Value	-1.28
X Value	4.44
Find X Values Given a Percentage
Percentage	95.00%
Z Value	-1.96
Lower X Value	3.08
Upper X Value	10.92

COMPUTE_FORMULAS

Normal Probabilities
Common Data
Mean	7
Standard Deviation	2
Probability for X <=
X Value	7
Z Value	0
P(X<=7)	0.5000
Probability for X >
X Value	9
Z Value	1
P(X>9)	0.1587
Probability for X<7 or X >9
P(X<7 or X >9)	0.6587
Probability for a Range
From X Value	5
To X Value	9
Z Value for 5	-1
Z Value for 9	1
P(X<=5)	0.1587
P(X<=9)	0.8413
P(5<=X<=9)	0.6827
Find X and Z Values Given Cum. Pctage.
Cumulative Percentage	10.00%
Z Value	-1.28
X Value	4.44
Find X Values Given Percentage
Percentage	95.00%
Z Value	-1.96
Lower X Value	3.08
Upper X Value	10.92

This worksheet makes extensive use of the ampersand operator (&) to create column A labels dynamically, based on the data values you enter. The ampersand allows the construction of a text value. For example, the cell A10 formula ="P(X<="&B8&")" results in the display of P(X<=7) because the contents of cell B8, 7, is combined with "P(X<=" and ")"

COMPUTE_OLDER

Normal Probabilities
Common Data
Mean	7
Standard Deviation	2
Probability for X <=
X Value	7
Z Value	0
P(X<=7)	0.5
Probability for X >
X Value	9
Z Value	1
P(X>9)	0.1587
Probability for X<7 or X >9
P(X<7 or X >9)	0.6587
Probability for a Range
From X Value	7
To X Value	9
Z Value for 7	0
Z Value for 9	1
P(X<=7)	0.5000
P(X<=9)	0.8413
P(7<=X<=9)	0.3413
Find X and Z Given Cum. Pctage.
Cumulative Percentage	10.00%
Z Value	-1.2815515655
X Value	4.4368968689

COMPUTE_OLDER_FORMULAS

Normal Probabilities
Common Data
Mean	7
Standard Deviation	2
Probability for X <=
X Value	7
Z Value	0
P(X<=7)	0.5
Probability for X >
X Value	9
Z Value	1
P(X>9)	0.1587
Probability for X<7 or X >9
P(X<7 or X >9)	0.6587
Probability for a Range
From X Value	7
To X Value	9
Z Value for 7	0
Z Value for 9	1
P(X<=7)	0.5000
P(X<=9)	0.8413
P(7<=X<=9)	0.3413
Find X and Z Given Cum. Pctage.
Cumulative Percentage	10.00%
Z Value	-1.2815515655
X Value	4.4368968689

MAT10251 Workbooks 2018/One-Way ANOVA Workbook.xlsx

ANOVA 3 Groups

Sydney	Darwin	Canberra	NJayne: Add or delete rows 3 to 10
126	126	146
130	126	147
134	126	165
145	126	167
155	126	173
164	129	180
177	136	213
193	141	227
234	171	243
256	179	248	ANOVA: Single Factor
			SUMMARY
			Groups	Count	Sum	Average	Variance
			Sydney	10	1714	171.4	1974.2666666667
			Darwin	10	1386	138.6	397.8222222222
			Canberra	10	1909	190.9	1487.8777777778
			ANOVA
			Source of Variation	SS	df	MS	F	P-value	F crit
			Between Groups	13971.2666666666	2	6985.6333333333	5.4292955898	0.0104277536	3.3541308285
			Within Groups	34739.7	27	1286.6555555556
			Total	48710.9666666667	29
							Level of significance		0.05

ANOVA 4 Groups

Sydney	Melbourne	Darwin	Canberra	NJayne: Add or delete rows 3 to 10
126	149	126	146
130	154	126	147
134	154	126	165
145	153	126	167
155	153	126	173
164	155	129	180
177	170	136	213
193	192	141	227
234	222	171	243
256	252	179	248	ANOVA: Single Factor
				SUMMARY
				Groups	Count	Sum	Average	Variance
				Sydney	10	1714	171.4	1974.2666666667
				Melbourne	10	1754	175.4	1264.0444444444
				Darwin	10	1386	138.6	397.8222222222
				Canberra	10	1909	190.9	1487.8777777778
				ANOVA
				Source of Variation	SS	df	MS	F	P-value	F crit
				Between Groups	14504.6749999998	3	4834.8916666666	3.7743022502	0.0187610771	2.8662655509
				Within Groups	46116.1000000001	36	1281.0027777778
				Total	60620.7749999999	39
								Level of significance		0.05

ANOVA 5 Groups

A	B	C	D	E	NJayne: Add or delete rows 3 to 6
15	16	8	5	12
18	17	7	6	19
17	21	10	13	18
19	16	15	11	12
19	19	14	9	17
20	17	14	10	14
					ANOVA: Single Factor
					SUMMARY
					Groups	Count	Sum	Average	Variance
					A	6	108	18	3.2
					B	6	106	17.6666666667	3.8666666667
					C	6	68	11.3333333333	11.8666666667
					D	6	54	9	9.2
					E	6	92	15.3333333333	9.4666666667
					ANOVA
					Source of Variation	SS	df	MS	F	P-value	F crit
					Between Groups	377.8666666667	4	94.4666666667	12.5620567376	0.0000097437	2.7587104697
					Within Groups	188	25	7.52
					Total	565.8666666667	29
									Level of significance		0.05

ANOVA 6 Groups

A	B	C	D	E	F	NJayne: Add or delete rows 3 to 6
15	16	15	8	5	12
18	17	18	7	6	19
17	21	21	10	13	18
19	16	17	15	11	12
19	19	20	14	9	17
20	17	15	14	10	14
						ANOVA: Single Factor
						SUMMARY
						Groups	Count	Sum	Average	Variance
						A	6	108	18	3.2
						B	6	106	17.6666666667	3.8666666667
						C	6	106	17.6666666667	6.2666666667
						D	6	68	11.3333333333	11.8666666667
						E	6	54	9	9.2
						F	6	92	15.3333333333	9.4666666667
						ANOVA
						Source of Variation	SS	df	MS	F	P-value	F crit
						Between Groups	435.6666666667	5	87.1333333333	11.9179331307	0.00000209	2.5335545476
						Within Groups	219.3333333333	30	7.3111111111
						Total	655	35
										Level of significance		0.05

ANOVA 7 Groups

Mon	Tues	Wed	Thur	Fri	Sat	Sun	NJayne: Add or delete rows 3 to 6
135.9	130.9	134.3	141.5	139.9	138.9	137.5
134.9	128.3	132.9	140.6	139.9	137.9	135.9
135.9	131.9	133.9	142.9	140.9	139.2	137.9	ANOVA: Single Factor
136.7	132.9	134.8	141.8	139.8	138.8	137.8
135.9	130.7	133.7	140.7	139.2	138.2	136.9	SUMMARY
							Groups	Count	Sum	Average	Variance
							Mon	5	679.3	135.86	0.408
							Tues	5	654.7	130.94	2.948
							Wed	5	669.6	133.92	0.502
							Thur	5	707.5	141.5	0.875
							Fri	5	699.7	139.94	0.373
							Sat	5	693	138.6	0.285
							Sun	5	686	137.2	0.68
							ANOVA
							Source of Variation	SS	df	MS	F	P-value	F crit
							Between Groups	394.2434285714	6	65.7072380952	75.761928293	5.26230918506228E-16	2.4452593951
							Within Groups	24.284	28	0.8672857143
							Total	418.5274285714	34
											Level of significance		0.05

MAT10251 Workbooks 2018/Paired T Workbook.xlsx

DATA

Sample 1	Sample 2	Di
41000	38000	3000	Copy formula in column C down to calculate differences
18000	46000	-28000
22000	51000	-29000
34000	30500	3500
31000	28000	3000
11000	19500	-8500
22000	34000	-12000

COMPUTE_ALL

Paired t Test
Data
Hypothesized Mean Diff.	0
Level of significance	0.05
Intermediate Calculations
Sample Size	7
DBar	-9714.2857
degrees of freedom	6
SD	14206.3869
Standard Error	5369.5095
t Test Statistic	-1.8092
Two-Tail Test		One-Tail Calculations
Lower Critical Value	-2.4469	T.DIST.RT	0.0602
Upper Critical Value	2.4469	1 - T.DIST.RT	0.9398
p-Value	0.1204
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.9432
p-Value	0.0602
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.9432
p-Value	0.9398
Do not reject the null hypothesis

CONFIDENCE_INTERVAL

Paired t Test
Data
DBar	-9714.2857142857
SD	14206.3868936274
Sample Size	7
Confidence Level	95.0%
Intermediate Calculations
Standard Error	5369.5095356151
Degrees of Freedom	6
t Value	2.4469
Interval Half Width	13138.7165
Confidence Interval
Interval Lower Limit	-22853.0022
Interval Upper Limit	3424.4308

COMPUTE

Paired t Test
Data
Hypothesized Mean Diff.	0
Level of Significance	0.05
Intermediate Calculations
Sample Size	7
DBar	-9714.2857
degrees of freedom	6
SD	14206.3869
Standard Error	5369.5095
t Test Statistic	-1.8092
Two-Tailed Test
Lower Critical Value	-2.4469
Upper Critical Value	2.4469
p-Value	0.1204
Do not reject the null hypothesis

COMPUTE_LOWER

Paired t Test
Data
Hypothesized Mean Diff.	0
Level of significance	0.05
Intermediate Calculations
Sample Size	7
DBar	-9714.2857
degrees of freedom	6
SD	14206.3869
Standard Error	5369.5095
t Test Statistic	-1.8092
Lower-Tail Test		One-Tail Calculations
Lower Critical Value	-1.9432	T.DIST.RT	0.0602
p-Value	0.0602	1 - T.DIST.RT	0.9398
Do not reject the null hypothesis

COMPUTE_UPPER

Paired t Test
Data
Hypothesized Mean Diff.	0
Level of significance	0.05
Intermediate Calculations
Sample Size	7
DBar	-9714.2857
degrees of freedom	6
SD	14206.3869
Standard Error	5369.5095
t Test Statistic	-1.8092
Upper-Tail Test		One-Tail Calculations
Upper Critical Value	1.9432	T.DIST.RT	0.0602
p-Value	0.9398	1 - T.DIST.RT	0.9398
Do not reject the null hypothesis

COMPUTE_ALL_FORMULAS

Paired t Test
Data
Hypothesized Mean Diff.	0
Level of significance	0.05
Intermediate Calculations
Sample Size	7
DBar	-9714.2857
degrees of freedom	6
SD	14206.3869
Standard Error	5369.5095
t Test Statistic	-1.8092
Two-Tail Test		One-Tail Calculations
Lower Critical Value	-2.4469	T.DIST.RT	0.0602
Upper Critical Value	2.4469	1 - T.DIST.RT	0.9398
p-Value	0.1204
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.9432
p-Value	0.0602
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.9432
p-Value	0.9398
Do not reject the null hypothesis

COMPUTE_OLDER

Paired t Test
Data
Hypothesized Mean Diff.	0
Level of significance	0.05
Intermediate Calculations
Sample Size	7
DBar	-9714.2857
degrees of freedom	6
SD	14206.3869
Standard Error	5369.5095
t Test Statistic	-1.8092
Two-Tail Test		One-Tail Calculations
Lower Critical Value	-2.4469	TDIST	0.0602
Upper Critical Value	2.4469	1 - TDIST	0.9398
p-Value	0.1204
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.9432
p-Value	0.0602
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.9432
p-Value	0.9398
Do not reject the null hypothesis

CONFIDENCE_INTERVAL_OLDER

Paired t Test
Data
DBar	-9714.2857142857
SD	14206.3868936274
Sample Size	7
Confidence Level	95.0%
Intermediate Calculations
Standard Error	5369.5095356151
Degrees of Freedom	6
t Value	2.4469
Interval Half Width	13138.7165
Confidence Interval
Interval Lower Limit	-22853.0022
Interval Upper Limit	3424.4308

COMPUTE_OLDER_FORMULAS

Paired t Test
Data
Hypothesized Mean Diff.	0
Level of significance	0.05
Intermediate Calculations
Sample Size	7
DBar	-9714.2857
degrees of freedom	6
SD	14206.3869
Standard Error	5369.5095
t Test Statistic	-1.8092
Two-Tail Test		One-Tail Calculations
Lower Critical Value	-2.4469	TDIST	0.0602
Upper Critical Value	2.4469	1 - TDIST	0.9398
p-Value	0.1204
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.9432
p-Value	0.0602
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.9432
p-Value	0.9398
Do not reject the null hypothesis

DATA_FORMULAS

Sample 1	Sample 2	Di
41000	38000	3000
18000	46000	-28000
22000	51000	-29000
34000	30500	3500
31000	28000	3000
11000	19500	-8500
22000	34000	-12000

MAT10251 Workbooks 2018/Parameters Workbook.xlsx

DATA

Month	Total Monthly Road Fatalities
January	107
February	102
March	110
April	114
May	105
June	97
July	117
August	112
September	92
October	118
November	106
December	116

COMPUTE

Population Data
Parameters
	Total Monthly Road Fatalities
Mean	108.0000
Variance	60.6667
Standard Deviation	7.7889

COMPUTE_FORMULAS

Population Data
Parameters
	Total Monthly Road Fatalities
Mean	108.0000
Variance	60.6667
Standard Deviation	7.7889

COMPUTE_OLDER

Population Data
Parameters
	Total Monthly Road Fatalities
Mean	108.0000
Variance	60.6667
Standard Deviation	7.7889

COMPUTE_OLDER_FORMULAS

Population Data
Parameters
	Total Monthly Road Fatalities
Mean	108.0000
Variance	60.6667
Standard Deviation	7.7889

MAT10251 Workbooks 2018/Polygon Workbook Use When Zero in Data.xlsx

Data

Price of Main Meal
City Restaurants	Bin Values	Class Midpoints	Minimum	14
50	9.999	7.5	Maximum	63
38	14.999	12.5	Range	49
43	19.999	17.5
56	24.999	22.5
51	29.999	27.5
36	34.999	32.5
25	39.999	37.5
33	44.999	42.5
41	49.999	47.5
44	54.999	52.5
34	59.999	57.5
39	64.999	62.5
49	69.999	67.5
37	74.999	72.5
40	79.999	77.5
50
50
35
22
45
44
38
14
44
51
27
44
39
50
35
31
34
48
48
30
42
26
35
32
63
36
38
53
23
39
45
37
31
39
53

Frequency, Polygon and Ogive

City Restaurants
Bins	Frequency	Percentage	Cumulative Pctage	Class Midpoints
9.999	0	0.00%	0.00%	7.5
14.999	1	2.00%	2.00%	12.5
19.999	0	0.00%	2.00%	17.5
24.999	2	4.00%	6.00%	22.5
29.999	3	6.00%	12.00%	27.5
34.999	7	14.00%	26.00%	32.5
39.999	14	28.00%	54.00%	37.5
44.999	8	16.00%	70.00%	42.5
49.999	5	10.00%	80.00%	47.5
54.999	8	16.00%	96.00%	52.5
59.999	1	2.00%	98.00%	57.5
64.999	1	2.00%	100.00%	62.5
69.999	0	0.00%	100.00%	67.5
74.999	0	0.00%	100.00%	72.5
79.999	0	0.00%	100.00%	77.5

Percentage Polygons

City Restaurants 7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5 77.5 0 0.02 0 0.04 0.06 0.14000000000000001 0.28000000000000003 0.16 0.1 0.16 0.02 0.02 0 0 0 Price of Main Meal

Cumulative Percentage

City Restaurants 9.9990000000000006 14.999000000000001 19.999000000000002 24.999000000000002 29.999000000000002 34.999000000000002 39.999000000000002 44.999000000000002 49.999000000000002 54.999000000000002 59.999000000000002 64.998999999999995 69.998999999999995 74.998999999999995 79.998999999999995 0 0.02 0.02 0.06 0.12 0.26 0.54 0.7000000000000000 7 0.8 0.96000000000000008 0.98000000000000009 1 1 1 1 Suburban Restaurants 9.9990000000000006 14.999000000000001 19.999000000000002 24.999000000000002 29.999000000000002 34.999000000000002 39.999000000000002 44.99900000000 0002 49.999000000000002 54.999000000000002 59.999000000000002 64.998999999999995 69.998999999999995 74.998999999999995 79.998999999999995 1 Price of Main Meal

MAT10251 Workbooks 2018/Polygon Workbook.xlsx

Data

Price of Main Meal
City Restaurants	Suburban Restaurants	Bin Values	Class Midpoints	Minimum	14
50	37	9.999	7.5	Maximum	63
38	37	14.999	12.5	Range	49
43	29	19.999	17.5
56	38	24.999	22.5
51	37	29.999	27.5
36	38	34.999	32.5
25	39	39.999	37.5
33	29	44.999	42.5
41	36	49.999	47.5
44	38	54.999	52.5
34	44	59.999	57.5
39	27	64.999	62.5
49	24	69.999	67.5
37	34
40	44
50	23
50	30
35	32
22	25
45	29
44	43
38	31
14	26
44	34
51	23
27	41
44	32
39	30
50	28
35	33
31	26
34	51
48	26
48	48
30	39
42	55
26	24
35	38
32	31
63	30
36	51
38	30
53	27
23	38
39	26
45	28
37	33
31	38
39	32
53	25

Percentage Polygons

City Restaurants 7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 0 0.02 0 0.04 0.06 0.14000000000000001 0.28000000000000003 0.16 0.1 0.16 0.02 0.02 0 Suburban Restaurants 0 0 0.08 0.26 0.26 0.24 0.08 0.02 0.04 0.02 0 0 0 Price of Main Meal

Cumulative Percentage Polygons

Cumulative Percentage

City Restaurants 9.9990000000000006 14.999000000000001 19.999000000000002 24.999000000000002 29.999000000000002 34.999000000000002 39.999000000000002 44.999000000000002 49.999000000000002 54.999000000000002 59.999000000000002 64.998999999999995 0 0.02 0.02 0.06 0.12 0.26 0.54 0.70000000000000007 0.8 0.96000000000000008 0.98000000000000009 1 Suburban Restaurants 9.999 14.999 19.999 24.999 29.999 34.999 39.999 44.999 49.999 54.999 59.999 64.999 0 0 0.08 0.34 0.60000000000000009 0.84000000000000008 0.92 0.94000000000000006 0.98000000000000009 1 1 1 Price of Main Meal

Sample 1 Frequency

City Restaurants
Bins	Frequency	Percentage	Cumulative Pctage	Class Midpoints
9.999	0	0.00%	0.00%	7.5
14.999	1	2.00%	2.00%	12.5
19.999	0	0.00%	2.00%	17.5
24.999	2	4.00%	6.00%	22.5
29.999	3	6.00%	12.00%	27.5
34.999	7	14.00%	26.00%	32.5
39.999	14	28.00%	54.00%	37.5
44.999	8	16.00%	70.00%	42.5
49.999	5	10.00%	80.00%	47.5
54.999	8	16.00%	96.00%	52.5
59.999	1	2.00%	98.00%	57.5
64.999	1	2.00%	100.00%	62.5
69.999	0	0.00%	100.00%	67.5
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0

Sample 2 Frequency

Suburban Restaurants
Bins	Frequency	Percentage	Cumulative Pctage	Class Midpoints
9.999	0	0.00%	0.00%	7.5
14.999	0	0.00%	0.00%	12.5
19.999	0	0.00%	0.00%	17.5
24.999	4	8.00%	8.00%	22.5
29.999	13	26.00%	34.00%	27.5
34.999	13	26.00%	60.00%	32.5
39.999	12	24.00%	84.00%	37.5
44.999	4	8.00%	92.00%	42.5
49.999	1	2.00%	94.00%	47.5
54.999	2	4.00%	98.00%	52.5
59.999	1	2.00%	100.00%	57.5
64.999	0	0.00%	100.00%	62.5
69.999	0	0.00%	100.00%	67.5
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0
0	0	0.00%	100.00%	0

MAT10251 Workbooks 2018/Pooled-Variance T Test Workbook.xlsx

DATA

A	B
80	152
120	96
52	123
96	98
102	181
85	133
106	76
117	47
98	115
89	104

COMPUTE_ALL

Pooled-Variance t Test for Differences in Two Means
(assumes equal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.1
Population 1 Sample		Data
Sample Size	10	Confidence Level	95%
Sample Mean	94.5
Sample Standard Deviation	19.7104	Intermediate Calculations
Population 2 Sample		Degrees of Freedom	18
Sample Size	10	t Value	2.1009
Sample Mean	112.5	Interval Half Width	28.4147
Sample Standard Deviation	37.9568
		Confidence Interval
Intermediate Calculations		Interval Lower Limit	-46.4147
Population 1 Sample Degrees of Freedom	9	Interval Upper Limit	10.4147
Population 2 Sample Degrees of Freedom	9
Total Degrees of Freedom	18
Pooled Variance	914.6111
Standard Error	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two-Tail Test		One-Tail Calculations
Lower Critical Value	-1.7341	T.DIST.RT value	0.0999
Upper Critical Value	1.7341	1 - T.DIST.RT value	0.9001
p-Value	0.1998
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.3304
p-Value	0.0999
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.3304
p-Value	0.9001
Do not reject the null hypothesis

COMPUTE_ALL_STATISTICS

Pooled-Variance t Test for Differences in Two Means
(assumes equal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.1
Population 1 Sample		Data
Sample Size	10	Confidence Level	95%
Sample Mean	94.5
Sample Standard Deviation	19.7104	Intermediate Calculations
Population 2 Sample		Degrees of Freedom	18
Sample Size	10	t Value	2.1009
Sample Mean	112.5	Interval Half Width	28.4147
Sample Standard Deviation	37.9568
		Confidence Interval
Intermediate Calculations		Interval Lower Limit	-46.4147
Population 1 Sample Degrees of Freedom	9	Interval Upper Limit	10.4147
Population 2 Sample Degrees of Freedom	9
Total Degrees of Freedom	18
Pooled Variance	914.6111
Standard Error	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two-Tail Test		One-Tail Calculations
Lower Critical Value	-1.7341	T.DIST.RT value	0.0999
Upper Critical Value	1.7341	1 - T.DIST.RT value	0.9001
p-Value	0.1998
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.3304
p-Value	0.0999
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.3304
p-Value	0.9001
Do not reject the null hypothesis

COMPUTE

Pooled-Variance t Test for Differences in Two Means
(assumes equal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	95%
Sample Mean	94.5
Sample Standard Deviation	19.7104	Intermediate Calculations
Population 2 Sample		Degrees of Freedom	18
Sample Size	10	t Value	2.1009
Sample Mean	112.5	Interval Half Width	28.4147
Sample Standard Deviation	37.9568
		Confidence Interval
Intermediate Calculations		Interval Lower Limit	-46.4147
Population 1 Sample Degrees of Freedom	9	Interval Upper Limit	10.4147
Population 2 Sample Degrees of Freedom	9
Total Degrees of Freedom	18
Pooled Variance	914.6111
Standard Error	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two-Tail Test
Lower Critical Value	-2.1009
Upper Critical Value	2.1009
p-Value	0.1998
Do not reject the null hypothesis

COMPUTE_LOWER

Pooled-Variance t Test for Differences in Two Means
(assumes equal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	95%
Sample Mean	94.5
Sample Standard Deviation	19.7104	Intermediate Calculations
Population 2 Sample		Degrees of Freedom	18
Sample Size	10	t Value	2.1009
Sample Mean	112.5	Interval Half Width	28.4147
Sample Standard Deviation	37.9568
		Confidence Interval
Intermediate Calculations		Interval Lower Limit	-46.4147
Population 1 Sample Degrees of Freedom	9	Interval Upper Limit	10.4147
Population 2 Sample Degrees of Freedom	9
Total Degrees of Freedom	18
Pooled Variance	914.6111
Standard Error	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Lower-Tail Test		One-Tail Calculations
Lower Critical Value	-1.7341	T.DIST.RT value	0.0999
p-Value	0.0999	1 - T.DIST.RT value	0.9001
Do not reject the null hypothesis

COMPUTE_UPPER

Pooled-Variance t Test for Differences in Two Means
(assumes equal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	95%
Sample Mean	94.5
Sample Standard Deviation	19.7104	Intermediate Calculations
Population 2 Sample		Degrees of Freedom	18
Sample Size	10	t Value	2.1009
Sample Mean	112.5	Interval Half Width	28.4147
Sample Standard Deviation	37.9568
		Confidence Interval
Intermediate Calculations		Interval Lower Limit	-46.4147
Population 1 Sample Degrees of Freedom	9	Interval Upper Limit	10.4147
Population 2 Sample Degrees of Freedom	9
Total Degrees of Freedom	18
Pooled Variance	914.6111
Standard Error	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Upper-Tail Test		One-Tail Calculations
Upper Critical Value	1.7341	T.DIST.RT value	0.0999
p-Value	0.9001	1 - T.DIST.RT value	0.9001
Do not reject the null hypothesis

COMPUTE_ALL_FORMULAS

Pooled-Variance t Test for Differences in Two Means
(assumes equal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	95%
Sample Mean	94.5
Sample Standard Deviation	19.7104	Intermediate Calculations
Population 2 Sample		Degrees of Freedom	18
Sample Size	10	t Value	2.1009
Sample Mean	112.5	Interval Half Width	28.4147
Sample Standard Deviation	37.9568
		Confidence Interval
Intermediate Calculations		Interval Lower Limit	-46.4147
Population 1 Sample Degrees of Freedom	9	Interval Upper Limit	10.4147
Population 2 Sample Degrees of Freedom	9
Total Degrees of Freedom	18
Pooled Variance	914.6111
Standard Error	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two-Tail Test		One-Tail Calculations
Lower Critical Value	-2.1009	T.DIST.RT value	0.0999
Upper Critical Value	2.1009	1 - T.DIST.RT value	0.9001
p-Value	0.1998
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7341
p-Value	0.0999
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7341
p-Value	0.9001
Do not reject the null hypothesis

COMPUTE_OLDER

Pooled-Variance t Test for Differences in Two Means
(assumes equal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	95%
Sample Mean	94.5
Sample Standard Deviation	19.7104	Intermediate Calculations
Population 2 Sample		Degrees of Freedom	18
Sample Size	10	t Value	2.1009
Sample Mean	112.5	Interval Half Width	28.4147
Sample Standard Deviation	37.9568
		Confidence Interval
Intermediate Calculations		Interval Lower Limit	-46.4147
Population 1 Sample Degrees of Freedom	9	Interval Upper Limit	10.4147
Population 2 Sample Degrees of Freedom	9
Total Degrees of Freedom	18
Pooled Variance	914.6111
Standard Error	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two - Tail Test		One - Tail Calculations
Lower Critical Value	-2.1009	TDIST value	0.0999
Upper Critical Value	2.1009	1 - TDIST value	0.9001
p-Value	0.1998
Do not reject the null hypothesis
Lower - Tail Test
Lower Critical Value	-1.7341
p-Value	0.0999
Do not reject the null hypothesis
Upper - Tail Test
Upper Critical Value	1.7341
p-Value	0.9001
Do not reject the null hypothesis

COMPUTE_OLDER_FORMULAS

Pooled-Variance t Test for Differences in Two Means
(assumes equal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	95%
Sample Mean	94.5
Sample Standard Deviation	19.7104	Intermediate Calculations
Population 2 Sample		Degrees of Freedom	18
Sample Size	10	t Value	2.1009
Sample Mean	112.5	Interval Half Width	28.4147
Sample Standard Deviation	37.9568
		Confidence Interval
Intermediate Calculations		Interval Lower Limit	-46.4147
Population 1 Sample Degrees of Freedom	9	Interval Upper Limit	10.4147
Population 2 Sample Degrees of Freedom	9
Total Degrees of Freedom	18
Pooled Variance	914.6111111111
Standard Error	13.5248742036
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two - Tail Test		One - Tail Calculations
Lower Critical Value	-2.1009	TDIST value	0.0999
Upper Critical Value	2.1009	1 - TDIST value	0.9001
p-Value	0.1998
Do not reject the null hypothesis
Lower - Tail Test
Lower Critical Value	-1.7341
p-Value	0.0999
Do not reject the null hypothesis
Upper - Tail Test
Upper Critical Value	1.7341
p-Value	0.9001
Do not reject the null hypothesis

MAT10251 Workbooks 2018/Probabilities Workbook.xlsx

COMPUTE

Probabilities
Sample Space		Pacific Cruise
		Yes	No	Totals
New Zealand Cruise	YES	210	70	280
	NO	110	110	220
	Totals	320	180	500
Simple Probabilities
P(YES)	0.56
P(NO)	0.44
P(Yes)	0.64
P(No)	0.36
Joint Probabilities
P(YES and Yes)	0.42
P(YES and No)	0.14
P(NO and Yes)	0.22
P(NO and No)	0.22
Addition Rule
P(YES or Yes)	0.78
P(YES or No)	0.78
P(NO or Yes)	0.86
P(NO or No)	0.58
Conditional Probabilities
P(YES \| Yes)	0.66
P(NO \| Yes)	0.34
P(YES \| No)	0.39
P(NO \| No)	0.61
P(Yes \| YES)	0.75
P(No \| YES)	0.25
P(Yes \| NO)	0.50
P(No \| NO)	0.50

COMPUTE Formulas

Probabilities
Sample Space		Pacific Cruise
		Yes	No	Totals
New Zealand Cruise	YES	210	70	280
	NO	110	110	220
	Totals	320	180	500
Simple Probabilities
P(YES)	0.56
P(NO)	0.44
P(Yes)	0.64
P(No)	0.36
Joint Probabilities
P(YES and Yes)	0.42
P(YES and No)	0.14
P(NO and Yes)	0.22
P(NO and No)	0.22
Addition Rule
P(YES or Yes)	0.78
P(YES or No)	0.78
P(NO or Yes)	0.86
P(NO or No)	0.58
Conditional Probabilities
P(YES \| Yes)	0.66
P(NO \| Yes)	0.34
P(YES \| No)	0.39
P(NO \| No)	0.61
P(Yes \| YES)	0.75
P(No \| YES)	0.25
P(Yes \| NO)	0.50
P(No \| NO)	0.50

MAT10251 Workbooks 2018/Scatter Plot Workbook.xlsx

&UnStack

	Selling Price
Row1	118000
Row2	283500
Row3	289000
Row4	93000
Row5	211000
Row6	199500
Row7	148000
Row8	198000
Row9	340000
Row10	422500
Row11	259000
Row12	219500
Row13	240000
Row14	306500
Row15	219500
Row16	130000
Row17	196000
Row18	266000
Row19	200000
Row20	224000
Row21	122000
Row22	225000
Row23	395000
Row24	155000
Row25	364000
Row26	295000
Row27	218000
Row28	256000
Row29	222000
Row30	198000
Row31	244000
Row32	252000
Row33	262000
Row34	179500
Row35	122000
Row36	128000
Row37	148000
Row38	315000
Row39	149500
Row40	268000
Row41	297000
Row42	200000
Row43	310500
Row44	97000
Row45	480000
Row46	389000
Row47	222000
Row48	399000
Row49	315000
Row50	285000
Row51	305000
Row52	385000
Row53	198000
Row54	349500
Row55	200000
Row56	204000
Row57	282000
Row58	181000
Row59	261000
Row60	142000
Row61	312500
Row62	319000
Row63	158000
Row64	305000
Row65	385500
Row66	242000
Row67	323000
Row68	590000
Row69	270000
Row70	213000
Row71	260500
Row72	146500
Row73	339000
Row74	227000
Row75	282000
Row76	255900
Row77	325000
Row78	468000
Row79	210000
Row80	179000
Row81	133000
Row82	148000
Row83	396000
Row84	185000
Row85	179000
Row86	385000
Row87	248000
Row88	306000
Row89	225000
Row90	381000
Row91	157000
Row92	375000
Row93	229000
Row94	191000
Row95	245000
Row96	355000
Row97	200000
Row98	323000
Row99	625000
Row100	188000

&DataIndices

&DataCopy

Sheet1:1 Nicola Jayne:	Selling Price
Row1	118000
Row2	283500
Row3	289000
Row4	93000
Row5	211000
Row6	199500
Row7	148000
Row8	198000
Row9	340000
Row10	422500
Row11	259000
Row12	219500
Row13	240000
Row14	306500
Row15	219500
Row16	130000
Row17	196000
Row18	266000
Row19	200000
Row20	224000
Row21	122000
Row22	225000
Row23	395000
Row24	155000
Row25	364000
Row26	295000
Row27	218000
Row28	256000
Row29	222000
Row30	198000
Row31	244000
Row32	252000
Row33	262000
Row34	179500
Row35	122000
Row36	128000
Row37	148000
Row38	315000
Row39	149500
Row40	268000
Row41	297000
Row42	200000
Row43	310500
Row44	97000
Row45	480000
Row46	389000
Row47	222000
Row48	399000
Row49	315000
Row50	285000
Row51	305000
Row52	385000
Row53	198000
Row54	349500
Row55	200000
Row56	204000
Row57	282000
Row58	181000
Row59	261000
Row60	142000
Row61	312500
Row62	319000
Row63	158000
Row64	305000
Row65	385500
Row66	242000
Row67	323000
Row68	590000
Row69	270000
Row70	213000
Row71	260500
Row72	146500
Row73	339000
Row74	227000
Row75	282000
Row76	255900
Row77	325000
Row78	468000
Row79	210000
Row80	179000
Row81	133000
Row82	148000
Row83	396000
Row84	185000
Row85	179000
Row86	385000
Row87	248000
Row88	306000
Row89	225000
Row90	381000
Row91	157000
Row92	375000
Row93	229000
Row94	191000
Row95	245000
Row96	355000
Row97	200000
Row98	323000
Row99	625000
Row100	188000

&Miscel_Area

118000	93000	X Variable	Coefficient	X Predictor Value	No. of Pairs	0	Y Axis	v	X Axis
283500	97000						Select Y below		Select X below
289000	118000						for each case		for each case
93000	122000								Click Add 'Y v X' pair
211000	122000								button for each case
199500	128000
148000	130000
198000	133000
340000	142000
422500	146500
259000	148000
219500	148000
240000	148000
306500	149500
219500	155000
130000	157000
196000	158000
266000	179000
200000	179000
224000	179500
122000	181000
225000	185000
395000	188000
155000	191000
364000	196000
295000	198000
218000	198000
256000	198000
222000	199500
198000	200000
244000	200000
252000	200000
262000	200000
179500	204000
122000	210000
128000	211000
148000	213000
315000	218000
149500	219500
268000	219500
297000	222000
200000	222000
310500	224000
97000	225000
480000	225000
389000	227000
222000	229000
399000	240000
315000	242000
285000	244000
305000	245000
385000	248000
198000	252000
349500	255900
200000	256000
204000	259000
282000	260500
181000	261000
261000	262000
142000	266000
312500	268000
319000	270000
158000	282000
305000	282000
385500	283500
242000	285000
323000	289000
590000	295000
270000	297000
213000	305000
260500	305000
146500	306000
339000	306500
227000	310500
282000	312500
255900	315000
325000	315000
468000	319000
210000	323000
179000	323000
133000	325000
148000	339000
396000	340000
185000	349500
179000	355000
385000	364000
248000	375000
306000	381000
225000	385000
381000	385000
157000	385500
375000	389000
229000	395000
191000	396000
245000	399000
355000	422500
200000	468000
323000	480000
625000	590000
188000	625000

&GraphData

&WorkArea

DATA

Real Estate Information
X = Bedrooms	Y = Asking Price	njayne: njayne: Add or delete rows at row 4
1	338000
3	486000
4	493000
1	324000
4	425000
3	411000
3	384000
2	405000
1	537000
2	658000
3	460000
3	424000
3	435000
5	524000
3	415000
3	363000
2	396000
4	477000
2	405000
3	451000
4	329000
3	451000
8	587000
2	362000
4	578000
3	496000
3	435000
3	479000
3	446000
2	423000
5	460000
3	461000
2	516000
3	389000
3	330000
1	340000
2	361000
3	530000
2	365000
4	480000
4	522000
2	407000
3	529000
1	319000
4	684000
4	607000
3	465000
4	602000
3	512000
4	485000
4	523000
4	629000
3	454000
4	603000
2	412000
3	433000
4	475000
3	390000
5	464000
1	354000
3	540000
3	412000
2	397000
3	558000
4	621000
3	452000
4	547000
4	843000
5	505000
3	439000
3	493000
2	383000
4	539000
3	425000
3	519000
2	461000
4	527000
3	676000
3	411000
3	411000
3	356000
2	355000
3	624000
2	396000
2	386000
4	618000
4	471000
3	511000
4	448000
3	593000
3	391000
3	589000
3	326000
2	380000
3	335000
4	572000
3	434000
3	548000
6	841000
2	413000

Scatter Diagram

Real Estate Information

Y = Asking Price

1 3 4 1 4 3 3 2 1 2 3 3 3 5 3 3 2 4 2 3 4 3 8 2 4 3 3 3 3 2 5 3 2 3 3 1 2 3 2 4 4 2 3 1 4 4 3 4 3 4 4 4 3 4 2 3 4 3 5 1 3 3 2 3 4 3 4 4 5 3 3 2 4 3 3 2 4 3 3 3 3 2 3 2 2 4 4 3 4 3 3 3 3 2 3 4 3 3 6 2 338000 486000 493000 324000 425000 411000 384000 405000 537000 658000 460000 424000 435000 524000 415000 363000 396000 477000 405000 451000 329000 451000 587000 362000 578000 496000 435000 479000 446000 423000 460000 461000 516000 389000 330000 340000 361000 530000 365000 480000 522000 407000 529000 319000 684000 607000 465000 602000 512000 485000 523000 629000 454000 603000 412000 433000 475000 390000 464000 354000 540000 412000 397000 558000 621000 452000 547000 843000 505000 439000 493000 383000 539000 425000 519000 461000 527000 676000 411000 411000 356000 355000 624000 396000 386000 618000 471000 511000 448000 593000 391000 589000 326000 380000 335000 572000 434000 548000 841000 413000 X = Bedrooms

Y = Asking Price

MAT10251 Workbooks 2018/Separate-Variance T Test Workbook.xlsx

DATA

A	B
80	152
120	96
52	123
96	98
102	181
85	133
106	76
117	47
98	115
89	104

COMPUTE_ALL

Separate-Variances t Test
(assumes unequal population variances)
Data				Confidence Interval Estimate
Hypothesized Difference	0			for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample				Data
Sample Size	10			Confidence Level	95%
Sample Mean	94.5
Sample Standard Deviation	19.7104			Intermediate Calculations
Population 2 Sample				Degrees of Freedom	13
Sample Size	10			t Value	2.1604
Sample Mean	112.5			Interval Half Width	29.2187
Sample Standard Deviation	37.9568
				Confidence Interval
Intermediate Calculations		One-Tail Calculations		Interval Lower Limit	-47.2187
Pop. 1 Sample Variance	388.5000	T.DIST.RT value	0.1030	Interval Upper Limit	11.2187
Pop. 2 Sample Variance	1440.7222	1 - T.DIST.RT value	0.8970
Pop. 1 Sample Var./Sample Size	38.8500
Pop. 2 Sample Var./Sample Size	144.0722
Numerator of Degrees of Freedom	33460.5394
Denominator of Degrees of Freedom	2474.0142
Total Degrees of Freedom	13.5248
Degrees of Freedom	13
Separate Variance Denominator	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two-Tail Test
Lower Critical Value	-2.1604
Upper Critical Value	2.1604
p-Value	0.2061
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7709
p-Value	0.1030
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7709
p-Value	0.8970
Do not reject the null hypothesis

COMPUTE_ALL_STATISTICS

Separate-Variances t Test
(assumes unequal population variances)
Data				Confidence Interval Estimate
Hypothesized Difference	0			for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample				Data
Sample Size	10			Confidence Level	95%
Sample Mean	94.5
Sample Standard Deviation	19.7104			Intermediate Calculations
Population 2 Sample				Degrees of Freedom	13
Sample Size	10			t Value	2.1604
Sample Mean	112.5			Interval Half Width	29.2187
Sample Standard Deviation	37.9568
				Confidence Interval
Intermediate Calculations		One-Tail Calculations		Interval Lower Limit	-47.2187
Pop. 1 Sample Variance	388.5000	T.DIST.RT value	0.1030	Interval Upper Limit	11.2187
Pop. 2 Sample Variance	1440.7222	1 - T.DIST.RT value	0.8970
Pop. 1 Sample Var./Sample Size	38.8500
Pop. 2 Sample Var./Sample Size	144.0722
Numerator of Degrees of Freedom	33460.5394
Denominator of Degrees of Freedom	2474.0142
Total Degrees of Freedom	13.5248
Degrees of Freedom	13
Separate Variance Denominator	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two-Tail Test
Lower Critical Value	-2.1604
Upper Critical Value	2.1604
p-Value	0.2061
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7709
p-Value	0.1030
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7709
p-Value	0.8970
Do not reject the null hypothesis

COMPUTE

Separate-Variances t Test
(assumes unequal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	95%
Sample Mean	94.5
Sample Standard Deviation	19.7104	Intermediate Calculations
Population 2 Sample		Degrees of Freedom	13
Sample Size	10	t Value	2.1604
Sample Mean	112.5	Interval Half Width	29.2187
Sample Standard Deviation	37.9568
		Confidence Interval
Intermediate Calculations		Interval Lower Limit	-47.2187
Pop. 1 Sample Variance	388.5000	Interval Upper Limit	11.2187
Pop. 2 Sample Variance	1440.7222
Pop. 1 Sample Var./Sample Size	38.8500
Pop. 2 Sample Var./Sample Size	144.0722
Numerator of Degrees of Freedom	33460.5394
Denominator of Degrees of Freedom	2474.0142
Total Degrees of Freedom	13.5248
Degrees of Freedom	13
Separate Variance Denominator	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two-Tail Test
Lower Critical Value	-2.1604
Upper Critical Value	2.1604
p-Value	0.2061
Do not reject the null hypothesis

COMPUTE_LOWER

Separate-Variances t Test
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	10
Sample Mean	94.5
Sample Standard Deviation	19.7104
Population 2 Sample
Sample Size	10
Sample Mean	112.5
Sample Standard Deviation	37.9568
Intermediate Calculations		One-Tail Calculations
Pop. 1 Sample Variance	388.5000	T.DIST.RT value	0.1030
Pop. 2 Sample Variance	1440.7222	1 - T.DIST.RT value	0.8970
Pop. 1 Sample Var./Sample Size	38.8500
Pop. 2 Sample Var./Sample Size	144.0722
Numerator of Degrees of Freedom	33460.5394
Denominator of Degrees of Freedom	2474.0142
Total Degrees of Freedom	13.5248
Degrees of Freedom	13
Separate Variance Denominator	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Lower-Tail Test
Lower Critical Value	-1.7709
p-Value	0.1030
Do not reject the null hypothesis

COMPUTE_UPPER

Separate-Variances t Test
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	10
Sample Mean	94.5
Sample Standard Deviation	19.7104
Population 2 Sample
Sample Size	10
Sample Mean	112.5
Sample Standard Deviation	37.9568
Intermediate Calculations		One-Tail Calculations
Pop. 1 Sample Variance	388.5000	T.DIST.RT value	0.1030
Pop. 2 Sample Variance	1440.7222	1 - T.DIST.RT value	0.8970
Pop. 1 Sample Var./Sample Size	38.8500
Pop. 2 Sample Var./Sample Size	144.0722
Numerator of Degrees of Freedom	33460.5394
Denominator of Degrees of Freedom	2474.0142
Total Degrees of Freedom	13.5248
Degrees of Freedom	13
Separate Variance Denominator	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Upper-Tail Test
Upper Critical Value	1.7709
p-Value	0.8970
Do not reject the null hypothesis

COMPUTE_ALL_FORMULAS

Separate-Variances t Test
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	10
Sample Mean	94.5
Sample Standard Deviation	19.7104
Population 2 Sample
Sample Size	10
Sample Mean	112.5
Sample Standard Deviation	37.9568
Intermediate Calculations		One-Tail Calculations
Pop. 1 Sample Variance	388.5000	T.DIST.RT value	0.1030
Pop. 2 Sample Variance	1440.7222	1 - T.DIST.RT value	0.8970
Pop. 1 Sample Var./Sample Size	38.8500
Pop. 2 Sample Var./Sample Size	144.0722
Numerator of Degrees of Freedom	33460.5394
Denominator of Degrees of Freedom	2474.0142
Total Degrees of Freedom	13.5248
Degrees of Freedom	13
Separate Variance Denominator	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two-Tail Test
Lower Critical Value	-2.1604
Upper Critical Value	2.1604
p-Value	0.20609991231457800
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7709
p-Value	0.1030
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7709
p-Value	0.8970
Do not reject the null hypothesis

COMPUTE_OLDER

Separate-Variances t Test
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	10
Sample Mean	94.5
Sample Standard Deviation	19.7104
Population 2 Sample
Sample Size	10
Sample Mean	112.5
Sample Standard Deviation	37.9568
Intermediate Calculations		One-Tail Calculations
Pop. 1 Sample Variance	388.5000	TDIST value	0.1030
Pop. 2 Sample Variance	1440.7222	1 -TDIST value	0.8970
Pop. 1 Sample Var./Sample Size	38.8500
Pop. 2 Sample Var./Sample Size	144.0722
Numerator of Degrees of Freedom	33460.5394
Denominator of Degrees of Freedom	2474.0142
Total Degrees of Freedom	13.5248
Degrees of Freedom	13
Separate Variance Denominator	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two-Tail Test
Lower Critical Value	-2.1604
Upper Critical Value	2.1604
p-Value	0.2061
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7709
p-Value	0.1030
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7709
p-Value	0.8970
Do not reject the null hypothesis

COMPUTE_OLDER_FORMULAS

Separate-Variances t Test
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	10
Sample Mean	94.5
Sample Standard Deviation	19.7104
Population 2 Sample
Sample Size	10
Sample Mean	112.5
Sample Standard Deviation	37.9568
Intermediate Calculations		One-Tail Calculations
Pop. 1 Sample Variance	388.5000	TDIST value	0.1030
Pop. 2 Sample Variance	1440.7222	1 - TDIST value	0.8970
Pop. 1 Sample Var./Sample Size	38.8500
Pop. 2 Sample Var./Sample Size	144.0722
Numerator of Degrees of Freedom	33460.5394
Denominator of Degrees of Freedom	2474.0142
Total Degrees of Freedom	13.5248
Degrees of Freedom	13
Separate Variance Denominator	13.5249
Difference in Sample Means	-18
t Test Statistic	-1.3309
Two-Tail Test
Lower Critical Value	-2.1604
Upper Critical Value	2.1604
p-Value	0.2061
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7709
p-Value	0.1030
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7709
p-Value	0.8970
Do not reject the null hypothesis

MAT10251 Workbooks 2018/Simple Linear Regression Workbook.xlsx

SLRData

Scatter Plot Title
Mean Mathematics Literacy Score - X	Human Development Index - Y	Add or delete middle rows.
498.0	93.8	Row 4 to 20
514.3	93.7
519.3	90.7
487.4	90.2
487.1	89.5
536.0	89.1
525.8	89.0
526.8	88.8
512.8	88.5
562.0	84.6
431.0	71.3
385.8	69.9
380.8	68.9
371.5	68.3
386.7	68.1
445.5	67.9
418.6	65.4
371.3	60.0
331.2	59.8

COMPUTE

Simple Linear Regression									Calculations
									b1, b0 Coefficients	0.1582	6.4483
Regression Statistics									b1, b0 Standard Error	0.0183	8.4715
Multiple R	0.9024587434								R Square, Standard Error	0.8144	5.4709
R Square	0.8144317835								F, Residual df	74.6105	17.0000
Adjusted R Square	0.803516006								Regression SS, Residual SS	2233.1274	508.8179
Standard Error	5.4708741765
Observations	19								Confidence level	95%
									t Critical Value	2.1098
ANOVA									Half Width b0	17.8734
	df	SS	MS	F	Significance F				Half Width b1	0.0386
Regression	1	2233.1273708191	2233.1273708191	74.6105156197	0.0000001265
Residual	17	508.8178923388	29.9304642552
Total	18	2741.9452631579
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95%	Upper 95%
Intercept	6.4483358568	8.4715473064	0.7611756889	0.4569817456	-11.4250666186	24.3217383322	-11.4250666186	24.3217383322
Mean Mathematics Literacy Score - X	0.1581911456	0.0183139553	8.6377378763	0.0000001265	0.1195520774	0.1968302139	0.1195520774	0.1968302139

CIEandPI

Confidence Interval Estimate and Prediction Interval
Data
X Value	500
Confidence Level	0.95
Intermediate Calculations
Sample Size	19
Degrees of Freedom	17
t Value	2.1098155778
Sample Mean	457.4684210526
Sum of Squared Difference	89237.8610526315
Standard Error of the Estimate	5.4708741765
h Statistic	0.0729025176
Predicted Y (YHat)	85.5439086729
For Average Y
Interval Half Width	3.1165384153
Confidence Interval Lower Limit	82.4273702576
Confidence Interval Upper Limit	88.6604470883
For Individual Response Y
Interval Half Width	11.9558746603
Prediction Interval Lower Limit	73.5880340126
Prediction Interval Upper Limit	97.4997833333

Scatter Plot

Scatter Plot Title

Human Development Index - Y

498 514.29999999999995 519.29999999999995 487.4 487.1 536 525.79999999999995 526.79999999999995 512.79999999999995 562 431 385.8 380.8 371.5 386.7 445.5 418.6 371.3 331.2 93.8 93.7 90.7 90.2 89.5 89.1 89 88.8 88.5 84.6 71.3 69.899999999999991 68.899999999999991 68.300000000000011 68.100000000000009 67.900000000000006 65.400000000000006 60 59.8 Mean Mathematics Literacy Score - X

Human Development Index - Y

MAT10251 Workbooks 2018/T Mean Workbook.xlsx

DATA

Data
3
10
10
11
12
13
14
15
15
18
19
21
24
25
32
33
35
39
43
56
119

COMPUTE_ALL

t Test for the Hypothesis of the Mean
Data
Null Hypothesis m=	30
Level of Significance	0.05
Sample Size	21
Sample Mean	27
Sample Standard Deviation	24.8112877538
Intermediate Calculations		One-Tail Calculations
Standard Error of the Mean	5.4143	T.DIST.RT value	0.2928294622
Degrees of Freedom	20	1-T.DIST.RT value	0.7071705378
t Test Statistic	-0.5541
Two-Tail Test
Lower Critical Value	-2.0860
Upper Critical Value	2.0860
p-Value	0.5857
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7247
p-Value	0.2928
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7247
p-Value	0.7072
Do not reject the null hypothesis

COMPUTE_ALL_STATISTICS

t Test for the Hypothesis of the Mean
Data
Null Hypothesis m=	30
Level of Significance	0.05
Sample Size	21
Sample Mean	27
Sample Standard Deviation	24.8112877538
Intermediate Calculations		One-Tail Calculations
Standard Error of the Mean	5.4143	T.DIST.RT value	0.2928294622
Degrees of Freedom	20	1-T.DIST.RT value	0.7071705378
t Test Statistic	-0.5541
Two-Tail Test
Lower Critical Value	-2.0860
Upper Critical Value	2.0860
p-Value	0.5857
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7247
p-Value	0.2928
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7247
p-Value	0.7072
Do not reject the null hypothesis

COMPUTE

t Test for the Hypothesis of the Mean
Data
Null Hypothesis m =	25
Level of Significance	0.05
Sample Size	21
Sample Mean	27
Sample Standard Deviation	24.8112877538
Intermediate Calculations
Standard Error of the Mean	5.4143
Degrees of Freedom	20
t Test Statistic	0.3694
Two-Tail Test
Lower Critical Value	-2.0860
Upper Critical Value	2.0860
p-Value	0.7157
Do not reject the null hypothesis

COMPUTE_LOWER

t Test for the Hypothesis of the Mean
Data
Null Hypothesis m=	20
Level of Significance	0.05
Sample Size	21
Sample Mean	27
Sample Standard Deviation	24.8112877538
Intermediate Calculations		One-Tail Calculations
Standard Error of the Mean	5.4143	T.DIST.RT value	0.1054
Degrees of Freedom	20	1-T.DIST.RT value	0.8946
t Test Statistic	1.2929
Lower-Tail Test
Lower Critical Value	-1.7247
p-Value	0.8946
Do not reject the null hypothesis

COMPUTE_UPPER

t Test for the Hypothesis of the Mean
Data
Null Hypothesis m=	25
Level of Significance	0.05
Sample Size	21
Sample Mean	27
Sample Standard Deviation	24.8112877538
Intermediate Calculations		One-Tail Calculations
Standard Error of the Mean	5.4143	T.DIST.RT value	0.3579
Degrees of Freedom	20	1-T.DIST.RT value	0.6421
t Test Statistic	0.3694
Upper-Tail Test
Upper Critical Value	1.7247
p-Value	0.3579
Do not reject the null hypothesis

COMPUTE_ALL_FORMULAS

t Test for the Hypothesis of the Mean
Data
Null Hypothesis m=	120
Level of Significance	0.05
Sample Size	21
Sample Mean	27
Sample Standard Deviation	24.8112877538
Intermediate Calculations		One-Tail Calculations
Standard Error of the Mean	5.4143	T.DIST.RT value	0
Degrees of Freedom	20	1-T.DIST.RT value	1
t Test Statistic	-17.1768
Two-Tail Test
Lower Critical Value	-2.0860
Upper Critical Value	2.0860
p-Value	0.0000
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7247
p-Value	0.0000
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7247
p-Value	1.0000
Do not reject the null hypothesis

COMPUTE_OLDER

t Test for the Hypothesis of the Mean
Data
Null Hypothesis m=	120
Level of Significance	0.05
Sample Size	21
Sample Mean	27
Sample Standard Deviation	24.8112877538
Intermediate Calculations		One-Tail Calculations
Standard Error of the Mean	5.4143	TDIST value	0
Degrees of Freedom	20	1 - TDIST value	1
t Test Statistic	-17.1768
Two-Tail Test
Lower Critical Value	-2.0860
Upper Critical Value	2.0860
p-Value	0.0000
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7247
p-Value	0.0000
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7247
p-Value	1.0000
Do not reject the null hypothesis

COMPUTE_OLDER_FORMULAS

t Test for the Hypothesis of the Mean
Data
Null Hypothesis m=	120
Level of Significance	0.05
Sample Size	21
Sample Mean	27
Sample Standard Deviation	24.8112877538
Intermediate Calculations		One-Tail Calculations
Standard Error of the Mean	5.4143	TDIST value	0
Degrees of Freedom	20	1 - TDIST value	1
t Test Statistic	-17.1768
Two-Tail Test
Lower Critical Value	-2.0860
Upper Critical Value	2.0860
p-Value	0.0000
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7247
p-Value	0.0000
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7247
p-Value	1.0000
Do not reject the null hypothesis

MAT10251 Workbooks 2018/Z Mean Workbook.xlsx

DATA

Data
3
10
10
11
12
13
14
15
15
18
19
21
24
25
32
33
35
39
43
56
119

COMPUTE_ALL_SAMPLE_SD

Z Test for the Mean
Data
Null Hypothesis m =	368
Level of Significance	0.05
Sample Standard Deviation	24.8112877538
Sample Size	21
Sample Mean	27
Intermediate Calculations
Standard Error of the Mean	5.4142668677
Z Test Statistic	-62.9817495766
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0000
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.0000
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	1.0000
Do not reject the null hypothesis

COMPUTE_ALL_POP_SD

Z Test for the Mean
Data
Null Hypothesis m =	368
Level of Significance	0.05
Population Standard Deviation	25
Sample Size	21
Sample Mean	27
Intermediate Calculations
Standard Error of the Mean	5.4554472559
Z Test Statistic	-62.5063324792
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0000
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.0000
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	1.0000
Do not reject the null hypothesis

COMPUTE_ALL_STATISTICS

Z Test for the Mean
Data
Null Hypothesis m =	368
Level of Significance	0.05
Population/Sample Standard Deviation	25
Sample Size	21
Sample Mean	27
Intermediate Calculations
Standard Error of the Mean	5.4554472559
Z Test Statistic	-62.5063324792
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0000
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.0000
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	1.0000
Do not reject the null hypothesis

COMPUTE_POP_SD

Z Test for the Mean
Data
Null Hypothesis m =	368
Level of Significance	0.05
Population Standard Deviation	25
Sample Size	21
Sample Mean	27
Intermediate Calculations
Standard Error of the Mean	5.4554472559
Z Test Statistic	-62.5063324792
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0000
Reject the null hypothesis

COMPUTE_LOWER

Z Test for the Mean
Data
Null Hypothesis m =	368
Level of Significance	0.05
Population Standard Deviation	25
Sample Size	21
Sample Mean	27
Intermediate Calculations
Standard Error of the Mean	5.4554472559
Z Test Statistic	-62.5063324792
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.0000
Reject the null hypothesis

COMPUTE_UPPER

Z Test for the Mean
Data
Null Hypothesis m =	368
Level of Significance	0.05
Population Standard Deviation	25
Sample Size	21
Sample Mean	27
Intermediate Calculations
Standard Error of the Mean	5.4554472559
Z Test Statistic	-62.5063324792
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	1.0000
Do not reject the null hypothesis

COMPUTE_ALL_FORMULAS

Z Test for the Mean
Data
Null Hypothesis m =	368
Level of Significance	0.05
Population Standard Deviation	25
Sample Size	21
Sample Mean	27
Intermediate Calculations
Standard Error of the Mean	5.4554472559
Z Test Statistic	-62.5063324792
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0000
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.0000
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	1.0000
Do not reject the null hypothesis

COMPUTE_OLDER

Z Test for the Mean
Data
Null Hypothesis m=	368
Level of Significance	0.05
Population Standard Deviation	25
Sample Size	21
Sample Mean	27
Intermediate Calculations
Standard Error of the Mean	5.4554472559
Z Test Statistic	-62.5063324792
Two - Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p - Value	0.0000
Reject the null hypothesis
Lower - Tail Test
Lower Critical Value	-1.6449
p - Value	0.0000
Reject the null hypothesis
Upper - Tail Test
Upper Critical Value	1.6449
p - Value	1.0000
Do not reject the null hypothesis

COMPUTE_OLDER_FORMULAS

Z Test for the Mean
Data
Null Hypothesis m=	368
Level of Significance	0.05
Population Standard Deviation	25
Sample Size	21
Sample Mean	27
Intermediate Calculations
Standard Error of the Mean	5.4554472559
Z Test Statistic	-62.5063324792
Two - Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p - Value	0.0000
Reject the null hypothesis
Lower - Tail Test
Lower Critical Value	-1.6449
p - Value	0.0000
Reject the null hypothesis
Upper - Tail Test
Upper Critical Value	1.6449
p - Value	1.0000
Do not reject the null hypothesis

MAT10251 Workbooks 2018/Z Proportion Workbook.xlsx

COMPUTE

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis p=	0.3
Level of Significance	0.05
Number of Items of Interest	320
Sample Size	1000
Intermediate Calculations
Sample Proportion	0.3200
Standard Error	0.0145
Z Test Statistic	1.3801
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical value	1.9600
p-Value	0.1675
Do not reject the null hypothesis

COMPUTE_LOWER

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis p=	0.3
Level of Significance	0.05
Number of Items of Interest	320
Sample Size	1000
Intermediate Calculations
Sample Proportion	0.3200
Standard Error	0.0145
Z Test Statistic	1.3801
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.9162
Do not reject the null hypothesis

COMPUTE_UPPER

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis p=	0.3
Level of Significance	0.05
Number of Items of Interest	320
Sample Size	1000
Intermediate Calculations
Sample Proportion	0.3200
Standard Error	0.0145
Z Test Statistic	1.3801
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	0.0838
Do not reject the null hypothesis

COMPUTE_ALL

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis p=	0.3
Level of Significance	0.05
Number of Items of Interest	320
Sample Size	1000
Intermediate Calculations
Sample Proportion	0.3200
Standard Error	0.0145
Z Test Statistic	1.3801
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical value	1.9600
p-Value	0.1675
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.9162
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	0.0838
Do not reject the null hypothesis

COMPUTE_ALL FORMULAS

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis p=	0.3
Level of Significance	0.05
Number of Items of Interest	320
Sample Size	1000
Intermediate Calculations
Sample Proportion	0.3200
Standard Error	0.0145
Z Test Statistic	1.3801
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical value	1.9600
p-Value	0.1675
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.9162
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	0.0838
Do not reject the null hypothesis

COMPUTE_OLDER

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis p=	0.3
Level of Significance	0.05
Number of Items of Interest	320
Sample Size	1000
Intermediate Calculations
Sample Proportion	0.3200
Standard Error	0.0145
Z Test Statistic	1.3801
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical value	1.9600
p-Value	0.1675
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.9162
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	0.0838
Do not reject the null hypothesis

COMPUTE_OLDER_FORMULAS

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis p=	0.3
Level of Significance	0.05
Number of Items of Interest	320
Sample Size	1000
Intermediate Calculations
Sample Proportion	0.3200
Standard Error	0.0145
Z Test Statistic	1.3801
Two - Tail Test
Lower Critical Value	-1.9600
Upper Critical value	1.9600
p-Value	0.1675
Do not reject the null hypothesis
Lower - Tail Test
Lower Critical Value	-1.6449
p-Value	0.9162
Do not reject the null hypothesis
Upper - Tail Test
Upper Critical Value	1.6449
p-Value	0.0838
Do not reject the null hypothesis

MAT10251 Workbooks 2018/Z Test Two Means Workbook.xlsx

Data

A	B
80	152
120	96
52	123
96	98
102	181
85	133
106	76
117	47
98	115
89	104

All Sample SD

Z Test for Differences in Two Means
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	95.00%
Sample Mean	94.5
Sample Standard Deviation	19.7104033444	Intermediate Calculations
Population 2 Sample		Z Value	1.9600
Sample Size	10	Interval Half Width	26.5082663344
Sample Mean	112.5
Sample Standard Deviation	37.9568468425	Confidence Interval
		Interval Lower Limit	-44.5082663344
Intermediate Calculations		Interval Upper Limit	8.5083
Difference in Sample Means	-18
Standard Error of the Difference in Means	13.5249
Z Test Statistic	-1.3309
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.18323
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.644853627
p-Value	0.908386
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.644853627
p-Value	0.091614
Do not reject the null hypothesis

All Pop SD

Z Test for Differences in Two Means
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	99.00%
Sample Mean	94.5
Population Standard Deviation	20	Intermediate Calculations
Population 2 Sample		Z Value	2.5758
Sample Size	10	Interval Half Width	34.9782065468
Sample Mean	112.5
Population Standard Deviation	38	Confidence Interval
		Interval Lower Limit	-52.9782
Intermediate Calculations		Interval Upper Limit	16.9782065468
Difference in Sample Means	-18
Standard Error of the Difference in Means	13.5794
Z Test Statistic	-1.3255
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.18499
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.644853627
p-Value	0.907504
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.644853627
p-Value	0.092496
Do not reject the null hypothesis

All Statistics

Z Test for Differences in Two Means
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	99.00%
Sample Mean	94.5
Population/Sample Standard Deviation	20	Intermediate Calculations
Population 2 Sample		Z Value	2.5758
Sample Size	10	Interval Half Width	34.9782065468
Sample Mean	112.5
Population Standard Deviation	38	Confidence Interval
		Interval Lower Limit	-52.9782065468
Intermediate Calculations		Interval Upper Limit	16.9782065468
Difference in Sample Means	-18
Standard Error of the Difference in Means	13.5794
Z Test Statistic	-1.3255
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.18499
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.644853627
p-Value	0.907504
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.644853627
p-Value	0.092496
Do not reject the null hypothesis

Upper Tail

Z Test for Differences in Two Means
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	10
Sample Mean	94.5
Population Standard Deviation	20
Population 2 Sample
Sample Size	10
Sample Mean	112.5
Population Standard Deviation	38
Intermediate Calculations
Difference in Sample Means	-18
Standard Error of the Difference in Means	13.5793961574
Z-Test Statistic	-1.3255375859
Upper-Tail Test
Upper Critical Value	1.644853627
p-Value	0.9075035441
Do not reject the null hypothesis

Lower Tail

Z Test for Differences in Two Means
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	10
Sample Mean	94.5
Population Standard Deviation	20
Population 2 Sample
Sample Size	10
Sample Mean	112.5
Population Standard Deviation	38
Intermediate Calculations
Difference in Sample Means	-18
Standard Error of the Difference in Means	13.5793961574
Z-Test Statistic	-1.3255375859
Lower-Tail Test
Lower Critical Value	-1.644853627
p-Value	0.092496
Do not reject the null hypothesis

Two-Tail

Z Test for Differences in Two Means
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	99.00%
Sample Mean	94.5
Population Standard Deviation	20	Intermediate Calculations
Population 2 Sample		Z Value	2.5758
Sample Size	10	Interval Half Width	34.9782065468
Sample Mean	112.5
Population Standard Deviation	38	Confidence Interval
		Interval Lower Limit	-52.9782065468
Intermediate Calculations		Interval Upper Limit	16.9782065468
Difference in Sample Means	-18
Standard Error of the Difference in Means	13.5794
Z Test Statistic	-1.3255
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.18499
Do not reject the null hypothesis

All Sample SD Old

Z Test for Differences in Two Means
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	99.00%
Sample Mean	94.5
Sample Standard Deviation	19.7104033444	Intermediate Calculations
Population 2 Sample		Z Value	2.5758
Sample Size	10	Interval Half Width	34.8377673004
Sample Mean	112.5
Sample Standard Deviation	37.9568468425	Confidence Interval
		Interval Lower Limit	-52.8377673004
Intermediate Calculations		Interval Upper Limit	16.8377673004
Difference in Sample Means	-18
Standard Error of the Difference in Means	13.5249
Z Test Statistic	-1.3309
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.18323
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.644853627
p-Value	0.9084
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.644853627
p-Value	0.091614
Do not reject the null hypothesis

All Sample SD Formula

Z Test for Differences in Two Means
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample		Data
Sample Size	10	Confidence Level	99.00%
Sample Mean	94.5
Sample Standard Deviation	19.7104033444	Intermediate Calculations
Population 2 Sample		Z Value	2.5758
Sample Size	10	Interval Half Width	34.8377673004
Sample Mean	112.5
Sample Standard Deviation	37.9568468425	Confidence Interval
		Interval Lower Limit	-52.8377673004
Intermediate Calculations		Interval Upper Limit	16.8377673004
Difference in Sample Means	-18
Standard Error of the Difference in Means	13.5249
Z Test Statistic	-1.3309
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.18323
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.644853627
p-Value	0.908386
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.644853627
p-Value	0.091614
Do not reject the null hypothesis

MAT10251 Workbooks 2018/Z Test Two Proportions Workbook.xlsx

COMPUTE_ALL

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Proportions
Level of Significance	0.05
Group 1		Data
Number of Successes	163	Confidence Level	95%
Sample Size	227
Group 2		Intermediate Calculations
Number of Successes	154	Z Value	-1.9600
Sample Size	262	Std. Error of the Diff. Between Two Proportions	0.0426
		Interval Half Width	0.0835
Intermediate Calculations
Group 1 Proportion	0.7181	Confidence Interval
Group 2 Proportion	0.5878	Interval Lower Limit	0.0467
Difference in Two Proportions	0.1303	Interval Upper Limit	0.2138
Average Proportion	0.6483
Z Test Statistic	3.0088
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0026
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.9987
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	0.0013
Reject the null hypothesis

COMPUTE

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Proportions
Level of Significance	0.05
Group 1		Data
Number of Successes	163	Confidence Level	95%
Sample Size	227
Group 2		Intermediate Calculations
Number of Successes	154	Z Value	-1.9600
Sample Size	262	Std. Error of the Diff. Between Two Proportions	0.0426
		Interval Half Width	0.0835
Intermediate Calculations
Group 1 Proportion	0.7181	Confidence Interval
Group 2 Proportion	0.5878	Interval Lower Limit	0.0467
Difference in Two Proportions	0.1303	Interval Upper Limit	0.2138
Average Proportion	0.6483
Z Test Statistic	3.0088
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0026
Reject the null hypothesis

COMPUTE_LOWER

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Proportions
Level of Significance	0.05
Group 1		Data
Number of Successes	163	Confidence Level	95%
Sample Size	227
Group 2		Intermediate Calculations
Number of Successes	154	Z Value	-1.9600
Sample Size	262	Std. Error of the Diff. Between Two Proportions	0.0426
		Interval Half Width	0.0835
Intermediate Calculations
Group 1 Proportion	0.7181	Confidence Interval
Group 2 Proportion	0.5878	Interval Lower Limit	0.0467
Difference in Two Proportions	0.1303	Interval Upper Limit	0.2138
Average Proportion	0.6483
Z Test Statistic	3.0088
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.9987
Do not reject the null hypothesis

COMPUTE_UPPER

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Proportions
Level of Significance	0.05
Group 1		Data
Number of Successes	163	Confidence Level	95%
Sample Size	227
Group 2		Intermediate Calculations
Number of Successes	154	Z Value	-1.9600
Sample Size	262	Std. Error of the Diff. Between Two Proportions	0.0426
		Interval Half Width	0.0835
Intermediate Calculations
Group 1 Proportion	0.7181	Confidence Interval
Group 2 Proportion	0.5878	Interval Lower Limit	0.0467
Difference in Two Proportions	0.1303	Interval Upper Limit	0.2138
Average Proportion	0.6483
Z Test Statistic	3.0088
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	0.0013
Reject the null hypothesis

COMPUTE_ALL_FORMULAS

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Proportions
Level of Significance	0.05
Group 1		Data
Number of Successes	163	Confidence Level	95%
Sample Size	227
Group 2		Intermediate Calculations
Number of Successes	154	Z Value	-1.9600
Sample Size	262	Std. Error of the Diff. Between Two Proportions	0.0426
		Interval Half Width	0.0835
Intermediate Calculations
Group 1 Proportion	0.7181	Confidence Interval
Group 2 Proportion	0.5878	Interval Lower Limit	0.0467
Difference in Two Proportions	0.1303	Interval Upper Limit	0.2138
Average Proportion	0.6483
Z Test Statistic	3.0088
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0026
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.9987
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	0.0013
Reject the null hypothesis

COMPUTE_OLDER

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0	for the Difference Between Two Proportions
Level of Significance	0.05
Group 1		Data
Number of Successes	163	Confidence Level	95%
Sample Size	227
Group 2		Intermediate Calculations
Number of Successes	154	Z Value	-1.9600
Sample Size	262	Std. Error of the Diff. Between Two Proportions	0.0426
		Interval Half Width	0.0835
Intermediate Calculations
Group 1 Proportion	0.7181	Confidence Interval
Group 2 Proportion	0.5878	Interval Lower Limit	0.0467
Difference in Two Proportions	0.1303	Interval Upper Limit	0.2138
Average Proportion	0.6483
Z Test Statistic	3.0088
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0026
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.9987
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	0.0013
Reject the null hypothesis

COMPUTE_OLDER_FORMULAS

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0	of the Difference Between Two Proportions
Level of Significance	0.05
Group 1		Data
Number of Successes	163	Confidence Level	95%
Sample Size	227
Group 2		Intermediate Calculations
Number of Successes	154	Z Value	-1.9600
Sample Size	262	Std. Error of the Diff. Between Two Proportions	0.0426
		Interval Half Width	0.0835
Intermediate Calculations
Group 1 Proportion	0.7181	Confidence Interval
Group 2 Proportion	0.5878	Interval Lower Limit	0.0467
Difference in Two Proportions	0.1303	Interval Upper Limit	0.2138
Average Proportion	0.6483
Z Test Statistic	3.0088
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0026
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.6449
p-Value	0.9987
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.6449
p-Value	0.0013
Reject the null hypothesis