Unit 7 305 A

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DotScaleWS

Data
	0.975	Mean				Quartile Calculations
	0.975	0	0.95			Initial first quartile rank	0.25
	0.975	0	0.7				Rule 3 applies
	0.975	Median				use rank:	0	0
	0.975	0	0.95			value of rank:	0	0
	0.975	0	0.7			first quartile:	0
	0.975	1st Quartile				Initial third quartile rank	0.75
	0.975	0	0.95				Rule 3 applies
	0.975	0	0.7			use rank:	1	0
	0.975	3rd Quartile				value of rank:	0	0
	0.975	0	0.95			third quartile:	0
	0.975	0	0.7
	0.975	Std. Deviation
	0.975	0	0	0
	0.975	1 Std. Dev
	0.975	0	0.9
	0.975	0	0.9
		2 Std Dev.
		0	0.8
		0	0.8
		3 Std Dev
		0	0.7
		0	0.7
				Summary
				Mean	0.0000
				Median	0.0000
				1st Quartile	0.0000
				3rd Quartile	0.0000
				Std. Deviation	0.0000

DotScaleWS

0	0	0	0	0	0	0
0	0	0	0	0	0	0

Values

Mean

Median

1st Quartile

3rd Quartile

+/- 1 Std. Dev.

+/- 2 Std. Dev.

+/- 3 Std. Dev.

Dot Scale Diagram

CIPVWS

Confidence Interval Estimate for the Population Variance
Data
Sample Size	2
Sample Standard Deviation	1
Confidence Level	95%
Intermediate Calculations
Degrees of Freedom	1
Sum of Squares	1
Half Area	0.025
Lower Chi-Square Value	0.0009820691
Upper Chi-Square Value	5.0238864702
Results
Interval Lower Limit for Variance	0.20
Interval Upper Limit for Variance	1018.26
Interval Lower Limit for Standard Deviation	0.45
Interval Upper Limit for Standard Deviation	31.91
Assumptions:
Population from which sample was drawn has an approximate normal distribution.

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CSTVWS

Chi-Square Test of Hypothesis for the Variance
Data
Null Hypothesis s^2=	1
Level of Significance	0.05
Sample Size	10
Sample Standard Deviation	2
Intermediate Calculations
Degrees of Freedom	9
Half Area	0.025
Chi-Square Statistic	36
Two-Tail Test
Lower Critical Value	2.7003895222
Upper Critical Value	19.0227678027
p-Value	0.0000396466
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	3.3251128638
p-Value	0.9999603534
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	16.9189776161
p-Value	0.0000396466
Reject the null hypothesis

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CovarianceWS

Covariance Analysis
Probabilities & Outcomes:	P	X	Y
Weight Assigned to X	0.5
Statistics
E(X)	0			Calculations Area
E(Y)	0			For variance and standard deviation:				For covariance:
Variance(X)	0			X-mu	Y-mu	(X-mu)^2	(Y-mu)^2	(X-mu)(Y-mu)
Standard Deviation(X)	0			0	0	0	0	0
Variance(Y)	0			0	0	0	0	0
Standard Deviation(Y)	0
Covariance(XY)	0
Variance(X+Y)	0
Standard Deviation(X+Y)	0
Portfolio Management
Weight Assigned to X	0.5
Weight Assigned to Y	0.5
Portfolio Expected Return	0
Portfolio Risk	0

BESTWS

Best Subset Analysis
Intermediate Calculations
R2T
1 - R2T	1
n
T	5
n - T	-5
Model	Cp	k+1	R Square	Adj. R Square	Std. Error
X1	-1	2

RXChartWS

Control Charts
		Control Chart Factors Table.
Data		Subgroup size	D3	D4	A2
Sample/Subgroup Size	5	2	0	3.267	1.880
		3	0	2.575	1.023
R Chart Intermediate Calculations		4	0	2.282	0.729
RBar		5	0	2.114	0.577
D3 Factor	0	6	0	2.004	0.483
D4 Factor	2.114	7	0.076	1.924	0.419
		8	0.136	1.864	0.373
R Chart Control Limits		9	0.184	1.816	0.337
Lower Control Limit	0	10	0.223	1.777	0.308
Center	0	11	0.256	1.744	0.285
Upper Control Limit	0	12	0.283	1.717	0.266
		13	0.307	1.693	0.249
XBar Chart Intemediate Calculations		14	0.328	1.672	0.235
Average of Subgroup Averages		15	0.347	1.653	0.223
A2 Factor	0.577	16	0.363	1.637	0.212
A2 Factor * RBar	0	17	0.378	1.622	0.203
		18	0.391	1.609	0.194
XBar Chart Control Limits		19	0.404	1.596	0.187
Lower Control Limit	0	20	0.415	1.585	0.180
Center	0	21	0.425	1.575	0.173
Upper Control Limit	0	22	0.435	1.565	0.167
		23	0.443	1.557	0.162
		24	0.452	1.548	0.157
		25	0.459	1.541	0.153
		26	Factor value not available. Possible error in sample/subgroup size.	Factor value not available. Possible error in sample/subgroup size.	Factor value not available. Possible error in sample/subgroup size.
		Factor value not available. Possible error in sample/subgroup size.

pChartWS

p Chart Summary
Intermediate Calculations
Sum of Subgroup Sizes
Number of Subgroups Taken
Average Sample/Subgroup Size	0
Average Proportion of Nonconforming Items
Three Standard Deviations	0
Preliminary Lower Control Limit	0
p Chart Control Limits
Lower Control Limit	0
Center	0
Upper Control Limit	0

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cChartWS

c Chart Summary
Intermediate Calculations
Sum of Nonconformities	=SUM(cChartData!B:B)
Number of Units Sampled	=COUNT(cChartData!B:B)
Cbar	0
Preliminary Lower Control Limit	0.0000
c Chart Control Limits
Lower Control Limit	0.0000
Center	0.0000
Upper Control Limit	0.0000

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TSTTSVWS

Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	10
Sample Mean	50.3
Sample Standard Deviation	18.7264
Population 2 Sample
Sample Size	10
Sample Mean	72
Sample Standard Deviation	12.5433
Intermediate Calculations		Calculations Area
Numerator of Degrees of Freedom	2580.7663	Pop. 1 Sample Variance	350.6781
Denominator of Degrees of Freedom	164.1436	Pop. 2 Sample Variance	157.3344
Total Degrees of Freedom	15.7226	Pop. 1 Sample Var./Sample Size	35.0678
Degrees of Freedom	15	Pop. 2 Sample Var./Sample Size	15.7334
Separate Variance Denominator	7.1275	For one-tailed tests:
Difference in Sample Means	-21.7	TDIST value	0.0041
Separate-Variance t Test Statistic	-3.0445	1-TDIST value	0.9959
Two-Tail Test
Lower Critical Value	-2.1314
Upper Critical Value	2.1314
p-Value	0.0082
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7531
p-Value	0.0041
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.7531
p-Value	0.9959
Do not reject the null hypothesis

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TSTTWS

Pooled-Variance t Test for the Difference Between 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	1
Sample Standard Deviation	1	Intermediate Calculations
Population 2 Sample		Degrees of Freedom	18
Sample Size	10	t Value	2.1009220369
Sample Mean	2	Interval Half Width	1.485576219
Sample Standard Deviation	2
		Confidence Interval
Intermediate Calculations		Interval Lower Limit	-2.485576219
Population 1 Sample Degrees of Freedom	9	Interval Upper Limit	0.485576219
Population 2 Sample Degrees of Freedom	9
Total Degrees of Freedom	18
Pooled Variance	2.5
Difference in Sample Means	-1
t Test Statistic	-1.4142135624
Two-Tail Test
Lower Critical Value	-2.1009220369
Upper Critical Value	2.1009220369
p-Value	0.1743634883
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.7340635923	Calculations Area
p-Value	0.0871817442	For one-tailed tests:
Do not reject the null hypothesis		TDIST value	0.0871817442
		1-TDIST value	0.9128182558
Upper-Tail Test
Upper Critical Value	1.7340635923
p-Value	0.9128182558
Do not reject the null hypothesis

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TSZTPWS

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 Items of Interest	1	Confidence Level	95%
Sample Size	10
Group 2		Intermediate Calculations
Number of Items of Interest	2	Z Value	-1.9599639845
Sample Size	20	Std. Error of the Diff. between two Proportions	0.1161895004
		Interval Half Width	0.2277272361
Intermediate Calculations
Group 1 Proportion	0.1	Confidence Interval
Group 2 Proportion	0.1	Interval Lower Limit	-0.2277272361
Difference in Two Proportions	0	Interval Upper Limit	0.2277272361
Average Proportion	0.1
Z Test Statistic	0
Two-Tail Test
Lower Critical Value	-1.9599639845
Upper Critical Value	1.9599639845
p-Value	1
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.644853627
p-Value	0.5
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.644853627
p-Value	0.5
Do not reject the null hypothesis

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TSFTWS

F Test for Differences in Two Variances
Data
Level of Significance	0.05
Larger-Variance Sample
Sample Size	10
Sample Standard Deviation	1
Smaller-Variance Sample
Sample Size	10
Sample Standard Deviation	1
Intermediate Calculations
F Test Statistic	1
Population 1 Sample Degrees of Freedom	9
Population 2 Sample Degrees of Freedom	9
		Calculations Area
Two-Tail Test		FDIST value	0.5
Upper Critical Value	4.0259941583
p-Value	1
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	3.1788931046
p-Value	0.5
Do not reject the null hypothesis
0
0

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WilcoxonWS

Wilcoxon Rank Sum Test for Differences in Two Medians
Data
Level of Significance	0.05
Population 1 Sample
Sample Size	1
Sum of Ranks	1
Population 2 Sample
Sample Size	1
Sum of Ranks	1
Intermediate Calculations
Total Sample Size n	2
T1 Test Statistic	1
T1 Mean	1.5
Standard Error of T1	0.5
Z Test Statistic	-1
Two-Tail Test
Lower Critical Value	-1.9599639845
Upper Critical Value	1.9599639845
p-Value	0.3173105079
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.644853627
p-Value	0.1586552539
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.644853627
p-Value	0.8413447461
Do not reject the null hypothesis

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ZTPWS

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis p =	0.1
Level of Significance	0.05
Number of Items of Interest	11
Sample Size	200
Intermediate Calculations
Sample Proportion	0.055
Standard Error	0.0212132034
Z Test Statistic	-2.1213203436
Two-Tail Test
Lower Critical Value	-1.9599639845
Upper Critical Value	1.9599639845
p-Value	0.0338948535
Reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.644853627
p-Value	0.0169474268
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.644853627
p-Value	0.9830525732
Do not reject the null hypothesis

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TTMeanWS

t Test for the Hypothesis of the Mean
Data
Null Hypothesis m=	120
Level of Significance	0.05
Sample Size	2
Sample Mean	1
Sample Standard Deviation	1
Intermediate Calculations
Standard Error of the Mean	0.7071067812
Degrees of Freedom	1
t Test Statistic	-168.2914139224
Two-Tail Test
Lower Critical Value	-12.706204734
Upper Critical Value	12.706204734
p-Value	0.0037827971
Reject the null hypothesis
		Calculations Area
Lower-Tail Test		For one-tailed tests:
Lower Critical Value	-6.3137515136	TDIST value	0.0018913986
p-Value	0.0018913986	1-TDIST value	0.9981086014
Reject the null hypothesis
Upper-Tail Test
Upper Critical Value	6.3137515136
p-Value	0.9981086014
Do not reject the null hypothesis

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ZTMeanWS

Z Test of the Hypothesis for the Mean
Data
Null Hypothesis m=	1
Level of Significance	0.05
Population Standard Deviation	2
Sample Size	10
Sample Mean	1
Intermediate Calculations
Standard Error of the Mean	0.632455532
Z Test Statistic	0
Two-Tail Test
Lower Critical Value	-1.9599639845
Upper Critical Value	1.9599639845
p-Value	1
Do not reject the null hypothesis
Lower-Tail Test
Lower Critical Value	-1.644853627
p-Value	0.5
Do not reject the null hypothesis
Upper-Tail Test
Upper Critical Value	1.644853627
p-Value	0.5
Do not reject the null hypothesis

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CITDWS

Confidence Interval Estimate for the Total Difference
Data
Population Size	5000
Sample Size	100
Confidence Level	95%
Intermediate Calculations
Sum of Differences	=SUM(Data!A:A)	Calculations Area
Average Difference in Sample	0	For standard deviation of differences:
Total Difference	0	Number of Differences Not = 0	=COUNT(Data!A:A)
Standard Deviation of Differences	0	Number of Differences = 0	0
FPC Factor	0.9900485035	SS for Differences Not = 0	=SUM(Data!B:B)
Standard Error of the Total Diff.	0	SS for Differences = 0	0
Degrees of Freedom	99	Sum of Squares	0
t Value	1.9842169002	Variance of Differences	0
Interval Half Width	0
Confidence Interval
Interval Lower Limit	0.00
Interval Upper Limit	0.00

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CIPTWS

Confidence Interval Estimate for the Population Total
Data
Population Size	5000
Sample Mean	100
Sample Size	100
Sample Standard Deviation	20
Confidence Level	95%
Intermediate Calculations
Population Total	500000.00
FPC Factor	0.9900485035
Standard Error of the Total	9900.4850346225
Degrees of Freedom	99
t Value	1.9842169002
Interval Half Width	19644.71
Confidence Interval
Interval Lower Limit	480355.29
Interval Upper Limit	519644.71

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SSPWS

Sample Size for Estimating the Proportion
Data
Estimate of True Proportion	0.15
Sampling Error	0.07
Confidence Level	95%
Intermediate Calculations
Z Value	-1.9599639845
Calculated Sample Size	99.9563264568
Result
Sample Size Needed	100
Finite Populations
Population Size	5,000
Calculated Sample Size	98.0164567582
Sample Size Needed	99

SSMWS

Sample Size for Estimating the Mean
Data
Population Standard Deviation	25
Sampling Error	5
Confidence Level	95%
Intemediate Calculations
Z Value	-1.9599639845
Calculated Sample Size	96.0364705174
Result
Sample Size Needed	97
Finite Populations
Population Size	5000
Sample Size with FPC	94.2451256954
Sample Size Needed	95

CIPWS

Confidence Interval Estimation for the Proportion
Data
Sample Size	100
Number of Successes	10
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.1
Z Value	-1.9599639845
Standard Error of the Proportion	0.03
Interval Half Width	0.0587989195
Confidence Interval
Interval Lower Limit	0.0412010805
Interval Upper Limit	0.1587989195
Finite Populations
Population Size	5000
FPC Factor	0.9900485035
Interval Half Width	0.0582137823
Interval Lower Limit	0.0417862177
Interval Upper Limit	0.1582137823

CIMSUWS

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	20
Sample Mean	10
Sample Size	100
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	2
Degrees of Freedom	99
t Value	1.9842169002
Interval Half Width	3.9684338004
Confidence Interval
Interval Lower Limit	6.03
Interval Upper Limit	13.97
Finite Populations
Population Size	5000
FPC Factor	0.9900485035
Interval Half Width	3.9289419452
Interval Lower Limit	6.07
Interval Upper Limit	13.93

CIMSKWS

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	0.02
Sample Mean	10
Sample Size	100
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.002
Z Value	-1.9599639845
Interval Half Width	0.003919928
Confidence Interval
Interval Lower Limit	9.996080072
Interval Upper Limit	10.003919928
Finite Populations
Population Size	10000
FPC Factor	0.9950371902
Interval Half Width	0.0039004741
Interval Lower Limit	9.9960995259
Interval Upper Limit	10.0039004741

ExponentialWS

Exponential Probability
Data
Mean	20
X Value	0.1
Results
P(<=X)	0.8647

NormalWS

Normal Probabilities
Common Data
Mean	75
Standard Deviation	6
		Probability for a Range
Probability for X <=		From X Value	69
X Value		To X Value	81
Z Value	-12.5	Z Value for 69	-1
P(X<=)	3.73256429887771E-36	Z Value for 81	1
		P(X<=69)	0.1587
Probability for X >		P(X<=81)	0.8413
X Value		P(69<=X<=81)	0.6827
Z Value	-12.5
P(X>)	1.0000	Find X and Z Given Cum. Pctage.
		Cumulative Percentage	10.00%
Probability for X< or X >		Z Value	-1.2815515655
P(X< or X >)	1.0000	X Value	67.3106906067

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HypergeoWS

Hypergeometric Probabilities
Data
Sample size	1
No. of events of interest in population	1
Population size	2
Hypergeometric Probabilities Table
	X	P(X)
	0	0.5
	1	0.5

PoissonWS

Poisson Probabilities
Data
Mean/Expected number of events of interest:				3
Poisson Probabilities Table
	X	P(X)	P(<=X)	P(<X)	P(>X)	P(>=X)
	0	0.049787	0.049787	0.000000	0.950213	1.000000
	1	0.149361	0.199148	0.049787	0.800852	0.950213
	2	0.224042	0.423190	0.199148	0.576810	0.800852
	3	0.224042	0.647232	0.423190	0.352768	0.576810
	4	0.168031	0.815263	0.647232	0.184737	0.352768
	5	0.100819	0.916082	0.815263	0.083918	0.184737
	6	0.050409	0.966491	0.916082	0.033509	0.083918
	7	0.021604	0.988095	0.966491	0.011905	0.033509
	8	0.008102	0.996197	0.988095	0.003803	0.011905
	9	0.002701	0.998898	0.996197	0.001102	0.003803
	10	0.000810	0.999708	0.998898	0.000292	0.001102
	11	0.000221	0.999929	0.999708	0.000071	0.000292
	12	0.000055	0.999984	0.999929	0.000016	0.000071
	13	0.000013	0.999997	0.999984	0.000003	0.000016
	14	0.000003	0.999999	0.999997	0.000001	0.000003
	15	0.000001	1.000000	0.999999	0.000000	0.000001
	16	0.000000	1.000000	1.000000	0.000000	0.000000
	17	0.000000	1.000000	1.000000	0.000000	0.000000
	18	0.000000	1.000000	1.000000	0.000000	0.000000
	19	0.000000	1.000000	1.000000	0.000000	0.000000
	20	0.000000	1.000000	1.000000	0.000000	0.000000

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BinomialWS

Binomial Probabilities
Data
Sample size	4
Probability of an event of interest	1
Statistics
Mean	4
Variance	0
Standard deviation	0
Binomial Probabilities Table
	X	P(X)	P(<=X)	P(<X)	P(>X)	P(>=X)
	0	0	0	0	1	1

Basic Probabilities

Probabilities Calculations
Sample Space		Event B
		B1	B2	Totals
Event A	A1	1	1	2
	A2	1	1	2
	Totals	2	2	4
Simple Probabilities
P(A1)	0.50
P(A2)	0.50
P(B1)	0.50
P(B2)	0.50
Joint Probabilities
P(A1 and B1)	0.25
P(A1 and B2)	0.25
P(A2 and B1)	0.25
P(A2 and B2)	0.25
Addition Rule
P(A1 or B1)	0.75
P(A1 or B2)	0.75
P(A2 or B1)	0.75
P(A2 or B2)	0.75

PHStat2 Note: Enter the labels and values for both events in cells A5, C3, and the cell ranges B5:B6, C4:C5, and C5:D6. Enter replacement labels for A1, A2, B1, and B2, in cell ranges B5:B6 and C4:D4, if desired. (Before continuing, press the Delete key to delete this note.)