who really know about statistics

T-test 1

MEGASTATS Hypothesis Test: Independent Groups (t-test, pooled variance)							Megastat
Two different prototype turbo engines are tested. Nautical miles flown before reserve are recorded.							Hypothesis Tests
Is there a difference?							Compare Two Independent Groups
Ho: μ1 = μ2 H1: μ1 ≠ μ2 α = .01							Highlight Data
TYPE A	TYPE B					Descriptive statistics
4230	4110
4220	4090						TYPE A	TYPE B
4100	4070					count	10	10
4300	4160					mean	4,230.00	4,135.00
4420	4230					sample variance	11,400.00	5,183.33
4110	4120					sample standard deviation	106.77	72.00
4230	4000					minimum	4090.0	4000.0
4280	4200					maximum	4420.0	4230.0
4090	4150					range	330.0	230.0
4320	4220
						standard error of the mean	33.76	22.77
Hypothesis Test: Independent Groups (t-test, pooled variance)						confidence interval 95.% lower	4,153.62	4,083.50
						confidence interval 95.% upper	4,306.38	4,186.50
	TYPE A	TYPE B				half-width	76.38	51.50
	4,230.00	4,135.00	mean
	106.77	72.00	std. dev.			skewness	0.16	-0.40
	10	10	n			kurtosis	-0.52	-0.22
						coefficient of variation (CV)	2.52%	1.74%
		18	df
		95.000	difference (TYPE A - TYPE B)			normal curve GOF
		8,291.667	pooled variance			p-value	.5271	.5271
		91.059	pooled std. dev.			chi-square(df=1)	0.40	0.40
		40.723	standard error of difference			E	2.50	2.50
		0	hypothesized difference			O(-0.67)	3	2
						O(+0.00)	3	3
		2.33	t			O(+0.67)	2	2
		.0315	p-value (two-tailed)			O(inf.)	2	3
RETAIN. There is no significant difference. P=.03 which is larger than .01.
The bright yellow indicates Reject at the .01 level.
Dull yellow indicates Reject at the .05 alpha level / Retain at the .01 alpha level.
Black & white indicates Retain. There is no difference.

Runs Plot

4230 4220 4100 4300 4420 4110 4230 4280 4090 4320

Time

TYPE A

Runs Plot

4110 4090 4070 4160 4230 4120 4000 4200 4150 4220

Time

TYPE B

T-test 2

Megastat T-Test Compare Two Independent Groups
Compairing heating costs of all electric homes and all gas homes. Eight similar homes in January							Megastat
Is there a significant difference?							Hypothesis Tests
Ho: μ1= μ2 H1: μ1 ≠ μ2 α = .05				Descriptive statistics			Mean vs Hypothesized Value
Electric	Gas						Highlight Data
265	260				Electric	Gas
271	270			count	8	8
260	250			mean	261.63	260.00
250	255			sample variance	111.70	78.57
248	250			sample standard deviation	10.57	8.86
280	275			minimum	248.0	250.0
257	260			maximum	280.0	275.0
262	260			range	32.0	25.0
				sum	2,093.00	2,080.00
Megastat T-Test Compare Two Independent Groups				sum of squares	548,363.00	541,350.00
Electric	Gas			deviation sum of squares (SSX)	781.88	550.00
261.63	260.00	mean
10.57	8.86	std. dev.		standard error of the mean	3.74	3.13
8	8	n
				confidence interval 95.% lower	252.79	252.59
	14	df		confidence interval 95.% upper	270.46	267.41
	1.625	difference (Electric - Gas)		half-width	8.84	7.41
	95.134	pooled variance
	9.754	pooled std. dev.		skewness	0.46	0.62
	4.877	standard error of difference		kurtosis	-0.09	-0.39
	0	hypothesized difference		coefficient of variation (CV)	4.04%	3.41%
	0.33	t		normal curve GOF
RETAIN	.7439	p-value (two-tailed)		p-value	1.0000	.0455
				chi-square(df=1)	0.00	4.00
				E	2.00	2.00
				O(-0.67)	2	2
				O(+0.00)	2	4
RETAIN. There is no difference in heating costs.				O(+0.67)	2	0
Retain the Null. P=.74 is larger that the Alpha of .05.				O(inf.)	2	2
There is no difference in heating costs
The bright yellow indicates Reject at the .01 level.
Dull yellow indicates Reject at the .05 alpha level / Retain at the .01 alpha level.
Black & white indicates Retain. There is no difference.

Runs Plot

265 271 260 250 248 280 257 262

Time

Electric

Runs Plot

260 270 250 255 250 275 260 260

Time

Gas

T-test 3

MEGASTATS Hypothesis Test: Independent Groups (t-test, pooled variance)							Megastat
Sales in two different geographic zones.							Hypothesis Tests
Is there a difference?							Compare Two Independent Groups
Ho: μ1 = μ2 H1: μ1 ≠ μ2 α = .05							Highlight Data
						Descriptive statistics
ZONE 1	ZONE 2
101	367						# 1	# 2
233	1000					count	12	12
251	578					mean	399.50	716.00
232	492					sample variance	36,143.00	57,075.45
211	1200					sample standard deviation	190.11	238.90
388	955					minimum	101.0	367.0
450	511					maximum	672.0	1200.0
566	603					range	571.0	833.0
532	722
514	699					standard error of the mean	54.88	68.97
672	665
644	800					confidence interval 95.% lower	278.71	564.21
						confidence interval 95.% upper	520.29	867.79
						half-width	120.79	151.79
Hypothesis Test: Independent Groups (t-test, pooled variance)
						normal curve GOF
	Group 1	Group 2				p-value	.2231	.5134
	399.50	716.00	mean			chi-square(df=2)	3.00	1.33
	190.11	238.90	std. dev.			E	2.40	2.40
	12	12	n			O(-0.84)	4	3
						O(-0.25)	1	2
		22	df			O(+0.25)	1	3
		-316.500	difference (Group 1 - Group 2)			O(+0.84)	3	1
		46,609.227	pooled variance			O(inf.)	3	3
		215.892	pooled std. dev.
		88.137	standard error of difference
		0	hypothesized difference
		-3.59	t
		.0016	p-value (two-tailed)
REJECT. There is a significant difference. P=.001 which is smaller than .05.
The bright yellow indicates Reject at the .01 level.
Dull yellow indicates Reject at the .05 alpha level / Retain at the .01 alpha level.
Black & white indicates Retain. There is no difference.

Runs Plot

101 233 251 232 211 388 450 566 532 514 672 644

Time

# 1

Runs Plot

367 1000 578 492 1200 955 511 603 722 699 665 800

Time

# 2