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Review Session: �Two-sample Hypothesis Testing Using MS Excel

Each slide has its own narration in an audio file. �For the explanation of any slide click on the audio icon to begin.

Professor Friedman's Statistics Course by H & L Friedman is licensed under a �Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

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Overview

In this review, we look at two-sample tests for the mean (μ) using MS Excel. In the next few slides we will see a few different two-sample hypothesis testing problems and how to interpret the output.

Two-Sample t tests Using MS Excel - Review Problems

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Problem 1�

Two-Sample t tests Using MS Excel - Review Problems

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What is the difference in means between the two groups?
Is the difference significant at α = .05?
How many degrees of freedom?
What is the calculated t-statistic?
What does .00057651 mean?

Critical Thinking Scores (0 to 10)-- Comparing Two Colleges
	Variable 1	Variable 2
	College A	College B
	0	10	t-Test: Two-Sample Assuming Equal Variances
	1	10
	1	9		Variable 1	Variable 2
	5	9	Mean	3.86666667	7.692307692
	3	7	Variance	7.55238095	5.564102564
	7	3	Observations	15	13
	9	5	Pooled Variance	6.634714
	3	8	Hypothesized Mean Difference	0
	2	7	df	26
	4	9	t Stat	-3.9195066
	8	9	P(T<=t) one-tail	0.00028825
	7	10	t Critical one-tail	1.70561792
	3	4	P(T<=t) two-tail	0.00057651
	2		t Critical two-tail	2.05552944
	3

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Problem 1�

Two-Sample t tests Using MS Excel - Review Problems

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Is the difference significant at α = .05? Yes

What does .00057651 mean? This is the probability of getting the sample evidence or worse given that the two groups are the same with regard to their means. P(sample evidence | H₀ is true)

Critical Thinking Scores (0 to 10)-- Comparing Two Colleges
	Variable 1	Variable 2
	College A	College B
	0	10	t-Test: Two-Sample Assuming Equal Variances
	1	10
	1	9		Variable 1	Variable 2
	5	9	Mean	3.86666667	7.692307692
	3	7	Variance	7.55238095	5.564102564
	7	3	Observations	15	13
	9	5	Pooled Variance	6.634714
	3	8	Hypothesized Mean Difference	0
	2	7	df	26
	4	9	t Stat	-3.9195066
	8	9	P(T<=t) one-tail	0.00028825
	7	10	t Critical one-tail	1.70561792
	3	4	P(T<=t) two-tail	0.00057651
	2		t Critical two-tail	2.05552944
	3

What is the difference in means between the two groups? 3.83

How many degrees of freedom? 15+13-2=26

What is the calculated t-statistic? -3.92

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Problem 2�

Two-Sample t tests Using MS Excel - Review Problems

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What is the difference in means between the two groups?
Is the difference significant at α = .05?
How many degrees of freedom?
What is the calculated t-statistic?
What does 0.37910519 mean?

Life of Computer Chip (Years) -- Comparing Two Companies
	Variable 1	Variable 2
	Company X	Company Z
	4.5	3.4	t-Test: Two-Sample Assuming Equal Variances
	4.7	3.9
	4.3	4.1		Variable 1	Variable 2
	3.8	4.2	Mean	4.55714286	4.80666667
	4.2	4.3	Variance	0.49186813	0.63066667
	5.1	4.4	Observations	14	15
	4.9	4.5	Pooled Variance	0.56383774
	6.1	4.7	Hypothesized Mean Difference	0
	4.9	6.1	df	27
	4.8	4.9	t Stat	-0.8942224
	4.1	5.6	P(T<=t) one-tail	0.18955259
	5.2	5.1	t Critical one-tail	1.70328845
	3.3	5.7	P(T<=t) two-tail	0.37910519
	3.9	5.9	t Critical two-tail	2.05183052
		5.3

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Problem 2�

Two-Sample t tests Using MS Excel - Review Problems

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What is the difference in means between the two groups? 0.25 years
Is the difference significant at α = .05? No
How many degrees of freedom? �14+15-2=27
What is the calculated t-statistic? -0.894
What does 0.37910519 mean? The probability of getting this difference in the means or worse (further apart) if H₀ is true. This probability is about .38 and considerably larger than .05.

Life of Computer Chip (Years) -- Comparing Two Companies
	Variable 1	Variable 2
	Company X	Company Z
	4.5	3.4	t-Test: Two-Sample Assuming Equal Variances
	4.7	3.9
	4.3	4.1		Variable 1	Variable 2
	3.8	4.2	Mean	4.55714286	4.80666667
	4.2	4.3	Variance	0.49186813	0.63066667
	5.1	4.4	Observations	14	15
	4.9	4.5	Pooled Variance	0.56383774
	6.1	4.7	Hypothesized Mean Difference	0
	4.9	6.1	df	27
	4.8	4.9	t Stat	-0.8942224
	4.1	5.6	P(T<=t) one-tail	0.18955259
	5.2	5.1	t Critical one-tail	1.70328845
	3.3	5.7	P(T<=t) two-tail	0.37910519
	3.9	5.9	t Critical two-tail	2.05183052
		5.3

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Problem 3�

Two-Sample t tests Using MS Excel - Review Problems

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Lifespan of Meth users vs. non-users (Years)

Users	Non-Users
44	77	t-Test: Two-Sample Assuming Equal Variances
32	73
39	61		Variable 1	Variable 2
68	79	Mean	47.2857143	69.4375
59	74	Variance	190.21978	249.7292
55	86	Observations	14	16
49	80	Pooled Variance	222.099809
61	58	Hypothesized Mean Difference	0
70	88	df	28
27	74	t Stat	-4.06160824
29	69	P(T<=t) one-tail	0.00017807
42	62	t Critical one-tail	1.70113093
40	44	P(T<=t) two-tail	0.00035615
47	28	t Critical two-tail	2.04840714
	81
	77

What is the difference in means between the two groups? 22.15 years
Is the difference significant at α = .05? Yes
How many degrees of freedom? 14+16-2=28
What is the calculated t-statistic? -4.06
What is the probability of getting this difference or larger, if the two groups really have the same longevity? Approx .0004

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Conclusion

This lecture was designed in part to help students review and get comfortable with the interpretation of two-sample t test problems done with MS Excel.

Remember, the best way to prepare for the exam is to do as many practice problems as you can possibly find.

Two-Sample t tests Using MS Excel - Review Problems

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