10. Hypothesis Testing for Two Samples

"In Exercises 9–12, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.05,d.f.N=6,d.f.D=50"

Which statement about the $F$-distribution is always true?

"In Exercises 9–12, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.01,d.f.N=12,d.f.D=10"

List five properties of the F-distribution.

Explain how to determine the values of d.f.N and d.f.D when performing a two-sample F-test.

"In Exercises 17–20, (a) identify the claim and state H₀ and Hₐ, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.

A travel consultant claims that the standard deviations of hotel room rates for Sacramento, CA, and San Francisco, CA, are the same. A sample of 36 hotel room rates in Sacramento has a standard deviation of \$51 and a sample of 31 hotel room rates in San Francisco has a standard deviation of \$37. At α=0.10, can you reject the travel consultant’s claim? (Adapted from Expedia)"

In Exercises 13–18, test the claim about the difference between two population variances σ₁² and σ₂² at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: σ₁² > σ₂²; α = 0.05.

Sample statistics: s₁² = 44.6, n₁ = 16 and s₂² = 39.3, n₂ = 12

In Exercises 13–18, test the claim about the difference between two population variances σ₁² and σ₂² at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: σ₁² ≤ σ₂²; α = 0.01.

Sample statistics: s₁² = 842, n₁ = 11 and s₂² = 836, n₂ = 10

Two machines produce metal rods. You take independent random samples of their lengths (shown below) as part of a hypothesis test. Calculate the F statistic for this test.

Sample A: $s^2=2.1,n=10$

Sample B: $s^2=4.2,n=12$

"In Exercises 9–12, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.10,d.f.N=5,d.f.D=12"

List the three conditions that must be met in order to use a two-sample F-test.

In Exercises 13–16, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.01,d.f.N=40,d.f.D=60

F Test Statistic

c. If testing the claim that sigma2,1 is not equals to sigma2,2 what do we know about the two samples if the test statistic F is very close to 1?

Color and Creativity Researchers from the University of British Columbia conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given below. Use a 0.05 significance level to test the claim that creative task scores have the same variation with a red background and a blue background.

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