Explain how to perform a two-sample z-test for the difference between two population means using independent samples with and known.

A researcher is comparing average number of hours spelt per night by college students who work part-time versus those who don't. From survey data, they calculate ${\bar{x}}_1=6.82$ hours and $x_{\bar{2}}=6.57$ hours with a margin of error of 0.41. Should they reject or fail to reject the claim that there is no difference in hours slept between the two groups?

Randomization with Commute Times Given the two samples of commute times (minutes) shown here, which of the following are randomizations of them?

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a. Boston: 10 10 60. New York: 5 20 25 30 45.

b. Boston: 10 10 60 20 25. New York: 5 30 45.

c. Boston: 5 10 25 25 60. New York: 5 30 30 60.

d. Boston: 10 10 60. New York: 5 20 25 30 45.

e. Boston: 10 10 10 10 10. New York: 60 60 60.

Finding Critical Values Assume that we have two treatments (A and B) that produce quantitative results, and we have only two observations for treatment A and two observations for treatment B. We cannot use the Wilcoxon signed-ranks test given in this section because both sample sizes do not exceed 10.

a. Complete the accompanying table by listing the five rows corresponding to the other five possible outcomes, and enter the corresponding rank sums for treatment A.

Comparing Two Means Treating the data as samples from larger populations, test the claim that there is a significant difference between the mean of presidents and the mean of popes.

Describe another way you can perform a hypothesis test for the difference between the means of two populations using independent samples with and known that does not use rejection regions.

Independent and Dependent Samples In Exercises 5–8, classify the two samples as independent or dependent and justify your answer.

Sample 1: The commute times of 10 workers when they use their own vehicles

Sample 2: The commute times of the same 10 workers when they use public transportation

In Exercises 11–14, test the claim about the difference between two population means and at the level of significance . Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ1<μ2; α=0.05

Population statistics:σ1=75 and σ2=105

Sample Statistics: x̅1=2435, n1=35, x̅2=2432, n2=90

In Exercises 11–14, test the claim about the difference between two population means and at the level of significance . Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ1<μ2; α=0.03

Population statistics:σ1=136 and σ2=215

Sample Statistics: x̅1=5004, n1=144, x̅2=4895, n2=156