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Chapter 10: Q. 10.68 (page 418)

Suppose that you want to perform a hypothesis test to compare the means of two populations, using independent simple random samples. Assume that the two distributions of the variable under consideration have the same shape, but are not normal, and both sample sizes are large. Answer the following questions and explain your answers.

a. Is it permissible to use the pooled t-test to perform the hypothesis test?

b. Is it permissible to use the Mann-Whitney test to perform the hypothesis test?

c. Which procedure is preferable, the pooledt-test or the Mann-Whitney test?

Short Answer

Expert verified

Part a: Yes, it is permissible to use the pooled t-test to perform the hypothesis test.

Part b: Yes, it is permissible to use the Mann-Whitney test to perform the hypothesis test.

Part c: The pooled t-test should be preferable.

Step by step solution

01

Part a: Step 1. Given information

Assume that the two distributions of the variable under consideration have the same shape, but are not normal, and both sample sizes are large.

02

Part a Step 2. Assumption for the pooled t-test is given below:

  • The selected sample should be a simple random sample from two populations.
  • The samples are independent of one another.
  • Population is approximately normal.
  • Equal population standard deviations.

So, it is permissible to use the pooledt-test to perform the hypothesis test because the given information satisfied the assumptions of the pooledt-test.

03

Part b Step 1. Explanation for the answer:

Yes, it is permissible to use the Mann-Whitney test to perform the hypothesis test because the two distributions of the variable under the consideration have the same shape but it is not normal.

04

Part c Step 1. Explanation for the answer:

Here, the pooled t-test procedure should be preferable because the pooledt-test provide more accurate results than the Mann-Whitney test.

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Most popular questions from this chapter

In this Exercise, we have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t-test and the pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.

x炉1=20,s1=4,n1=10,x炉2=23,s2=5,n2=15

a. Left-tailed test,伪=0.05

b. 90%confidence interval

Suppose that you want to perform a hypothesis test to compare the means of two populations, using independent simple random samples. Assume that the two distributions (one for each population) of the variable under consideration are normally distributed and have equal standard deviations. Answer the following questions and explain your answers.

a. Is it permissible to use the pooled t-test to perform the hypothesis test?

b. Is it permissible to use the Mann-Whitney test to perform the hypothesis test?

c. Which procedure is preferable, the pooled t-test or the Mann-Whitney test?

In each of Exercises 10.35-10.38, we have provided summary statistics for independent simple random samples from two populations. Preliminary data analyses indicate that the variable under consideration is normally distributed on each population. Decide, in each case, whether use of the pooled t-test and pooled t-interval procedure is reasonable. Explain your answer.

10.38 x1=39.04,s1=18.82,n1=51

x2=49.92,s2=18.97,n2=53

In Exercise 10.83, you conducted a nonpooled t-test to decide whether the mean number of acute postoperative days spent in the hospital is smaller with the dynamic system than with the static system. Use the technology of your choice to perform the following tasks.

a. Using a pooledt-test, repeat that hypothesis test.

b. Compare your results from the pooled and nonpooled t-tests.

c. Which test do you think is more appropriate, the pooled or nonpooled t-test? Explain your answer.

Define the phrase independent samples.
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