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Chapter 8: Q. 9.126 (page 391)

Suppose that you want to perform a hypothesis test for a population mean. Assume that the variable under consideration is normally distributed and that the population deviation standard is unknown.

(a). Is it permissible to use t-test to perform hypothesis test? Explain your answer.

(b). Is it permissible to use the Wilcoxon signed-rank test to perform hypothesis test? Explain your answer.

(c). Which procedure is better to use, thet-test or Wilcoxon signed-test? Explain your answer.

Short Answer

Expert verified

a). t-test

b). Wilcoxon signed-rank test

c). t-test.

Step by step solution

01

Step 1. Solution (a).

Yes t-test can be used to perform the hypothesis test because all the assumptions of t-test are satisfied in this case.

02

Step 2. Solution (b).

Yes, Wilcoxon signed rank test can be used to perform the hypothesis test because the variable under consideration is normally distributed and normal distribution is symmetric.

03

Step 3. Solution (c).

Here one mean t-test is preferable because for a normally distributed variablet-test is more powerful than the Wilcoxon signed rank test.

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