Answer: The sign test is a very simple procedure for

Chapter 15, Problem 15.33

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The sign test is a very simple procedure for testing hypotheses about a population median assuming only that the underlying distribution is continuous. To illustrate, consider the following sample of 20 observations on component lifetime (hr): We wish to test H0: ~ 25.0 versus Ha: ~ 25.0. The test statistic is Y the number of observations that exceed 25. a. Consider rejecting H0 if Y 15. What is the value of (the probability of a type I error) for this test? [Hint: Think of a success as a lifetime that exceeds 25.0. Then Y is the number of successes in the sample.] What kind of a distribution does Y have when ~ 25.0? b. What rejection region of the form Y c specifies a test with a significance level as close to .05 as possible? Use this region to carry out the test for the given data. [Note: The test statistic is the number of differences Xi 25 that have positive signs, hence the name sign test.] 34