The sign test is a very simple procedure for testinghypotheses about a population median

Chapter 15, Problem 33

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The sign test is a very simple procedure for testinghypotheses about a population median assuming onlythat the underlying distribution is continuous. To illustrate,consider the following sample of 20 observationson component lifetime (hr): 1.7 3.3 5.1 6.9 12.6 14.4 16.4 24.6 26.0 26.5 32.1 37.4 40.1 40.5 41.5 72.4 80.1 86.4 87.5 100.2We wish to test H0: m, 5 25.0 versus Ha: m, . 25.0. Thetest statistic is Y 5 the number of observations thatexceed 25.a. Determine the P-value of the test when Y 5 15.[Hint: Think of a success as a lifetime that exceeds25.0. Then Y is the number of successes in the sample.What kind of a distribution does Y have whenm, 5 25.0?]b. For the given data, should H0 be rejected at significancelevel .05?[Note: The test statistic is the number of differencesXi 2 25 that have positive signs, hence the name signtest.]