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: μ̃ = 25.0 versus Ha: μ̃ > 25.0. The test statistic is Y = the number of observations that exceed 25.
a. Determine the P-value of the test when Y = 15. [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 μ̃ = 25.0?]
b. For the given data, should H0 be rejected at significance level .05? [The test statistic is the number of differences Xi - 25 that have positive signs, hence the name sign test.]

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