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 . The test statistic is Y = the number of observations that exceed 25.
a. Consider rejecting H0 if Y ≥ 15. What is the value of a (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 ?
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.]
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