Refer to Exercise 33, and consider a confidence interval associated with the sign test:...

Refer to Exercise 33, and consider a confidence interval associated with the sign test: the sign interval. The relevant hypotheses are now Let’s use the following rejection region: either Y ≥15 or Y ≥ 5.

a. What is the significance level for this test?

b. The confidence interval will consist of all values for which H0 is not rejected. Determine the CI for the given data, and state the confidence level.

Reference to Exercise 33

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 X_i – 25 that have positive signs, hence the name sign test.]