Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
9th Edition
ISBN: 9798214004020
Author: Jay L. Devore
Publisher: Cengage Learning US
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Chapter 15, Problem 33SE

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):

Chapter 15, Problem 33SE, The sign test is a very simple procedure for testing hypotheses about a population median assuming

We wish to test H0: μ ˜ = 25.0 versus Ha: μ ˜ > 25.0. The test statistic is Y = the number of observations that exceed 25.

  1. a. Determine the P-value of the test when Y = 15. [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 μ ˜ = 25.0?]
  2. b. For the given data, should H0 be rejected at significance level .05?

[Note: The test statistic is the number of differences Xi − 25 that have positive signs, hence the name sign test.]

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Chapter 15 Solutions

Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th

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