. Power in Tests on Means To test H0: m = 50 versus H1: m 6 50 a simple random sample of

Chapter 10, Problem 19

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. Power in Tests on Means To test H0: m = 50 versus H1: m 6 50 a simple random sample of size n = 24 is obtained from a population that is known to be normally distributed, and the sample standard deviation is found to be 6. (a) A researcher decides to test the hypothesis at the a = 0.05 level of significance. Determine the sample mean that separates the rejection region from the nonrejection region. [Hint: Follow the same approach as that laid out in the summary on page 518, but use Students t-distribution to find the critical value.] (b) Suppose the true population mean is m = 48.9. Use technology to find the area under the t-distribution to the right of the sample mean found in part (a) assuming m = 48.9. [Hint: This can be accomplished by performing a onesample t-test.] This represents the probability of making a Type II error, b. What is the power of the test?