When X1, X2, p , Xn is a random sample from a normal distribution and n is large, the
Chapter 9, Problem 9-152(choose chapter or problem)
When X1, X2, p , Xn is a random sample from a normal distribution and n is large, the sample standard deviation has approximately a normal distribution with mean and variance . Therefore, a large-sample test for H0: 0 can be based on the statistic (a) Use this result to test H0: 10 versus H1: 10 for the golf ball overall distance data in Exercise 6-33. (b) Find an approximately unbiased estimator of the 95 percentile 1.645 . From the fact that and S are independent random variables, find the standard error of the estimator of . How would you estimate the standard error? (c) Consider the golf ball overall distance data in Exercise 6-33. We wish to investigate a claim that Xthe 95 percentile of overall distance does not exceed 285 yards. Construct a test statistic that can be used for testing the appropriate hypotheses. Apply this procedure to the data from Exercise 6-33. What are your conclusions?
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