When X₁, X₂, €¦, X_nis a random sample from a normal distribution and n is large, the sample standard deviation has approximately a normal distribution with mean σ and variance σ²(2n). Therefore, a large-sample test for H₀: σ = σ₀can be based on the statistic

(a) Use this result to test H₀: s = 10 versus H₁: s,10 for the golf ball overall distance data in Exercise 6-41.

(b) Find an approximately unbiased estimator of the 95th percentile θ = μ + 1.645σ. From the fact that X and S are independent random variables, find the standard error of the estimator of θ. How would you estimate the standard error?

(c) Consider the golf ball overall distance data in Exercise 6-41. We wish to investigate a claim that the 95th 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 6-41. What are your conclusions?

Z= Vi (2n)