When X 1 , X 2 , brvbar , X n is a random sample from a normal distribution and n is large, the sample standard deviation has approximately a normal distribution with mean Iuml and variance Iuml 2 (2n) Therefore, a large sample test for H 0 Iuml Iuml 0 can be based on the statistic (a) Use this res...

a 1 The parameter of interest is the true standard deviation of the golf ball distance 2 H ...

When X 1 , X 2 , ¦, X n is a random sample from a normal

Question:

When X₁, X₂, €¦, X_nis a random sample from a normal and n is large, the sample standard deviation has approximately a normal with mean Ïƒ and variance Ïƒ²(2n). Therefore, a large-sample test for H₀: Ïƒ = Ïƒ₀can 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 Î¸ = Î¼ + 1.645Ïƒ. From the fact that X and S are independent random variables, find the standard error of the estimator of Î¸. 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?

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...

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