Suppose that X1, X2,..., Xn are i. i.d, N(μ, δ²) and μ and δ² are estimated by the method of maximum likelihood, with resulting estimates μ_hat and δ²_hat. Suppose the bootstrap is used to estimate the sampling distribution of μ_hat.

a. Explain why the boostrap estimate of the distribution of μ_hat is N(μ_hat, δ²_hat/n)

b. Explain why the bootstrap estimate of the distribution of μ_hat -μ is N(0, δ²_hat/n)

c. According to the result of the previous part, what is the form of the boostrap confidence interval for μ , and how does it compare to the exact confidence interval based on the t distribution?

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: minus2.00, minus1.00, 0, 1.00, 2.00? why? a. the z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores. b. the z score of 0 is most preferable because it corresponds to a test score equal to the mean. c. the z score of minus2.00 is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores. d. the z score of minus1.00 is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average