Two simple random samples of NFL players are taken. The first sample is drawn from cornerbacks, with the following summary statistics: sample size is 267, sample mean is 71.44 inches, sample standard deviation is 1.556 inches. The second sample is drawn from quarterbacks, with the following summary statistics: sample size is 112, sample mean is 70.69 inches, sample standard deviation is 1.773 inches. The samples can be assumed to be independent.

(a)Discuss whether the requirements to construct a CI estimate of the difference in the mean heights is fulfilled.

(b)Test the claim that cornerbacks have a greater mean height than quarterbacks at the 0.05 significance level. Make sure to state the null and alternative hypotheses, the P-Value, and write final conclusion carefully.

(c)Construct a 90% confidence interval estimate of the difference between quarterback and cornerback heights. Discuss how this confirms or contradicts the results of (b).

(d)Is it true that 90% of all differences between quarterback and cornerback heights will fall in the CI estimate in (c)? Explain why or why not.