At Western University the historical mean of scholarship examination scores for freshman applications is 920. A historical population standard deviation s = 165 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.

a. State the hypotheses.

H0: µ
Ha: µ

b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean 935 (to the nearest whole number)?
(lower bound = , upper bound = )

c. Use the confidence interval to conduct a hypothesis test. Using a = .05, can the assistant dean conclude that the mean examination score for the new freshman applications has changed?

d. What is the p-value (to 3 decimals)?