At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical population standard deviation = 185 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.
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)? ( , )
c. Use the confidence interval to conduct a hypothesis test. Using = .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)?