47. At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical population standard deviation σ  180 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.

b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean of  935?

c. Use the confidence interval to conduct a hypothesis test. Using α  .05, what is your conclusion?

d. What is the p-value?