At western university the historical mean of scholarship examination scores for freshman applications is 900. a historical population standard deviation s = 175 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 =greater than or equal to 900, greater than 900, less than 900, etc?
ha: µ =greater than or equal to 900, greater than 900, less than 900, etc?

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 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)?