At Western University the historical mean of scholarship examination score for

freshman applications is 1000. Population standard deviation is known to be 200. 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 sample of 100 applications provided

a mean of 1050.

a) State the hypotheses to test 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?

c) Use the 95% confidence interval to conduct a hypothesis test. What is your conclusion?

d) Assuming = .05, conduct p-value based hypothesis test. What is the conclusion?

e) Assuming = .05 conduct a critical-value based hypothesis tests. What is the conclusion?

f) How do the results compare in all the three cases?