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1.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?