Subject: Mathematics / Statistics
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?