At Western University the historical mean of scholarship examination scores for freshmen applications is 900. A historical population standard deviation of 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 has changed.

1. 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?

2. Conduct a hypothesis test. Using alpha = .05, what is your conclusion?

3. What is the p-value?

4. Now assume that you don't know the population standard deviation, but calculated a sample standard deviation of 180. What is your conclusion for a hypothesis test using alpha = .05?

910.05 - 959.95, Reject Ho, .006, Fail to Reject Ho

910.05 - 959.95, Fail to Reject Ho, .006, Fail to Reject Ho

910.05 - 959.95, Reject Ho, .006, Reject Ho

875.05 - 924.95, Reject Ho, .006, Reject Ho

910.05 - 959.95, Reject Ho, .05, Reject Ho