The post-aesthesia care area (recovery room) at Centre Hospital was recently enlarged. The hope was that with the enlargement the mean number of patients per day would be more than 25. A random sample of 15 days revealed the following number of patients X : X 23 24 25 26 27 28 29 f 1 2 3 3 3 2 with EX = 390. (A) At the 0.05 significance level, examine that the mean number of patients per day is at most 24. State the necessary assumption(s). (7 marks) (B) Assume that the population mean shifts from 24 to 26.5. Estimate the sample size which is needed for the power of the test to be 0.9. (4 marks)