You are designing a quality control system for the waiting time to see a doctor in the emergency room for the TMC. (Toledo Medical Center). You are taking samples of size n on the hour every hour, measure the average time for the “most” recent n patients and use it to calculate the average. As per the null hypothesis, the population average is <= 40 minutes. Alpha value is 0.02. If the population mean has shifted to 46 minutes, it is no longer acceptable and we would like to detect it with a probability of 0.97 (beta is 0.03). Population s.d. is 9 minutes
What should be the sample size to do this?
What will be the critical value?