An administrator in a hospital emergency room ER suspects th

An administrator in a hospital emergency room (ER) suspects that the average amount of time patients have to wait to see a doctor has increased from the previous year. Last year, the average wait time was 129 minutes, with a corresponding standard deviation of 40 minutes. The administrator plans to take a random sample of 30 patients and conduct a hypothesis test to see if there is significant evidence that this year\'s average wait time is longer than last year\'s, using =0.05.

Suppose that the population mean wait time this year has indeed increased, to _a = 137 minutes. For this problem, you will compute the power associated with this test. (Round your answers to two decimal places.)

First, find the critical value under the null hypothesis.
t-crit=  

Next, find the value of the sample mean that is associated with this critical value.
x =  

Next, use this sample mean to convert the t-critical under the null hypothesis to a t-value under the alternative hypothesis (i.e. using our assumption for what the \"true mean\" actually is).
t =  

Finally, use critical value under the alternative hypothesis to determine the power of this test.
Power =  

Suppose the hospital administrator considers this test to be underpowered. She would like to know what will happen to the power if she increases the sample size to n = 100. Redo your power calculation using using n = 100.
Power =

Solution