A psychologist is working with people who have had a particular type of major surgery. This psychologist proposes that people will recover from the operation more quickly if friends and family are in the room with them for the first 48 hours after the operation. It is known that time to recover from this kind of surgery is normally distributed with a mean of 12 days and a standard deviation of 5 days. The procedure of having friends and family in the room for the period after the surgery is tried with a randomly selected patient. This patient recovers in 18 days.
(a) Using the .01 significance level, what should the researcher conclude? Solve this problem explicitly using all five steps of hypothesis testing, and illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution.
(b) Then explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores).