20. A psychologist is interested in the conditions that affect the number of dreams per month that people report in which they are alone. We will assume that based on extensive previous research, it is known that in the general population the number of such dreams per month follows a normal curve, with  = 5 and

 = 4. The researcher wants to test the prediction that the number of such dreams will be greater among people who have recently experienced a traumatic event. Thus, the psychologist studies 36 individuals who have recently experienced a traumatic event, having them keep a record of their dreams for a month. Their mean number of alone dreams is 8. Should you conclude that people who have recently had a traumatic experience have a significantly different number of dreams in which they are alone?

(a) Carry out a Z test using the five steps of hypothesis testing (use the .05 level).

(b) Make a drawing of the distributions involved.

(c) Explain your answer to a person who has never had a course in statistics.

(d) ADVANCED TOPIC: Figure the 95% confidence interval.