Problem 3 (10 pts).

Over the years, numerous studies have sought to characterize the nightmare su erer.

Out of these has emerged the stereotype of someone with high anxiety and poorer-than-average physical

health. What is no so well known, though, is whether men fall into this pattern with the same frequency

as women. To this end, an clinical survey looked at nightmare frequencies for a sample of 160 men and

192 women. Each subject was asked whether he or she experienced nightmares \often" or \seldom". The

proportions of men and women saying \often" were 55/160 and 60/192, respectively. Is the diference

between those two percentages statistically significant? Use a = 0.05.

(a) Define the hypotheses to be tested.

(b) Define the appropriate test statistic and compute its value.

(c) Find the critical value(s) and the critical region to a 1% level of significance

(d) Decide whether or not to reject the null hypothesis.

(e) What is your conclusion in terms of the original problem?