Exercise 3.58 describes a study in which college students found it unpleasant to sit alone and think. The same article describes a second study in which college students appear to prefer receiving an electric shock to sitting in solitude. The article states that "when asked to spend 15 minutes in solitary thought, 12 of 18 men and 6 of 24 women voluntarily gave themselves at least one electric shock." Use this information to estimate the difference between men and women in the proportion preferring pain over solitude. The standard error of the estimate is 0.154.

(a) Give notation for the quantity being estimated, and define any parameters used.

(b) Give notation for the quantity that gives the best estimate, and give its value.

(c) Give a \(95 \%\) confidence interval for the quantity being estimated.

(d) Is "no difference" between males and females a plausible value for the difference in proportions?

Data From Exercise 3.58:

“For many people, being left alone with their thoughts is a most undesirable activity,” says a psychologist involved in a study examining reactions to solitude.26 In the study, 146 college students were asked to hand over their cell phones and sit alone, thinking, for about 10 minutes. Afterward, 76 of the participants rated the experience as unpleasant. Use this information to estimate the proportion of all college students who would find it unpleasant to sit alone with their thoughts. (This reaction is not limited to college students: in a follow-up study involving adults ages 18 to 77, a similar outcome was reported.)