O One Method of Human Locomotion That Appears to Have

Essay

O One method of human locomotion that appears to have no function except to express joy is hopping, a skill usually learned in early and middle childhood. Each person in a random sample of female students and a random sample of male students at a large middle school was asked, "Approximately how long ago did you last spontaneously hop?" The total sample sizes and the numbers who responded "Less than 1 week ago" are given in the table below:
$\begin{array} { | l | c | c | } \hline{ \text { Number responding "2-3 weeks" } } \\ { \text { Gender } } & \boldsymbol { x } & \boldsymbol { n } \\\hline \text { Males } & 104 & 411 \\\text { Females } & 71 & 253 \\\hline\end{array}$

a) Construct a $95 \%$ confidence interval for the difference in the population proportions of males and the proportion of females at this school who would respond "2-3 weeks." b) Referring to your work in part (a), does there appear to be a difference between the population proportions of men and women responding "2-3 weeks?" Provide statistical justification for your answer.