One Method of Human Locomotion That Appears to Have No

One method of human locomotion that appears to have no function except to express
joy is skipping, 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
skip?" The total sample sizes and the numbers who responded "Less than 1 week
ago" are given in the table below: $$\begin{array} { | l | c | c | } \hline { \text { Number responding "Less than } 1 \text { week" } } \\ { \text { Gender } } & \boldsymbol { x } & \boldsymbol { n } \\\hline \text { Males } & 71 & 411 \\\text { Females } & 64 & 253 \\\hline\end{array}$$ a) Construct a $95 \%$ confidence interval for the difference in the proportions of males and the proportion of females at this school who would respond "Less than 1 week." b) Referring to your work in part (a), does there appear to be evidence of a difference
in the population proportions of males and females at this school who would
respond "Less than 1 week?" Provide appropriate statistical justification for your
answer.