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.

Question

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.

Quizplus · Accepted Answer

The Answer is a)
Assumption check: There are at least 10 "successes" and at least 10 "failures" in both samples. Thus, the large sample procedure (z) is appropriate.

\begin{array} { l } \left( \hat { p } _ { m } - \hat { p } _ { f } \right) \pm 1.96 \sqrt { \frac { \hat { p } _ { m } \left( 1 - \hat { p } _ { m } \right) } { n _ { m } } + \frac { \hat { p } _ { f } \left( 1 - \hat { p } _ { f } \right) } { n _ { f } } } \( 0.2530 - 0.2806 ) \pm 1.96 \sqrt { \frac { 0.2530 ( 1 - 0.2530 ) } { 411 } + \frac { 0.0 .2806 ( 1 - 0.2806 ) } { 253 } } \( - 0.0971 , + 0.0419 )\end{array}

b)
There does not appear to be evidence of a difference between the proportions of males and females responding "

2 - 3

weeks." Zero is in the

95 \%

confidence interval.

O One Method of Human Locomotion That Appears to Have