Chapter 11.2, Problem 27E

(a)

To determine

To calculate the conditional distribution of reported sports goals for each gender.

Explanation of Solution

Given:

The data students classified into four categories based on their responses of 67 males and 67 females are shown below

  

Calculation:

The conditional distribution of reported goals for each gender are shown below

  $\begin{array}{ccccc}& HSC-HM& HSC-LM& LSC-HM& LSC-LM\\ Female& \frac{14}{67}=0.209& \frac{7}{67}=0.104& \frac{21}{67}=0.313& \frac{25}{67}=0.373\\ Male& \frac{31}{67}=0.463& \frac{18}{67}=0.269& \frac{5}{67}=0.075& \frac{13}{67}=0.194\end{array}$

The proportions are calculated for each gender

For females proportions are calculated by dividing females with HSC-HM, HSC-LM, LSC-HM, LSC-LM by total females.

For males proportions are calculated by dividing males with HSC-HM, HSC-LM, LSC-HM, LSC-LM by total males.

(b)

To determine

To plot an appropriate graph to compare the conditional distribution.

Explanation of Solution

Given:

The data students classified into four categories based on their responses of 67 males and 67 females and its conditional distribution is shown below

  $\begin{array}{ccccc}& HSC-HM& HSC-LM& LSC-HM& LSC-LM\\ Female& \frac{14}{67}=0.209& \frac{7}{67}=0.104& \frac{21}{67}=0.313& \frac{25}{67}=0.373\\ Male& \frac{31}{67}=0.463& \frac{18}{67}=0.269& \frac{5}{67}=0.075& \frac{13}{67}=0.194\end{array}$

The comparison of goals for each gender in each category is done in multiple bar graph. Each category is along the horizontal axis and proportion along the vertical axis.

Graph:

  

(c)

To determine

To compare the distributions of sports goals for male and female undergraduates with reference to a multiple bar graph.

Explanation of Solution

Given:

The data students classified into four categories based on their responses of 67 males and 67 females and its conditional distribution is plotted as shown below

  

Interpretation:

From the bar graph we can conclude that females have goals with low social comparison and low mastery while male have goals with high social comparison and high mastery.