Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
9th Edition
ISBN: 9781319013387
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Chapter 9.1, Problem 25E
To determine

To find: The joint distribution, two marginal distributions and conditional distribution.

Expert Solution
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Answer to Problem 25E

Solution: The joint distribution of times by sex is shown below:

Joint Distribution

More and boys

37.23%

More and girls

34.13%

Never and boys

5.39%

Never and girls

7.12%

Once and boys

6.36%

Once and girls

9.77%

The marginal distribution of ‘gender’ is shown below:

Gender

Boys

Girls

Marginal distribution

(9631966×100%=48.98%)

(10031966×100%=51.02%)

The marginal distribution of ‘times’:

Times

Marginal distribution

More

(14031966×100%=71.36%)

Never

(2461966×100%=12.51%)

Once

(3171966×100%=16.12%)

The conditional distribution of ‘sex’ by time is shown below:

Gender

Times

Boys

Girls

Total

More

52.17%

47.83%

100%

Never

43.09%

56.91%

100%

Once

39.43%

60.57

100%

The conditional distribution of ‘time’ by sex is shown below:

Times

Boys

Girls

More

76.01%

66.90%

Never

11.01%

13.96%

Once

12.98%

19.14%

Total

100%

100%

Explanation of Solution

Calculation: Joint distributions are computed by dividing the cell element by the total observation. Hence, the table which shows the joint distribution is given below:

Gender

Times

Boys

Girls

Total

More

37.23%

34.13%

71.36%

Never

5.39%

7.12%

12.51%

Once

6.36%

9.77%

16.12%

Total

48.98%

51.02%

100%

The joint distribution of Boys who had more sexually harassed can be calculated as:

Joint distribution=7321966×100=37.23%

The joint distribution of Boys who had never sexually harassed times can be calculated as:

Joint distribution=1061966×100=5.39%

Thus, the remaining joint distribution can be calculated by using the above formula.

Marginal distributions are computed by dividing the row or column totals by the overall total. Marginal distribution provides information about the individual variables but it does not provide any information about the relationship between two variables. Marginal distribution of Gender:

Gender

Boys

Girls

Marginal distribution

(9631966×100%=48.98%)

(10031966×100%=51.02%)

Marginal distribution of Times:

Times

Marginal distribution

More

(14031966×100%=71.36%)

Never

(2461966×100%=12.51%)

Once

(3171966×100%=16.12%)

Conditional distributions of one variable restricted to a single outcome of another variable. Conditional distributions are computed by the row or column elements by the total of that row or column observation. Conditional distribution of gender who had sexually harassment is shown below:

Gender

Times

Boys

Girls

Total

More

52.17%

47.83%

100%

Never

43.09%

56.91%

100%

Once

39.43%

60.57

100%

The conditional distribution of Boys who had more sexually harassed can be calculated as:

Conditional distribution=7321403×100=52.17%

Thus, the remaining conditional distribution of gender by the category time can be calculated by using the above formula.

Now, the conditional distribution of time for each gender category is shown below:

Times

Boys

Girls

More

76.01%

66.90%

Never

11.01%

13.96%

Once

12.98%

19.14%

Total

100%

100%

The conditional distribution of time for each gender can be calculated as:

Conditional distribution=732963×100=76.01%

Thus, the remaining conditional distribution of time for each gender can be calculated by using the above formula.

To determine

To explain: Conditional distribution to explain the result of analysis.

Expert Solution
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Answer to Problem 25E

Solution: The distribution of times by sex is preferable for the analysis.

Explanation of Solution

The distribution of times by sex is preferable and more informative. It shows that boys had witnessed sexual harassment more than girls. In category ‘More’ boys had 10% higher than girls.

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