Chapter 1.1, Problem 31E

(a)

To determine

To find: The proportion of female of the respondents who felt their body weight was about right.

Answer to Problem 31E

The proportion of female of the respondents who felt their body weight was about right is 0.6550.

Explanation of Solution

Given information:

The two way table of the gender is given below

		Female	Male	Total
Body Image	About right	560	295	855
	Overweight	163	72	235
	Underweight	37	73	110
	Total	760	440	1200

Formula used:

  $\begin{array}{l}\text{P (female | body weight about right) = }\\ \frac{\text{Number of respondents who are female and felt that their body weight is about right}}{\text{Number of respondents who felt that their body weight is about right}}\end{array}$

Calculation:

From the given table-

Number of respondents who felt that their body weight is about right = 855

Number of respondents who are female and felt that their body weight is about right = 560

  $\text{P (female | body weight about right) =}\frac{560}{855}=0.6550$

To determine

(b)

To find: The proportion of the respondents who felt their body weight was about right of the population of female.

Answer to Problem 31E

The proportion of the respondents who felt their body weight was about right of the population of female is 0.7368.

Explanation of Solution

Formula used:

  $\begin{array}{l}\text{P (body weight about right | female) = }\\ \frac{\text{Number of respondents who are female and felt that their body weight is about right}}{\text{Number of female respondents }}\end{array}$

Calculation:

From the given table-

Number of respondents who are female = 760

Number of respondents who are female and felt that their body weight is about right = 560

  $\text{P (body weight about right | female) =}\frac{560}{760}=0.7368$

To determine

c)

To check: Whether there is any association between gender and body image or not.

Answer to Problem 31E

There seems to be some (but not significant) association between gender and body image.

Explanation of Solution

There is no association if the segmented regions of bars are of equal area.

In this case, the segment of about right is almost equal for female and male but is different for underweight and overweight.

So, as per the definition there is some association between gender and body image.