Question

Body image Refer to Exercise 25.

(a) Of the respondents who felt that their body weight was about right, what proportion were female?

(b) Of the female respondents, what percent felt that their body weight was about right?

(c) The segmented bar graph displays the distribution of perceived body image by gender. Describe what this graph reveals about the association between these two variables for the 1200 college students in the sample.

Short answer

Part (a) $\frac{112}{171}\mathrm{or}\approx 0.6550$

Part (b) 73.68%

Part (c) In comparison to males, more women believe they are overweight. Males are more likely than females to believe they are underweight.

Step-by-step solution

Part (a) Step 1. Given information.

The given table in exercise 25 is shown below:

Part (a) Step 2. Find the proportion of the female who felt that their body weight was about right.

The total number of college students who felt that their body weight was about right: 855

Out of them, females are 500.

Therefore, the required proportion is:

$\frac{560}{855}=\frac{112}{171}\mathrm{or}\approx 0.6550$

Part (b) Step 1. Find the percent of the female who felt that their body weight was about right out of all females.

The total number of college students who are females is: 760

out of them, 560 females felt that their weight is about right.

Therefore, the required proportion is:

$\frac{560}{760}=73.68\%$

Part (c) Step 1. Describe the association of variables in the given bar graph.

The given bar graph is shown below:

The majority of females believe their body weight is about right, whereas the majority of males believe the same.

As we can see that the blue area of the bars is larger for females, and more females believe their body weight is about right. Because the red area of the bars is greater for ladies than for males, more females believe they are overweight.

As we can see that the green area of the bars is greater for males than for females, more males believe they are underweight.