Question

preference for the students in the sample.

1. 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 mosaic plot 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.

Explanation:

Answer:

(a) To find the proportion, we need the number of females who felt their weight was about right divided by the total number of respondents who felt their weight was about right. From the mosaic plot, assume the relative frequency for females "About right" is, say, 75% (approximate from the plot) and males "About right" is 70% (approximate). But without exact numbers from Exercise 25, if we assume Exercise 25 had data like: total "about right" = number of females (about right) + number of males (about right). Suppose in Exercise 25, females about right: 500, males about right: 300, total about right: 800. Then proportion is 500/800 = 5/8 = 0.625. (But since we need to refer to Exercise 25, and without that data, but if we use the plot, the female "About right" relative frequency is higher than male? Wait, no, the plot shows female "About right" is from 0 - 75% (approx) and male from 0 - 70%? Wait, the y - axis is relative frequency (%). Let's assume the "About right" for female is 75% of female respondents, and for male 70% of male respondents. But to answer (a), we need the number of females with "about right" over total "about right". Let's say total respondents: 1200. Let's assume female respondents: 600, male: 600. Female "about right": 600 0.75 = 450, male "about right": 600 0.7 = 420. Total "about right": 450 + 420 = 870. Proportion female: 450/870 = 15/29 ≈ 0.517. (But this is with assumptions. Since the problem refers to Exercise 25, which we don't have, but if we use the mosaic plot, the key is that we need to take the number of females who think weight is about right divided by the total number of people who think weight is about right. )

(b) Percent of female respondents who felt weight was about right: (number of females with "about right" / total female respondents) 100. From the plot, the "About right" for female is from 0 to 75% (approx) of the female bar. So if female respondents are, say, 600, and "about right" is 450, then (450/600)100 = 75%.

(c) The mosaic plot shows that for both genders, the largest proportion of respondents feel their body weight is "about right". The proportion of females who feel "underweight" is slightly higher than males, and the proportion of females who feel "overweight" is higher than males (since the red bar for female is taller than for male, and the green bar for female is taller than for male, while the blue bar (about right) is slightly shorter for female than male? Wait, no, the y - axis is relative frequency (%). The female bar: "About right" is from 0 to ~75%, "Overweight" from ~75 to ~95%, "Underweight" from ~95 to 100%. Male bar: "About right" from 0 to ~70%, "Overweight" from ~70 to ~85%, "Underweight" from ~85 to 100%. So the association: Females are more likely to feel "overweight" or "underweight" compared to males, while males are more likely to feel "about right" than females? Wait, no, the "About right" for female is ~75% of female respondents, for male ~70%? Wait, no, the height of the "About right" segment: female's "About right" is from 0 to 75 (so 75% of female respondents), male's "About right" is from 0 to 70 (70% of male respondents). "Overweight": female from 75 to 95 (20% of female), male from 70 to 85 (15% of male). "Underweight": female from 95 to 100 (5% of female), male from 85 to 100 (15% of male). So overall, females are more likely to perceive themselves as overweight (higher percentage of females in "overweight" category) and less likely to perceive themselves as underweight? Wait, no, male's "underweight" is 15% and female's is 5%, so males are more likely to perceive as underweight. Females are more likely to perceive as overweight, males more likely as underweight, and both have most in "about right", with females having a slightly higher percentage in "about right" (75% vs 70%)? Wait, maybe I misread the plot. The key is to describe the association: Looking at the mosaic plot, the distribution of body image (underweight, overweight, about right) differs by gender. For example, a larger proportion of males feel underweight compared to females, a larger proportion of females feel overweight compared to males, and the proportion of those who feel their weight is about right is relatively high for both genders, with a slightly higher proportion of females (or males, depending on the plot) in the "about right" category.

But since the problem is about body image and gender, and analyzing proportions, the discipline is Mathematics (Statistics) as it involves analyzing data, proportions, and interpreting graphical displays of data.

So the subfield for this problem is Statistics (under Mathematics).