Question

a survey of adult men and women asked, \which one of the following jobs would you most like to have?\ the results of the survey are shown in the table. (a) construct a relative frequency distribution for men and women. (b) construct a side-by-side relative frequency bar graph. (c) what are the apparent differences in gender as it pertains to this question? (b) choose the correct graph below.
job \tmen \twomen
a \t44 \t18
b \t26 \t37
c \t12 \t12
d \t14 \t14
not sure \t3 \t19
graph options a, b, c, d with men (blue) and women (red) bars

Explanation:

To solve part (b), we first calculate the relative frequencies for men and women for each job:

Step 1: Calculate total number of men and women

• Total men: \( 44 + 26 + 12 + 14 + 3 = 99 \)
• Total women: \( 18 + 37 + 12 + 14 + 19 = 100 \)

Step 2: Calculate relative frequencies for each job

• Job A:
• Men: \( \frac{44}{99} \approx 0.444 \)
• Women: \( \frac{18}{100} = 0.18 \)
• Job B:
• Men: \( \frac{26}{99} \approx 0.263 \)
• Women: \( \frac{37}{100} = 0.37 \)
• Job C:
• Men: \( \frac{12}{99} \approx 0.121 \)
• Women: \( \frac{12}{100} = 0.12 \)
• Job D:
• Men: \( \frac{14}{99} \approx 0.141 \)
• Women: \( \frac{14}{100} = 0.14 \)
• Not sure:
• Men: \( \frac{3}{99} \approx 0.030 \)
• Women: \( \frac{19}{100} = 0.19 \)

Step 3: Analyze the bar graph options

• For Job A, men's relative frequency is higher (~0.44) than women's (0.18).
• For Job B, women's relative frequency (0.37) is higher than men's (~0.26).
• For Job D, women's relative frequency (0.19) is higher than men's (~0.03).
• Jobs C and D have similar relative frequencies for both genders.

Looking at the options, Option A matches these relative frequency patterns:

• Job A: Men (blue) bar is taller than Women (red).
• Job B: Women (red) bar is taller than Men (blue).
• Job D: Women (red) bar is taller than Men (blue).
• Jobs C and D have similar heights.
• "Not sure": Women (red) bar is taller than Men (blue) (matches 0.19 vs ~0.03).

Answer:

A. (The graph labeled A with Men in blue and Women in red, showing the correct relative frequency patterns as analyzed)