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?
job\tmen\twomen
a\t44\t18
b\t26\t37
c\t12\t12
d\t14\t14
not sure\t3\t19
(a) complete the table below.
job\tmen\twomen
a\t□\t□
b\t□\t□
c\t□\t□
d\t□\t□
not sure\t□\t□
(round to three decimal places as needed.)
(b) choose the correct graph below.

Explanation:

Part (a)

To construct the relative frequency distribution, we first need to find the total number of men and the total number of women.

Step 1: Calculate total for men

Sum the number of men for each job:
\[
44 + 26 + 12 + 14 + 3 = 99
\]

Step 2: Calculate total for women

Sum the number of women for each job:
\[
18 + 37 + 12 + 14 + 19 = 100
\]

Step 3: Calculate relative frequencies for men

• For Job A: \(\frac{44}{99} \approx 0.444\)
• For Job B: \(\frac{26}{99} \approx 0.263\)
• For Job C: \(\frac{12}{99} \approx 0.121\)
• For Job D: \(\frac{14}{99} \approx 0.141\)
• For Not sure: \(\frac{3}{99} \approx 0.030\)

Step 4: Calculate relative frequencies for women

• For Job A: \(\frac{18}{100} = 0.180\)
• For Job B: \(\frac{37}{100} = 0.370\)
• For Job C: \(\frac{12}{100} = 0.120\)
• For Job D: \(\frac{14}{100} = 0.140\)
• For Not sure: \(\frac{19}{100} = 0.190\)

The completed table is:

Job	Men	Women
B	0.263	0.370
C	0.121	0.120
D	0.141	0.140
Not sure	0.030	0.190

Part (b)

To construct the side - by - side relative frequency bar graph, we would have two bars for each job category, one representing the relative frequency of men and one representing the relative frequency of women. The x - axis would be the job categories (A, B, C, D, Not sure) and the y - axis would be the relative frequency. For example, for Job A, the bar for men would reach up to approximately 0.444 and the bar for women would reach up to 0.180. For Job B, the bar for men would reach up to approximately 0.263 and the bar for women would reach up to 0.370, and so on for the other job categories. (Since we don't have the actual graph options, we can describe the construction. If we had the options, we would look for a graph where for each job, there are two bars with heights corresponding to the relative frequencies we calculated above.)

Part (c)

• For Job A, men have a much higher relative frequency (\(0.444\)) compared to women (\(0.180\)), indicating a stronger preference for Job A among men.
• For Job B, women have a higher relative frequency (\(0.370\)) compared to men (\(0.263\)), showing a stronger preference for Job B among women.
• For "Not sure", women have a much higher relative frequency (\(0.190\)) compared to men (\(0.030\)), meaning women are more likely to be unsure about their job preference.
• For Jobs C and D, the relative frequencies for men and women are relatively close to each other, suggesting similar preferences for these two jobs between genders.

Answer:

(for part c):

• Men are more likely to prefer Job A, women are more likely to prefer Job B and be "Not sure". Preferences for Jobs C and D are similar between genders.