Question

example 2: voting preference and gender
a 2022 survey of college students in the u.s. asked about political preference by gender. results are
summarized below.
(source: american national election studies anes pilot survey, 2022)

a) what proportion of students in this sample identify as democrats?
b) what proportion of females in this sample are democrats?
c) what proportion of the people who identify as democrats in this sample are female?
d) what proportion of males in this sample are republicans?
e) using \\( \hat { p } f = \\) proportion of females who are democrats and \\( \hat { p } m = \\) proportion of males who are
democrats, find the difference \\( ( \hat { p } f - \hat { p } m ) \\)

Explanation:

Step1: Calculate proportion of Democrats

Proportion = $\frac{\text{Number of Democrats}}{\text{Total number of students}}$
$$\frac{92}{227}\approx0.405$$

Step2: Calculate proportion of female Democrats

Proportion = $\frac{\text{Number of female Democrats}}{\text{Total number of females}}$
$$\frac{58}{125}=0.464$$

Step3: Calculate proportion of female in Democrats

Proportion = $\frac{\text{Number of female Democrats}}{\text{Total number of Democrats}}$
$$\frac{58}{92}\approx0.630$$

Step4: Calculate proportion of male Republicans

Proportion = $\frac{\text{Number of male Republicans}}{\text{Total number of males}}$
$$\frac{27}{102}\approx0.265$$

Step5: Calculate difference in proportions

From step2, $\hat{p}F = 0.464$; from step1 (for males: $\hat{p}M=\frac{34}{102}\approx0.333$)
$$\hat{p}F-\hat{p}M=0.464 - 0.333=0.131$$

Answer:

a) Approximately \(0.405\)
b) \(0.464\)
c) Approximately \(0.630\)
d) Approximately \(0.265\)
e) \(0.131\)