Example: Dating Section
This example uses the course survey dataset:
A random sample of Penn State University Park undergraduate students were asked, "Would you date someone with a great personality even if you did not find them attractive?" Let's compare the proportion of males and females who responded "yes" to determine if there is convincing evidence of a difference.
We are looking for a "difference," so this is a two-tailed test.
\(H_{0} \colon p_1 - p_2 =0\)
\( H_{a} \colon p_1 - p_2 \neq 0 \)
Check assumptions
\(n_f p_f = 367\)
\(n_f (1-p_f) = 571 - 367 = 204\)
\(n_m p_m = 148\)
\(n_m (1 - p_m) = 433 - 148 = 285\)
All of these counts are at least 10 so we will use the normal approximation method.
From output, \(z=9.45\)
Event: DatePerly = Yes |
\(p_1\): proportion where DatePerly = Yes and Gender = Female |
\(p_2\): proportion where DatePerly = Yes and Gender = Male |
Difference: \(p_1-p_2\) |
Gender | N | Event | Sample p |
|---|---|---|---|
Female | 571 | 367 | 0.642732 |
Male | 433 | 148 | 0.341801 |
Difference | 95% CI for Difference |
|---|---|
0.300931 | (0.241427, 0.360435) |
Null hypothesis | \(H_0\): \(p_1-p_2=0\) |
|---|---|
Alternative hypothesis | \(H_1\): \(p_1-p_2\neq0\) |
Method | Z-Value | P-Value |
|---|---|---|
Fisher's exact | <0.0001 | |
Normal approximation | 9.45 | <0.0001 |
The pooled estimate of the proportion (0.512948) is used for the tests.
From output, \(p<0.0001\)
\(p \leq \alpha\), reject the null hypothesis
There is convincing evidence that in the population of all Penn State University Park undergraduate students the proportion of men who would date someone with a great personality even if they did not find them attractive is different from the proportion of women who would date someone with a great personality even if they did not find them attractive.