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 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 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.