# 9.1.2.2.1 - Example: Dating

## 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.

1. Check any necessary assumptions and write hypotheses.

We are looking for a "difference," so this is a two-tailed test.

$$H_{0} : p_1 - p_2 =0$$
$$H_{a} :p_1 - p_2 \neq 0$$

 Event: DatePerly = Yes $$p_1$$: proportion where DatePerly = Yes and Gender = Female $$p_2$$: proportion where DatePerly = Yes and Gender = Male Difference: $$p_1-p_2$$
Descriptive Statistics: DatePerly
Gender N Event Sample p
Female 571 367 0.642732
Male 433 148 0.341801
Estimation for Difference
Difference 95% CI for Difference
0.300931 (0.241427, 0.360435)
Null hypothesis $$H_0$$: $$p_1-p_2=0$$ $$H_1$$: $$p_1-p_2\neq0$$
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.

$$n_f p_f = 367$$

$$n_f (1-p_f) = 571 - 367 = 204$$

$$n_m p_m = 148$$

$$n_m (1 - p_m) = 433 - 148 = 285$$

All of these counts are at least 10 so we will use the normal approximation method.

2. Calculate an appropriate test statistic.

From output, $$z=9.45$$

3. Determine the p-value associated with the test statistic.

From output, $$p<0.0001$$

4. Decide between the null and alternative hypotheses.

$$p \leq \alpha$$, reject the null hypothesis

5. State a "real world" conclusion.

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.