# 9.1.2.2.1 - Example: Dating

9.1.2.2.1 - Example: Dating## Example: Dating

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.