# 9.2.2.1.3 - Example: Height by Sex

9.2.2.1.3 - Example: Height by SexThis example uses the following dataset:

**Research Question**: In the population of all college students, is the mean height of females less than the mean height of males?

Data concerning height (in inches) were collected from 99 females and 126 males.

We have two independent groups: females and males. Height in inches is a quantitative variable. This means that we will be comparing the means of two independent groups.

There are 126 females and 99 males in our sample. The sampling distribution will be approximately normally distributed because both sample sizes are at least 30.

This is a left-tailed test because we want to know if the mean for females is less than the mean for males.

(Note: Minitab Express will arrange the levels of the explanatory variable in alphabetical order. This is why "females" are listed before "males" in this example.)

\(H_{0}:\mu_f = \mu_m \)

\(H_{a}: \mu_f < \mu_m \)

- Open the Minitab Express file:
- On a
**PC**: In the menu bar select**STATISTICS > Two Samples > t**

On a**Mac**:**Statistics > 2-Sample Inference > t** - Double click the variable
*Height*in the box on the left to insert the variable into the*Samples*box - Double click the variable
*Gender**Sample IDs*box - Click OK

This should result in the following output:

\(\mu_1\): mean of Height when Gender = Female |

\(\mu_2\): mean of Height when Gender = Male |

Difference: \(\mu_1-\mu_2\) |

*Equal variances are not assumed for this analysis.*

Gender | N | Mean | StDev | SE Mean |
---|---|---|---|---|

Female | 126 | 65.6190 | 6.5322 | 0.5819 |

Male | 99 | 70.2424 | 3.6340 | 0.3652 |

Difference | 95% Upper Bound for Difference |
---|---|

-4.6234 | -3.4881 |

Null hypothesis |
\(H_0\): \(\mu_1-\mu_2=0\) |
---|---|

Alternative hypothesis | \(H_1\): \(\mu_1-\mu_2<0\) |

T-Value | DF | P-Value |
---|---|---|

-6.73 | 202 | <0.0001 |

The test statistic is t = -6.73

From the output given in Step 2, the p value is <0.0001

\(p\leq.05\), therefore we reject the null hypothesis.

There is evidence that the mean height of female students is less than the mean height of male students in the population.