# 9.2.2.1.3 - Example: Height by Sex

9.2.2.1.3 - Example: Height by Sex**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.

This example uses the following Minitab file: class_survey.csv

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 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 file and select
*Stat > Basic Statistics > 2 Sample t...* - Enter variable
*Height*into the*Samples*box - Enter the variable
*Biological Sex**Sample IDs*box - Choose Options and select 'Difference < Hypothesized difference' for the alternative hypothesis.
- Click OK

This should result in the following output:

## Method

\(\mu_1\): mean of Height when Biological Sex = Female

\(\mu_2\): mean of Height when Biological Sex = Male

Difference: \(\mu_1-\mu_2\)

*Equal variances are not assumed for this analysis.*

## Descriptive Statistics: Height

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

Female | 126 | 65.62 | 6.53 | 0.58 |

Male | 99 | 70.24 | 3.63 | 0.37 |

## Estimation for Difference

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

-4.623 |
-3.488 |

## Test

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 | 0.000 |

The test statistic is t = -6.73

From the output given in Step 2, the p-value is 0.000

\(p\leq.05\), 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.