# 9.2.2.1.3 - Example: Height by Sex

This example uses the following dataset:

CLASS_SURVEY.MTW

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.

1. Check assumptions and write hypotheses

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.)

$$H_{0}:\mu_f = \mu_m$$
$$H_{a}: \mu_f < \mu_m$$

2. Calculate the test statistic
1. Open the Minitab Express file:
2. On a PC: In the menu bar select STATISTICS > Two Samples > t
On a Mac: In the menu bar select Statistics > 2-Sample Inference > t
3. Double click the variable Height in the box on the left to insert the variable into the Samples box
4. Double click the variable Gender in the box on the left to insert the variable into the Sample IDs box
5. Click OK

This should result in the following output:

2-Sample t: Height by Gender
 $$\mu_1$$: 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.

Descriptive Statistics: Height
Gender N Mean StDev SE Mean
Female 126 65.6190 6.5322 0.5819
Male 99 70.2424 3.6340 0.3652
Estimation for Difference
Difference 95% Upper Bound for Difference
-4.6234 -3.4881
Null hypothesis $$H_0$$: $$\mu_1-\mu_2=0$$ $$H_1$$: $$\mu_1-\mu_2<0$$

T-Value DF P-Value
-6.73 202 <0.0001

The test statistic is t = -6.73

3. Determine the p-value

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

4. Make a decision

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

5. State a "real world" conclusion

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