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

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 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 file and select Stat > Basic Statistics > 2 Sample t...
  2. Enter variable Height into the Samples box
  3. Enter the variable Biological Sex in the box into the Sample IDs box
  4. Choose Options and select 'Difference < Hypothesized difference' for the alternative hypothesis.
  5. 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

3. Determine the p-value

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

4. Make a decision

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

5. State a "real world" conclusion

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

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