Minitab can be used to construct a confidence interval for the difference between two independent means. Note that the confidence intervals given in the Minitab output assume that either the populations are normally distributed or that both sample sizes are at least 30.
Minitab® – Confidence Interval Between 2 Independent Means
Let's estimate the difference between the mean weight (in pounds) of females and the mean weight of males. Both sample sizes are at least 30 so the sampling distribution can be approximated using the t distribution.
- Open the Minitab file: class_survey.mpx
- Select Stat > Basic Statistics > 2 Sample t
- Select Both samples are in one column from the dropdown
- Double click the variable Weight in the box on the left to insert the variable into the Samples box
- Double click the variable Biological Sex in the box on the left to insert the variable into the Sample IDs box
- Click OK
This should result in the following output:
Method
\(\mu_1\): mean of Weight when Biological Sex = Female
\(\mu_2\): mean of Weight when Biological Sex = Male
Difference: \(\mu_1-\mu_2\)
Equal variances are not assumed for this analysis.
Descriptive Statistics: Weight
| Gender | N | Mean | StDev | SE Mean |
|---|---|---|---|---|
| Female | 126 | 136.7 | 23.4 | 2.1 |
| Male | 99 | 172.7 | 27.3 | 2.7 |
Estimation for Difference
| Difference | 95% CI for Difference |
|---|---|
| -35.99 | (-42.79, -29.20) |
Interpret
I am 95% confident that in the population the mean weight of females is between 29.202 pounds and 42.787 pounds less than the mean weight of males.