Here we will use Minitab to conduct an independent means t-test. Note that Minitab uses a more complicated formula for computing the degrees of freedom for this test.
Within Minitab, the procedure for obtaining the test statistic and confidence interval for independent means is identical.
Minitab® – Conducting an Independent Means t Test
Let's compare the mean SAT-Math scores of students who have and have not ever cheated. 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...
- Enter the variable SATM into the Samples box
- Enter variable Ever_Cheat into the Sample IDs box
- Click OK
This should result in the following output:
Method
\(\mu_1\): mean of SATM when Ever_Cheat = No
\(\mu_2\): mean of SATM when Ever_Cheat = Yes
Difference: \(\mu_1-\mu_2\)
Equal variances are not assumed for this analysis.
Descriptive Statistics: SATM
| Ever_Cheat | N | Mean | StDev | SE Mean |
|---|---|---|---|---|
| No | 163 | 604.0 | 86.9 | 6.8 |
| Yes | 53 | 583.7 | 79.2 | 11 |
Estimation of Difference
| Difference | 95% CI for Difference |
|---|---|
| 20.3 | (-5.2, 45.8) |
Test
| Null hypothesis | \(H_0\): \(\mu_1-\mu_2=0\) |
|---|---|
| Alternative hypothesis | \(H_1\): \(\mu_1-\mu_2\neq0\) |
| T-Value | DF | P-Value |
|---|---|---|
| 1.58 | 95 | 0.117 |
The result of our two independent means t test is \(t(95) = 1.58, p = 0.117\). Our p-value is greater than the standard alpha level of 0.05 so we fail to reject the null hypothesis. There is not enough evidence to state that the mean SAT-Math scores of students who have and have not ever cheated are different.
Note that we could also interpret the confidence interval in this output. We are 95% confident that the mean difference in the population is between -5.16 and 45.78.
The example above uses a dataset. The following examples show how you can conduct this type of test using summarized data.