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:
\(\mu_1\): mean of SATM when Ever_Cheat = No
\(\mu_2\): mean of SATM when Ever_Cheat = Yes
Equal variances are not assumed for this analysis.
Descriptive Statistics: SATM
Estimation of Difference
|Difference||95% CI for Difference|
|Null hypothesis||\(H_0\): \(\mu_1-\mu_2=0\)|
|Alternative hypothesis||\(H_1\): \(\mu_1-\mu_2\neq0\)|
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.