Minitab® – One Sample Mean t Test Using Raw Data
Research question: Is the mean GPA in the population different from 3.0?
- Null hypothesis: \(\mu\) = 3.0
- Alternative hypothesis: \(\mu\) ≠ 3.0
The GPAs of 226 students are available.
A one sample mean \(t\) test should be performed because the shape of the population is unknown, however the sample size is large (\(n\) ≥ 30).
To perform a one sample mean \(t\) test in Minitab using raw data:
- Open the Minitab file: class_survey.mpx
- Select Stat > Basic Statistics > 1-sample t
- Select One or more samples, each in a column from the dropdown
- Double-click on the variable GPA to insert it into the Sample box
- Check the box Perform a hypothesis test
- For the Hypothesized mean enter 3
- Select Options
- Use the default Alternative hypothesis of Mean ≠ hypothesized value
- Use the default Confidence level of 95
- Click OK and OK
This should result in the following output:
N | Mean | StDev | SE Mean | 95% CI for \(\mu\) |
|---|---|---|---|---|
226 | 3.2311 | 0.5104 | 0.0340 | (3.1642, 3.2980) |
\(\mu\): population mean of GPA
Null hypothesis | H0: \(\mu\) = 3 |
|---|---|
Alternative hypothesis | H1: \(\mu\) ≠ 3 |
T-Value | P-Value |
|---|---|
6.81 | 0.000 |
Summary of Results Section
We could summarize these results using the five step hypothesis testing procedure:
We do not know if the population is normally distributed, however the sample size is large (\(n \ge 30\)) so we can perform a one sample mean t test.
\(H_0\colon \mu = 3.0\)
\(H_a\colon \mu \ne 3.0\)
\(t (225) = 6.81\)
\(p < 0.0001\)
\(p \le \alpha\), reject the null hypothesis
There is convincing evidence that the mean GPA in the population is different from 3.0