# 8.2.3.2.1 - Minitab Express: 1 Sample Mean t Test, Raw Data

## MinitabExpress – 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 $$n) = 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 Express using raw data:

1. Open Minitab data set:
2. On a PC: Select STATISTICS > One Sample > t
On a Mac: Select Statistics > 1-Sample Inference > t
3. Double-click on the variable GPA to insert it into the Sample box
4. Check the box Perform a hypothesis test
5. For the Hypothesized mean enter 3
6. Click the Options tab
7.  Use the default Alternative hypothesis of Mean ≠ hypothesized value
8. Use the default Confidence level of 95
9. Click OK

This should result in the following output:

1-Sample t: GPA
N Mean StDev SE Mean 95% CI for $$\mu$$
226 3.23106 0.51040 0.03395 (3.16416, 3.29796)

$$\mu$$: mean of GPA

Null hypothesis H0: $$\mu$$ = 3 H1: $$\mu$$ ≠ 3
T-Value P-Value
6.81 <0.0001
Video Walkthrough

Select your operating system below to see a step-by-step guide for this example.

We could summarize these results using the five step hypothesis testing procedure:

1. Check assumptions and write hypotheses

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.

$$H_0: \mu = 3.0$$
$$H_a: \mu \ne 3.0$$

2. Calculate the test statistic

$$t (225) = 6.81$$

3. Determine the p-value

$$p < 0.0001$$

4. Make a decision

$$p \le \alpha$$, reject the null hypothesis

5. State a "real world" conclusion

There is evidence that the mean GPA in the population is different from 3.0