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

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

## 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:

1. Open the Minitab file: class_survey.mpx
2. Select Stat > Basic Statistics > 1-sample t
3. Select One or more samples, each in a column from the dropdown
4. Double-click on the variable GPA to insert it into the Sample box
5. Check the box Perform a hypothesis test
6. For the Hypothesized mean enter 3
7. Select Options
8. Use the default Alternative hypothesis of Mean ≠ hypothesized value
9. Use the default Confidence level of 95
10. 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 H1: $$\mu$$ ≠ 3
T-Value P-Value
6.81 0.000

## Summary of Results

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.

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

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

 [1] Link ↥ Has Tooltip/Popover Toggleable Visibility