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

Minitab 18

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
Test
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:

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