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 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

Test
Null hypothesis H0: \(\mu\) = 3
Alternative hypothesis 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