# 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:

- 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 | H_{0}: \(\mu\) = 3 |
---|---|

Alternative hypothesis | H_{1}: \(\mu\) ≠ 3 |

T-Value | P-Value |
---|---|

6.81 | 0.000 |

## Summary of Results

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

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