# 8.3.3.1 - Example: SAT Scores

8.3.3.1 - Example: SAT Scores## Example: SAT Scores

This example uses the dataset from Lesson 8.3.3 to walk through the five-step hypothesis testing procedure using the Minitab output.

**Research question: **Do students score differently on the SAT-Math and SAT-Verbal tests?

1. Check assumptions and write hypotheses

Because the sample size is large (\(n \ge 30\)), the *t* distribution may be used to approximate the sampling distribution.

\(H_{0}:\mu_d=0\)

\(H_{a}:\mu_d \ne 0\)

2. Calculate the test statistic

Null hypothesis | H_{0}: \(\mu_d\) = 0 |
---|---|

Alternative hypothesis | H_{1}: \(\mu_d\) ≠ 0 |

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

3.18 | 0.002 |

The t test statistic is 3.18.

3. Determine the p value associated with the test statistic

From the output, the p value is 0.002

4. Make a decision

\(p\leq .05\), therefore our decision is to reject the null hypothesis

5. State a "real world" conclusion

There is evidence that in the population, on average, students' SAT-Math and their SAT-Verbal scores are different.