# 8.3.3.1 - Example: SAT Scores

## Example: SAT Scores Section

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 H0: $$\mu_d$$ = 0 H1: $$\mu_d$$ ≠ 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.