# 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 Express 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 0.0017

The t test statistic is 3.18.

3. Determine the p value associated with the test statistic

From the output, the p value is 0.0017

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.

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