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 |
---|---|
Alternative hypothesis | 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.