In order to use Pearson's \(r\) both variables must be quantitative and the relationship between \(x\) and \(y\) must be linear. We can use Minitab to create the scatterplot using the file: Exam.mpx

Note that when creating the scatterplot it does not matter what you designate as the x or y axis. We get the following which shows a fairly linear relationship.

Our hypotheses:

• Null Hypothesis, \(H_{0}\): \(\rho=0\)
• Alternative Hypothesis, \(H_{a}\): \(\rho\ne0\)

Use Minitab to compute \(r\) and the p-value.

1. Open the file in Minitab
2. Select Stat > Basic Statistics > Correlation
3. Enter the columns Quiz_Average and Final in the Variables box
4. Select the Results button and check the Pairwise correlation table in the new window
5. OK and OK

Pairwise Pearson Correlations

Our sample statistic r = 0.609.

From our output the p-value is 0.000.

If \(p \leq \alpha\) reject the null hypothesis, there is evidence of a relationship in the population.

There is evidence of a relationship between students' quiz averages and their final exam scores in the population.