12.2.1.1 - Example: Quiz & Exam Scores

Example: Quiz and exam scores Section

Is there a relationship between students' quiz averages in a course and their final exam scores in the course?

Let's use the 5 step hypothesis testing procedure to address this process research question.

1. Check assumptions and write hypotheses

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, $$H_{a}$$: $$\rho\ne0$$
2. Calculate the test statistic

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
Sample 1 Sample 2 N Correlation 95% CI for $$\rho$$ P-Value
Final Quiz_Average 50 0.609 (0.398, 0.758) 0.000

Our sample statistic r = 0.609.

3. Determine the p-value

From our output the p-value is 0.000.

4. Make a decision

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

5. State a "real world" conclusion.

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