- 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.

Scatter plot with exam scores on the x-axis and quiz scores on the y-axis

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 test 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.