# 12.2.1.1 - Example: Quiz & Exam Scores

12.2.1.1 - Example: Quiz & Exam Scores## Example: Quiz and exam scores

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.

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.

- Open the file in Minitab
- Select
*Stat > Basic Statistics > Correlation* - Enter the columns
*Quiz_Average*and*Final*in the*Variables*box - Select the
*Results*button and check the*Pairwise correlation table*in the new window *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.

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.