Question

An instructor for a test preparation course claims that the course will improve the test scores of students. The table shows the critical reading scores for 14 students the first two times they took the test. Before taking the test for the second​ time, the students took the​ instructor's course to try to improve their critical reading test scores. At a​ = 0.01, is there enough evidence to support the​ instructor's claim?

Answer 1

To verify the instructor's claim that a preparation course improves test scores, a paired-sample t-test should be conducted. By comparing the t-statistic to the critical t-value at the alpha level of 0.01, one can determine whether there is statistical evidence to support the claim.

To assess the instructor's claim that a test preparation class will improve test scores, we will conduct a hypothesis test. Specifically, we can use a paired-sample t-test since we are looking at scores from the same students before and after the course. If the class is effective, the scores after the course should be significantly higher than those before the course, on average.

Here is a step-by-step explanation of the process:

1. Set up the null hypothesis (H0): The mean difference in test scores (after - before) is 0.
2. Set up the alternative hypothesis (H1 or Ha): The mean difference in test scores (after - before) is greater than 0.
3. Choose the significance level (α), which is given as 0.01 in the problem.
4. Calculate the t-statistic for the paired-sample data.
5. Find the critical t-value for the chosen α level.
6. Compare the calculated t-statistic to the critical t-value to determine if the null hypothesis can be rejected.

In conclusion, if the t-statistic is greater than the critical t-value, there is evidence at the 0.01 significance level to support the claim that the class improves critical reading test scores.