Katherine believe that incorporating games into a curriculum can help students master new material, To test this hypothesis, she designed a gamified history course and asked the school administration to randomly assign 36 students to her class. At the end of the term, all of the students enrolled in History courses completed a departmental exam which had an average score of 72 with a standard deviation of 18. The average score for students in Katherine's class was 78. Can Katherine conclude that, on average, students in a gamified class had a significantly different score compared to the general population of history students in the department (use an alpha of 0.01 two-tailed test)?

1. Which statistical test would you use to solve this problem?

2. State the null and alternative hypothesis in complete sentences.

3. Locate the critical value that defines the critical region.

4. Calculate your statistic.

5. Make a decision with respect to the null hypothesis.

6. Write a concluding sentence in everyday language.

7. Calculate and evaluate Cohen's d

8. Calculate and evaluate r2