Question

Do students who take SAT coaching classes improve their test scores? Seven students were selected randomly from all of the students who completed an SAT coaching class in a given year. For each student, the first SAT score (before the class) and the second SAT score (after the coaching class) were recorded. The data is summarized below:

Student 1 2 3 4 5 6 7 First SAT score 920 820 960 920 1060 860 1010 Second SAT score 1030 800 980 980 1140 960 1040

Does this data provide sufficient evidence to conclude that the average SAT score after completing the coaching class was higher than the average score before the class for students in this year’s class?

Your answer should include:

- The parameter for the test and why you chose that parameter.

- The null hypothesis (H0) and alternative hypothesis (Ha ).

- Discussion of the conditions and why they are satisfied or why they are not satisfied. (Regardless of your answer here, assume the conditions are satisfied.)

- The sample statistic and its value.

- The test statistic used and its value

- The P-value and its significance.

- Your conclusion in the context of the claim as stated above

Answer 1

Here to test the given hypothesis that the average SAT score after completing the coaching class was higher than the average score before the class for students in this year’s class, Paired t-test is used. Here is attached the detailed solution: