10.(7 pts) A new prep class was designed to improve SAT math test scores. Five students were selected at random. Their scores on two practice exams were recorded; one before the class and one after. The data recorded in the table below. We want to test if the scores, on average, are higher after the class.

SAT Math Score

Student 1

Student 2

Student 3

Student 4

Student 5

Score before the class

620

700

650

640

620

Score after the class

640

700

670

670

630

(a) (1 pt) Which of the following is the appropriate test and best distribution to use for the test?

(i) Two independent means, normal distribution

(ii) Two independent means, Students t-distribution

(iii) Matched or paired samples, normal distribution

(iv) Matched or paired samples, Students t-distribution

(b) (1 pt) Let _d be the population mean for the differences of scores (scores after the class before the class).Fill in the correct symbol (=, , , >, , <) for the null and alternative hypotheses.

(i)H₀:_d ________ 0

(ii) H_a: _d ________ 0

(c) (2 pts)What is the test statistic? (Show work and round the answer to three decimal places)

(d)(2 pts) What is the p-value? (Show work and round the answer to three decimal places)

(e) (1 pt) What is your conclusion of the test at the = 0.05 level? Why? (Show work)