A tutoring agency claims that by completing a special course, students will improve their math SAT scores. In part of a study, 12 students take the math part of the SAT, complete the special course, then take the math part of the SAT again. The students' scores are shown below. At \(\alpha=0.05\), is there enough evidence to support the agency's claim?

(a) identify the claim and state \(H_{0}\) and \(H_{a}\),

(b) find the critical value,

(c) find the test statistic,

(d) decide whether to reject or fail to reject the null hypothesis,

(e) interpret the decision in the context of the original claim.

Transcribed Image Text:

Student 1 2 3 456 Score on first SAT 300 450. 350 430 300 470 Score on second SAT 300 520 400 410 300 480 Student 7 8 9 10 11 12 Score on first SAT 530 200 200 350 360 250 Score on second SAT 700 250 390 350 480 300