An instructor for a SAT preparation course claims that the course will improve the test scores of students. The table shows the critical reading scores for 10 students the first two times they took the SAT. Before taking the SAT for the second time, the students took the instructor’s course to try to improve their critical reading SAT scores. At α = 0.01, is there enough evidence to support the instructor’s claim?

(a) Identify the claim and state H₀ and H_a,

(b) Find the critical value(s) and identify the rejection region(s),

(c) Calculate d̅ and s_d,

(d) Find the standardized test statistic t,

(e) Decide whether to reject or fail to reject the null hypothesis, and

(f ) interpret the decision in the context of the original claim. Assume the samples are random and dependent, and the populations are normally distributed.

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Student 1 3 4 5 7 8 10 Score (first) 300 450 350 430 300 470 420 370 320 410 Score (second) 400 520 400 490 340 580 450 400 390 450 2.