An instructor for a test preparation course claims that the course will improve the test scores of students. The table shows the critical reading scores for 14 students the first two times they took the test. Before taking the test for the second time, the students took the instructor's course to try to improve their critical reading test scores. At a = 0.01, is there enough evidence to support the instructor's claim? Complete parts (a) through (f). Student Score on first test 10 11 12 13 14 0 384 450 400 585 556 351 409 590 386 584578 400 355 414 Score on second test 393 515 462 632 488 377 362 702 447 662 617 431 384 453 1 2 3 6 7 8 (a) Identify the claim and state H, and Ha. The claim is "The students' critical reading test scores the second time they took the test." Let H. be the hypothesized mean of the students' first score minus their second score. State Ho and Ha. Choose the correct answer below. OC. Ho: Hd 20 O A. Ho: Hd s0 Ha: Hd >0 O B. Ho: Hd sd Ha: Hd >d Hai Ha Prt :H (b) Find the critical value(s) and identify the rejection region(s). to =U (Use a comma to separate answers as needed. Type an integer or a decimal. Round to three decimal places as needed.) Identify the rejection region(s). Choose the correct answer below. O A. t < -2.650 O B. t> 3.012 OC. t < -2.650 or t> 2.650 O D. t < - 3.012 or t> 3.012 (c) Calculate d and sa. (Type an integer or a decimal. Round to three decimal places as needed.) Calculate sa. (Type an integer or a decimal. Round to three decimal places as needed.) (d) Use the t-test to find the standardized test statistic t. %3D (Type an integer or a decimal. Round to three decimal places as needed.) (e) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below. Reject the null hypothesis. Fail to reject the null hypothesis. (f) Interpret the decision in the context of the original claim. Choose the correct answer below. O A. At the 1% significance level, there is evidence that the students' critical reading scores got worse the second time they took the test. OB. The sample was not large enough to make a conclusion. C. At the 1% significance level, there is not enough evidence that the students' critical reading scores improved the second time they took the test. O D. At the 1% significance level, there is enough evidence that the students' critical reading scores improved the second time they took the test.