An instructor for a test preparation course claims that the course will improve the test scores of students. The table shows the critical reading 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 Student 2 3 4 5 6 7 8 9 10 11 12 13 14 Score on first test 542 387 511 414 458 524 533 336 631 627 524 530 459 390 Score on second test 551 404 526 456 404 541 499 338 659 649 546 541 493 433 (b) Find the critical value(s) and identify the rejection region(s). to = (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> 3.012 O B. t 3.012 O C. t 2.650 (c) Calculate d and sa. MacBook Air esc ". . F1 F2 20 F3 F4 F5 F6 F7An instructor for a test preparation course claims that the course will improve the test scores of students. The table shows the critical reading 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 Student 2 3 4 5 6 7 8 9 10 11 12 13 14 Score on first test 542 387 511 414 458 524 533 336 631 627 524 530 459 390 Score on second test 551 404 526 456 404 541 499 338 659 649 546 541 493 433 (c) Calculate d and sa a= (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. (Type an integer or a decimal. Round to three decimal places as needed.) MacBook AirScore on second test 551 404 526 456 404 541 499 338 659 649 546 541 493 433 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. The sample was not large enough to make a conclusion. O B. At the 1% significance level, there is enough evidence that the students' critical reading scores improved the second time they took the test. O C. At the 1% significance level, there is evidence that the students' critical reading scores got worse the second time they took the test O D. At the 1% significance level, there is not enough evidence that the students' critical reading scores improved the second time they took the test MacBook Air O F2 20 F3 F4 F5 F6 F7 FB @ # $ % & NO 4 5 8An 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 (1) Student 9 10 12 13 14 Score on first test 542 387 511 414 458 524 533 336 631 627 524 530 459 390 Score on second test 551 404 526 456 404 541 499 338 659 649 546 541 493 433(a) Identify the claim and state Ho and Ha. The claim is "The students' critical reading test scores the second time they took the test." Let u. be the hypothesized mean of the students' first score minus their second score. State Ho and Ha. Choose the correct answer below. O A. Ho: Ha #0 OB. Ho: Ha 2d O C. Ho: Ha 20 Ha : Ha = 0 Ha: Ha d Ha : H. >0