Question

&8.3.10 that their scores improved the second time they took the test? Assume the samples are random and dependent and the population is normally distributed. Complete Score on first test 431357 433 468 591 522 572 556 523 563 411 568 562 Question Help The table below shows the critical reading scores for 14 students the rst two times they took a standar oed test A O? is there enough evidence to con , a ude parts (a) through (f) Student 12 3 4 5 67 8 9 10 11 12 13 14 ore on second test 1434359 449 503 540 567 539 557 537 575 442 579 580 500 (a) Identfy the claim and state Ho and Ha claim is "The students' critical reading test scores improved the second time they took the test. Let ug be the hypothesized mean of the the students' first score minus their second score, State Ho and Ha Choose the correct answer below Ha Ha O (b) Find the critical value(s) and identify the rejection region's) Use a comma to separate answers as needed. Type an integer or a decimal Round to three decimal places as needed.)

Answer 1

Given that: - X: Score on first test Y: Score on second test a) To test hypothesis that H_0: mu_d greaterthanorequalto 0 vs H_1: mu_d < 0 To test statistic, T_cal = d^-/S.E(d^-) where d^- = x_i - y_i \r\n and SE(d^-) = Sd/squareroot n Where S_d is std dev of the difference Difference d = -3, -2, -16, -35, 51, -45, 33, -1, -14, -12, -31, -11, -18, -35 Where X^- Sigma X_i/n = 508.714 gamma^- = Sigma y_i/n = 518.643 and d^- = Sigma d_i/n = -9.929 S_d^- = squareroot Sigma (d_i - d^-)^2/n - 1 = squareroot 8800.9286/14 - 1 = 26.0191 SE(d^-) = Sd/squareroot n = 26.0191/squareroot 14 = 6.9539 Test statistic: - T_cal = d^-/SE(d^-) = -9.929/6.9539 = -1.428 Decision Rule: - This is right tail test Hence Reject H_0 if t_cal > t_critical from t - table we can find critical value at 13 degrees of freedom. \r\n where t_critical = 2.65 (from table) Decision: - Here t_cal < t_critical Rightarrow we fail to reject H_0 at alpha = 0.01