An agency offers preparation courses for a graduate school admissions test to students. As part of an experiment to evaluate the merits of the course, 40 students were chosen and divided into 20 pairs in such a way that the members of any pair had similar academic records. Before taking the test, one member of each pair was assigned at random to take the preparation course, while the other member did not take a course. The achievement test scores are contained in the accompanying table. Assuming that the differences in scores follow a normal distribution, test at the 5% level, the null hypothesis that the two population means are equal against the alternative that the true mean is higher for students taking the preparation course. E Click the icon to view the data table. E Click the icon to view the critical values of the Student's t distribution. Let u, be the mean test scores for those who took the preparation course and let u, be the mean test scores for those who did not take the course. Determine the null and alternative hypotheses. Choose the correct answer below OC. Họ: H1 - H2 =0 Achievement test scores O B. Ho: H1 - H2 <0 O A. Ho: H1 -H2 50 H: -2>0 0+ Z1 - :H O E. Ho: H1 -H220 H,: H1 -42 <0 OF. Ho: H1 - H2>0 H;: H1 -2 s0 OD. Ho: H-42 #0 Sample Took course Did not take course 94 H;: P -P2 =0 1 96 The test statistic is t= 81 82 71 (Round to three decimal places as needed.) 3 73 4 60 78 The critical value(s) is(are) (Round to three decimal places as needed. Use a comma to separate answers as needed.) 72 58 6. 80 70 7 91 86 Determine the correct conclusion. 74 61 V There is V evidence that the true mean is higher for students taking the preparation course. 68 52 the null hypothesis since the test statistic is 86 10 79 11 83 74 12 67 50 13 88 82 14 76 64 15 75 62 16 99 98 17 92 88 Click to select your answer(s). 18 61 81 19 79 68 20 69 53