Is a new method of teaching reading to first graders (Method B) more effective than the method now in use (Method A)? You design a matched pairs experiment to answer this question. You form 20 pairs of first graders, with two children in each pair carefully matched by IQ, socioeconomic status, and reading-readiness score. You assign at random one student from each pair to Method A. The other student in the pair is taught by Method B. At the end of the first grade, all the children take a test to determine their reading skill. Assume that the higher the score on this test, the more proficient the student is at reading. Let p stand for the proportion of all possible matched pairs of children for which the child taught by Method B has the higher score. Your hypotheses are Ho: p = 0.5 (no difference in effectiveness) Ha:p > 0.5 (Method B is more effective) 12 = 0.6. 20 The result of your experiment is that Method B gave a higher score in 12 of the 20 pairs, or p If Ho is true, the 20 pairs of students are 20 independent trials with probability 0.5 that Method B "wins" each trial (is the more effective method). Use Table A, starting at line 105, to simulate 10 repetitions of the experiment. Estimate from your simulation the probability that Method B will do better (be the more effective method) in 12 or more of the 20 pairs when Ho is true. (Of course, 10 repetitions are not enough to estimate the probability reliably. Once you understand the idea, more repetitions are easy.) The assignment of digits for the results of the reading skill test: • One digit represents which method is more effective for one randomly chosen pair of children. Assign 0, 1, 2, 3, 4 to "Method A wins a trial," 5, 6, 7, 8, 9 to "Method B wins a trial." (Use decimal notation. Give your answer as an exact number.) probability: Table A: 105 95592 94007 69971 91481 60779 53791 17297 59335 106 68417 35013 15529 72765 85089 57067 50211 47487 107 82739 57890 20807 47511 81676 55300 94383 14893 108 60940 72024 17868 24943 61790 90656 87964 18883 109 36009 19365 15412 39638 85453 46816 83485 41979 110 38448 48789 18338 24697 39364 42006 76688 08708 111 81486 69487 60513 09297 00412 71238 27649 39950 112 59636 88804 04634 71197 19352 73089 84898 45785 113 62568 70206 40325 03699 71080 22553 11486 11776 114 45149 32992 75730 66280 03819 56202 02938 70915 115 61041 77684 94322 24709 73698 14526 31893 32592 116 14459 26056 31424 80371 65103 62253 50490 61181 117 38167 98532 62183 70632 23417 26185 41448 75532 118 73190 32533 04470 29669 84407 90785 65956 86382 119 95857 07118 87664 92099 58806 66979 98624 84826 120 35476 55972 39421 65850 04266 35435 43742 11937 121 71487 09984 29077 14863 61683 47052 62224 51025 122 13873 81598 95052 90908 73592 75186 87136 95761 123 54580 81507 27102 56027 55892 33063 41842 81868 124 71035 09001 43367 49497 72719 96758 27611 91596 125 96746 12149 37823 71868 18442 35119 62103 39244 126 96927 19931 36809 74192 77567 88741 48409 41903 127 43909 99477 25330 64359 40085 16925 85117 36071 128 15689 14227 06565 14374 13352 49367 81982 87209 129 36759 58984 68288 22913 18638 54303 00795 08727 130 69051 64817 87174 09517 84534 06489 87201 97245 131 05007 16632 81194 14873 04197 85576 45195 96565