To compare two elementary schools regarding teaching of reading skills, 12 sets of identical twins were used. In each case, one child was selected at random and sent to school A, and his or her twin was sent to school B. Near the end of fifth grade, an achievement test was given to each child. The results follow: Twin Pair 1 2 3 4 5 6 School A 169 157 115 99 119 113 School B 123 157 112 99 121 122 Twin Pair 7 8 9 10 11 12 School A 120 121 124 145 138 117 School B 153 90 124 140 142 102 Suppose a sign test for matched pairs with a 1% level of significance is used to test the hypothesis that the schools have the same effectiveness in teaching reading skills against the alternate hypothesis that the schools have different levels of effectiveness in teaching reading skills. Let p denote portion of positive signs when the scores of school B are subtracted from the corresponding scores of school A. Verify that the sample test statistic is . Calculate the P-value. Round your answer to four decimal places.
To compare two elementary schools regarding teaching of reading skills, 12 sets of identical twins were used. In each case, one child was selected at random and sent to school A, and his or her twin was sent to school B. Near the end of fifth grade, an achievement test was given to each child. The results follow:
| Twin Pair |
1 |
2 |
3 |
4 |
5 |
6 |
| School A |
169 |
157 |
115 |
99 |
119 |
113 |
| School B |
123 |
157 |
112 |
99 |
121 |
122 |
| Twin Pair |
7 |
8 |
9 |
10 |
11 |
12 |
| School A |
120 |
121 |
124 |
145 |
138 |
117 |
| School B |
153 |
90 |
124 |
140 |
142 |
102 |
Suppose a sign test for matched pairs with a 1% level of significance is used to test the hypothesis that the schools have the same effectiveness in teaching reading skills against the alternate hypothesis that the schools have different levels of effectiveness in teaching reading skills. Let p denote portion of positive signs when the scores of school B are subtracted from the corresponding scores of school A. Verify that the sample test statistic is . Calculate the P-value. Round your answer to four decimal places.
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