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:
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 |
165 |
150 |
115 |
92 |
105 |
121 |
| School B |
94 |
160 |
92 |
107 |
100 |
115 |
| Twin Pair |
7 |
8 |
9 |
10 |
11 |
12 |
| School A |
99 |
115 |
120 |
138 |
126 |
94 |
| School B |
95 |
95 |
125 |
136 |
132 |
108 |
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. Calculate the P-value. Round your answer to four decimal places.
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