To compare two elementary schools regarding teaching of reading skills, 12 sets

Question

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 win Pair 12 168 128 11599 119 113 School B win Pair School A hool B 7 891012 120 121132 145 138 117 05 90124 142 148 104 10s Suppose a sign test for matched pairs with a 10% 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. State the conclusion of the test and interpret your results with a 10% level of significance Since the P-value is less than the given level of significance, the data are not statistically significant. Based on this, we reject the null hypothesis Since the P-value is less than the given level of significance, the data are statistically significant. Based on this, we do not reject the null hynothesis Since the P-value is greater than the given level of significance, the data are not statistically significant. Based on this, we do not reject the null hypothesis d. Sinoe the P-value is less than the given level of significance, the data are not statistically significant. Based on this, we do not reject the null hypothesis.

Explanation / Answer

we shall analyse this quickly in open source statistical package R , the snippet is as follows

We shall perform a sign rank test in R using the wilcox.test function

SchoolA <- c(168,128,115,99,119,113,120,121,132,145,138,117)
SchoolB <- c(123,142,110,110,120,122,105,90,124,142,148,104)

wilcox.test(SchoolA,SchoolB,paired = TRUE)

tHE RESULT OF THE TEST IS

wilcox.test(SchoolA,SchoolB,paired = TRUE)

   Wilcoxon signed rank test

data: SchoolA and SchoolB
V = 50, p-value = 0.4238 , as the p value is not less than 0.1 (level of significance) hence we fail to reject the null hypothesis. Hence the correct answer is C
alternative hypothesis: true location shift is not equal to 0

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