Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained. Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the Herbicide A group.What is the expected value of W under the null hypothesis that the two distributions are the same?
A)36
B)39
C)54
D)78

Question

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained.  Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the Herbicide A group.What is the expected value of W under the null hypothesis that the two distributions are the same?
A)36 
B)39 
C)54 
D)78

Quizplus · Accepted Answer

Since both groups have 6 observations, and the sum of ranks for all 12 observations would be 1+2+3+...+12 = 78, we would expect each group to have a sum of ranks of 78/2 = 39 under the null hypothesis that the two distributions are the same. Therefore, the expected value of W would also be 39.

Some Researchers Have Conjectured That Stem-Pitting Disease in Peach-Tree Seedlings