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 observed value of W?
A)24.5
B)52.0
C)53.5
D)54.5

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 observed value of W?
A)24.5 
B)52.0 
C)53.5 
D)54.5

Quizplus · Accepted Answer

To calculate W, we need to rank all 12 seedlings based on their height and add up the ranks for the group treated with Herbicide A. The ranks for the heights of each seedling are:

7, 11, 1.5, 5.5, 3, 9, 6, 10, 2, 12, 8, 4

The sum of the ranks for the Herbicide A group is:

1.5 + 3 + 5.5 + 6 + 7 + 11 = 34.5

Therefore, the observed value of W is 34.5. However, we need to compare this to the expected value of W under the null hypothesis of no difference between the two herbicides to determine if the difference is statistically significant.

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