An experiment is conducted to compare two brands of fertiliz

An experiment is conducted to compare two brands of fertilizers. In a random sample of 12 rose bushes, 6 were randomly selected to receive brand A and the other 6 received brand B with the following results:

Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to brand A. What is the expected value of W under the null hypothesis that the distributions are the same?

Brand A	76	82	80	75	76	80
Brand B	76	76	75	77	78	73

Solution

n

sum of ranks

6

46.5

Brand A

6

31.5

Brand B

12

78

total

No.

Label

Data

Rank

1

Brand A

76

5.5

2

Brand A

82

12

3

Brand A

80

10.5

4

Brand A

75

2.5

5

Brand A

76

5.5

6

Brand A

80

10.5

7

Brand B

76

5.5

8

Brand B

76

5.5

9

Brand B

75

2.5

10

Brand B

77

8

11

Brand B

78

9

12

Brand B

73

1

Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to brand A. What is the expected value of W under the null hypothesis that the distributions are the same?

the expected value of W under the null hypothesis that the distributions are the same =46.5

	n	sum of ranks
	6	46.5	Brand A
	6	31.5	Brand B
	12	78	total
No.	Label	Data	Rank
1	Brand A	76	5.5
2	Brand A	82	12
3	Brand A	80	10.5
4	Brand A	75	2.5
5	Brand A	76	5.5
6	Brand A	80	10.5
7	Brand B	76	5.5
8	Brand B	76	5.5
9	Brand B	75	2.5
10	Brand B	77	8
11	Brand B	78	9
12	Brand B	73	1