Question

The carapace lengths (in mm) of crayfish were recorded for samples from two sections of a stream

in Kansas.

section1 5, 11, 16, 8, 12

section2 17, 14,15, 21,19, 13

1. Use the data in problem 4 for the following:

a. For the Wilcoxon Rank-Sum Test Statistic, W, compute E(W) and Var(W).

b. Compute the Z-score for the normal approximation for the data provided in the text.

c. Give the approximate p-value for a two-sided test (you do not need to show all steps of the test) and compare with the two-sided exact p-value of 0.030.

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Answer 1

A	B	rank for sample 1	rank for sample 2
5	17	1	9
11	14	3	6
16	15	8	7
8	21	2	11
12	19	4	10
	13		5

A      
sample size ,    n1 =    5
sum of ranks ,    R1 =    18
      
B      
sample size ,    n2 =    6
sum of ranks ,   R2 =    48
      
a)

W=sum of ranks for smaller sample size =       18
      
mean ,µ =    n1(n1+n2+1)/2 =    30

Variance=(n1*n2*(n1+n2+1)/12) = 30
      
std dev,σ =    √(n1*n2*(n1+n2+1)/12) =   5.4772
      
b)

Z-stat =    (W - µ)/σ =    -2.1909
      
a)
      
P-value =        0.0285