Question

A researcher wants to know if the length of sentences received for a particular type of crime was the same for men and women. The length of sentence received was recorded for a random sample of men and women. The data, in years, are listed below. Use the Wilcoxon rank sum test to test the claim that there is no difference between the sentences received by men and the sentences received by women. Use α = 0.05. Men 6 18 12 14 15 22 10 18 8 15 19 20 Women 5 8 5 10 22 8 30 4 6 9 13 23

Answer 1

SOLUTION:-

2. H0: there is no difference between the sentences received by men and The sentences received by women.

H1: there is difference between the sentences received by men and sentences received by women.

Let the Los be alpha = 5%

From given data

			Ranks
S.No	Men	Women	R1	R2
1	6	5	4.5	2.5
2	18	8	17.5	7
3	12	5	12	2.5
4	14	10	14	10.5
5	15	22	15.5	21.5
6	22	8	21.5	7
7	10	30	10.5	24
8	18	4	17.5	1
9	8	6	7	4.5
10	15	9	15.5	9
11	19	13	19	13
12	20	23	20	23
		Total:-	174.5	125.5
		Count:-	12	12

W = Min(174.5,12.5,5) =125.5

W^{​​​​​​'} = n_{​​​​​​1}(n_{​​​​​​1} ​​+ _{​​​​​​}​​​​​​n_{​​​​​​2} +1) - W = 12(12+12+1) - 125.5 = 174=5

E(W') = n_{​​​​​​1}(n_{​​​​​​1}+n_{​​​​​​2}+1)/2 = 12(12+12+1) /2 =150

Var(W') = n_{​​​​​​1}​​​​​n_{​​​​2} (n_{​​​​​​1}+n_{​​​​​​2}+1)/12 = 12*12(12+12+1)/12 = 300

ZTest statistic

Z = [w' - E(w)]/[SD(w)] = (174.5-150)/√300 = 1.41451

Table : Z = Distribution

P - Value: 0.157213

Here P-Value > alpha 0.05 so we accept H0

Thus we conclude that there is no difference between the sentences received by men and The sentences received by women