Question

Suppose we are interested in whether there is a dierence between the median numbers of hours spent each week by men and woman watching television. Two random samples were taken: the numbers of hours taken by men and women watching television are shown below. You are about to test the null hypothesis that there is no dierence in weekly television watching hours between men and woman. Men: 5 10 12 15; Women: 0 7 4 3 6 8

a) calculate the rank sum for the smaller sample;

b) calculate the z statistic to test the null hypothesis;

c) what is the p value according to the above test?

d) give the possible range for the rank sum for the smaller sample;

Answer 1

A	B	rank for sample 1	rank for sample 2
5	0	4	1
10	7	8	6
12	4	9	3
15	3	10	2
	6		5
	8		7

A      
sample size ,    n1 =    4
sum of ranks ,    R1 =    31
      
B      
sample size ,    n2 =    6
sum of ranks ,   R2 =    24
      
a) W=sum of ranks for smaller sample size =       31
b)

mean ,µ =    n1(n1+n2+1)/2 =    22
      
std dev,σ =    √(n1*n2*(n1+n2+1)/12) =   4.6904
      
Z-stat =    (W - µ)/σ =    1.9188

c) P-value =        0.0550

d) sum of ranks for smaller sample size = 31