Question

Consider the following data to determine whether there is a significant difference between the values of Group 1 and Group 2. Let the significance level be 5%.

Group 1: 15, 17, 26, 11, 18, 21, 13, 29
Group 2: 23, 14, 24, 13, 22, 23, 18, 21

What rank will be given to the value 15? _______________.

What is the rank sum, W1, of Group 1? (round answer to 1 decimal place) ___________.

What is the value of the test statistic, U? (round answer to 1 decimal place) _____________.

Using the Mann Whitney Table of p-values, what is the p-value for this test? Round your U test statistic up to the next value to locate on the table. (round answer to 4 decimal places) ________________.

Answer 1

Trt A	Trt B	rank for sample 1	rank for sample 2
15	23	5	12.5
17	14	6	4
26	24	15	14
11	13	1	2.5
18	22	7.5	11
21	23	9.5	12.5
13	18	2.5	7.5
29	21	16	9.5

Trt A  
sample size ,n1 =    8
sum of ranks, R1 =    62.5
  
U1 = n1*n2+0.5*n1*(n1+1) - R1 =    37.5
  
Trt B  
sample size ,n2 =    8
sum of ranks , R2=   73.5
  
U2 = n1*n2 + 0.5*n2*(n2+1) - R2 =   26.5
===============

sum of ranks, W1 =    62.5
U =    26.50
p values= 2*0.3227=0.6454