Question

To find out if a new serum will stop leukemia, nine patients are selected who are in an advanced stage of the disease. Five patients receive the treatment and four do not. Survival times, in years, from the moment the experiment begins are

WITH TREATMENT 2.1 | 5.3 | 1.4 | 4.6 | 0.9
WITHOUT TREATMENT 1.9 | 0.5 | 2.8 | 3.1 |

Use the Wilcoxon rank-sum test statistic at a significance level of 0.05 to determine if the serum is effective.

Set the following

to. Null and alternating hypothesis
b. Test statistic
C. Critical Value
d. Decision rule

Answer 1

a)

Ho : median difference =   0
Ha : median difference > 0

A	B	rank for sample 1	rank for sample 2
2.1	1.9	5	4
5.3	0.5	9	1
1.4	2.8	3	6
4.6	3.1	8	7
0.9		2

A      
sample size ,    n1 =    5
sum of ranks ,    R1 =    27
      
B      
sample size ,    n2 =    4
sum of ranks ,   R2 =    18
      
b) test stat W=R1= 27

c) critical value=8

d) decision rule : reject Ho if test stat ≤8

Since in this case R = 27 >8, we do not reject Ho