Question

At the 0.05 level of significance, is there evidence of a difference in the median yield in the two groups?

With	Without
4.85	4.94
4.74	4.61
5.01	4.69
4.78	4.51
4.93	4.89
5.31	4.57
	4.46

Answer 1

Ho : median difference =   0
Ha : median difference ╪ 0

mann whitney test

Trt A	Trt B	rank for sample 1	rank for sample 2
4.85	4.94	8	11
4.74	4.61	6	4
5.01	4.69	12	5
4.78	4.51	7	2
4.93	4.89	10	9
5.31	4.57	13	3
	4.46		1

Trt A  
sample size ,n1 =    6
sum of ranks, R1 =    56
  
U1 = n1*n2+0.5*n1*(n1+1) - R1 =    7
  
Trt B  
sample size ,n2 =    7
sum of ranks , R2=   35
  
U2 = n1*n2 + 0.5*n2*(n2+1) - R2 =   35
  
test stat , U = smaller of U1 and U2 =    7.00

p value=2*0.0256=0.0512

p value ≥α=0.05, fail to reject ho

There is no enough evidence of significant difference in the median yield in the two groups