## Non parametric and F test!!!

morning mathematicians, i have this question i have a answer but im not sure that my method is completly correct!! if anyone could have a quick check ill be happy.

The question is as follows---
18 of the subjects are selected for a particular study. The value recorded for each is the % improvement over the 4 week period in their time for running 400 metres. 8 of these subjects (group A) were in the group which the doctor did not expect to benefit from the training. results were as follows!
sample mean sample variance
Group A 11 7 13 8 32 13 22 6 14 78.29
Group B 15 11 19 21 16 9 14 13 17 20 15.5 15.17

i) use a F test to determine wheter its reasobale to assume that the underlying pop have same variances
for this 1 i did as follows
Null Hypothese : variance A = Variance B
Alt Hypothses : Variance A doesnt equal Variance B

F test = Variace of A/variance of B
F test= 78.29\15.17
F test= 5.1608 (4dp)

Test statisitc at 5 percent two tail test= 4.197

5.1608 > 4.197 therefor we reject the null hypotheses.

ii) carry out a suitable non parametric test procedure to test whether the subjects in group A showed less improvement that those in group B.

group A rank sum=62.5
group b rank sume=108.5

test Null Hypothese: A=b
Alt Hypothese: A<B

if m is less than or equal to n , where m=8 and n=10 hence

mean= 0.5 * 8 *(8+10+1) mean=116
variance= (1/12 ) * 8 * 10 *(8+10+1) = 126.6666666

using normal approx X~(116, 126.6666)
z=(62.5 -116)/SQRT(126.666`)
z=-4.75360(5dp)
there was no sig level given so i tested at 5% so Z test=1.6449
so we cannot reject at the 5% level so we accept null hypotheses

thanks guys