Help with stats question.?

a)

Let d be the difference between the two levels (plasma and serum samples) and μ(d) be the mean of the differences

H0: μ(d) = 0 ---- null hypothesis

b)

Paired student's t-test

c)

Plasma - serum

44

47

37

24

31

4

-21

15

-3

36

12

30

48

Mean = 23.385

Standard deviation = 20.97

Sample mean = 23.385

Standard deviation = 20.97

Standard error of mean = s / √ n

Standard error of mean = 20.97 / √ 13

SE = 20.97/3.6056

Standard error of mean 5.816

t = (xbar- μ ) / SE

t = (23.385-0) / 5.816

t = 4.0208

(degrees of freedom is 12)

P-value = P( t > 4.0208) = 0.00085 (one-tailed)

d)

There is evidence that concentration of receptor in ligand is higher in the plasma sample.

e)

Paired t-test assume samples are drawn from a normal population. We may use the Wilcoxon-matched-pairs test which is non-parametric.