Human chorionic gonadotropin hCG is a naturally occurring su

Human chorionic gonadotropin (hCG) is a naturally occurring substance that has been abused by some athletes because of its ability to stimulate testosterone production. Two laboratories that conduct drug testing are to be evaluated for their ability to measure this hormone by using the same sample and analytical method. The first laboratory obtains a mean hCG level of 2.99 plusminus 0.06 |U/| (n = 4), while the second laboratory reports a mean level of 3.13 plusminus 0.08 |U/| (n = 5). a) Are these mean results the same at the 95% confidence level? b) Are these mean results the same at the 99% confidence level?

Solution

n=number of points here, s=>sample ,s(x\')=mean sample

a)

s(x\')=s/sqrt(n)     , we have n=4, s=0.06

s(x\')=0.06/sqrt(4)=0.06/2=0.03

CI(c0nfidence interval)=2.99+-(t-s(x\'))->A

t=2.776 at 95%

=>CI=2.99+-(2.776-0.06)=>2.99+- 2.73IU/l

This is the mean result at 95%confidencelevel=>=>CI=2.99+-(2.776-0.06)=>2.99+- 2.73IU/l

b)On the other hand for 99% we will change the value of t=4.032and put this in equation A

CI=>2.99+-(t-s(x\'))=>2.99+-(4.032-0.03)=2.99+-4.002IU/L

This shows the results are not same at both the levels at all.