Human chorionic gonadotropin (hCG) is naturally occurring substance that has bee

Question

Human chorionic gonadotropin (hCG) is naturally occurring substance that has been abused by some atheletes 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 analysis method. The first laboratory obtains a mean hCG level of 2.99 IU/L (n_1= 4) with a standard deviation of 0.06 IU/L, while the second laboratory reports a mean level of 3.13 IU/L (n2= 5) with a standard deviation of 0.08 IU/L. Are these mean results the same at the 95% confidence level?

Explanation / Answer

standard error of the mean = standard deviation/Sqrt(n), n= no of samples

for sample 1, standard error of the mean = 0.06/sqrt(4) = 0.03 for the second sample it is = 0.08/sqrt(5)=0.036

for sample, 1 lower limit at 95% confidence interval = mean- 1.96*std. error of the mean = 2.99-1.99*0.03=2.9303 and upper limit = 2.99+1.99*0.03=3.05

for sample2, lower limit = 3.13-1.96*0.036= 3.06 and upper limit = 3.13+1.96*0.036=3.2

The results are not same as shown by the bounds

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