Question

As part of quality control, a pharmaceutical company tests a sample of manufacturer pills to see the amount of active drug they contain is consistent with the labelled amount. That is, they are interested in testing the following hypotheses:

H0:μ=100H0:μ=100 mg (the mean levels are as labelled)

H1:μ≠100H1:μ≠100 mg (the mean levels are not as labelled)

Assume that the population standard deviation of drug levels is 55 mg. For testing, they take a sample of 1010 pills randomly from the manufacturing lines and would like to use a significance level of α=0.05α=0.05.

They find that the sample mean is 104104 mg. Calculate the zz statistic.

−17.89−17.89

−8.00−8.00

−5.66−5.66

−2.53−2.53

−0.80−0.80

0.800.80

2.532.53

5.665.66

8.008.00

17.8917.89

Answer 1

The z statistic is 0.23.

Explanation:

Test statistic (z) = (sample mean - population mean) ÷ sd/√n

sample mean = 104 mg

population mean (mu) = 100 mg

sd = 55 mg

n = 10

z = (104 - 100) ÷ 55/√10 = 4 ÷ 17.393 = 0.23