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

Question

Mathematics

Dominic Thomas

4 March, 22:35

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

+2

Answers (1)

Know the Answer?

Samara Johns · Answer 1

The z statistic is 0.23.

Step-by-step 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