Question

A chemistry lab is conducting quality control tests on a drug. A single dosage of the drug should contain 8 mg of active ingredient. Of course, there will be a small amount of variability due to imperfections in the production process, bu the mean of all dosages produced should be 8 mg with a standard deviation of 0.2 mg. In 40 random dosages, the mean amount of active ingredient is 8.1 mg. Does the data suggest that the mean amount of active ingredient in all dosages produced is different from 8 mg?

Answer 1

Populaiton Mean   = 8 mg

Population Standard Deviation = 0.2 mg

Sample Size n = 40

Sample Mean = 8.1 mg

Since we have Population standard Deviation we will use Z test.

To Test:-

H₀ :- Average amount of active ingredient in all dosages produced is equal to 8 mg

= 8 mg

H₁ :- Average amount of active ingredient in all dosages produced is different than 8 mg

8 mg

Test Statistic:-

Z = (8.1 - 8) / (0.2/ ) = 3.16

Z = 3.16

Test Criteria :-

Reject Null hypothesis if |Z| > Z_/2

Z_/2 = Z _0.05/2 = Z_0.025 = 1.96 Considering = 0.05

|Z| > Z_/2 = |3.16| > 1.96, hence reject Null Hyothesis

Conclusion :- Accept Alternative Hypothesis

Average amount of active ingredient in all dosages produced is different from 8 mg

8 mg