Question

The label on the cold medicine Dozenol lists 600 mg of acetaminophen per fluid ounce as an active ingredient. The FDA tests 64 one-ounce portions of the medicine and finds that the mean amount of acetaminophen for this sample is 589 mg with a standard deviation of 21 mg. Test the claim of the FDA that the medicine does not contain the required amount of acetaminophen. Use a 0.05 level of significance.

a. Identify the null and alternate hypothesis.

b. Identify whether this test is left-tailed, right-tailed, or two-tailed and the appropriate critical value(s).

c. Calculate the t-score.

d. State your conclusion.

Answer 1

a) Null and alternative hypothesis:

b) The test us two-tailed

At = 0.05 and df = 64-1= 63, critical value, = T.INV.2T(0.05,63) = 1.998

c) Test statistic:

d) Conclusion:

As |t| = 4.190 > 1.998, we reject the null hypothesis. There is enough evidence to claim that the medicine does not contain the required amount of acetaminophen at 0.05 level of significance.