8. Suppose you work for the Food and Drug Administration and receive a complaint

Question

8. Suppose you work for the Food and Drug Administration and receive a complaint that the Nosleepem Company is not putting enough caffeine into its anti-drowsiness pills. You have an employee obtain a random sample of 49 pills bottles and take one pill randomly from each. The bottles state that there are 100 milligram of caffeine in each pill. Your laboratory tests the pills and finds the pills average 97.8 milligrams of caffeine with a standard deviation of 5.2 milligram. Your employee comes to you and claims the pills have less than 100 milligrams of caffeine and you should file a lawsuit. You require 99% confidence before going to court.

a. State your employee’s claim using mathematical symbols (i.e., using >, <, =, µ, s, p, etc.).
b. State the null hypothesis for this claim using mathematical symbols.
c. State the alternative hypothesis for this claim using mathematical symbols.
d. If you were working the problem by using one of the tables in the book, which one would you use? If degrees of freedom are involved in using that table, state the degrees of freedom. If not, state that the degrees of freedom don’t apply.
e. Draw the distribution curve for this problem, showing the critical area, the percent of the curve under the critical area, the critical values that form the boundary for the critical area, and the value of the test statistic.
f. Based on this data, who is your employee correct? Should you file a lawsuit? Use complete and logical sentences and relate your answer to rejecting or failing to reject the null hypothesis.

Explanation / Answer

Given n=49, xbar=mean=97.8, s=5.2

The test hypothesis is
Ho:>=100
Ha:<100

The test statistic is

Z=(xbar - )/(s/n)

=(97.8 - 100)/(5.2/sqrt(49))

=-2.96

Given =0.01, the critical value is Z(0.01)=-2.326 (check normal table)

Since Z=-2.96<-2.326, we reject Ho. So we conclude that the pills have less than 100 milligrams of caffeine.

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