Problem 4

The production line for the Hersheys Special Dark chocolate bars is designed such that each bar contains at least 45% of cocoa solids. The quality control department at Hershey periodically samples Special Dark bars to ensure that the percentage of cocoa solids is up to the desired cocoa content target. Assume that a sample of 64 Special Dark bars is selected and analyzed. The mean cocoa solids content is found to be 44.3% with a standard deviation of 2%. Hershey strives to produce the highest quality chocolate, hence they want to understand whether the production line of Special Dark bars needs to be adjusted to insure that the bars are up to the desired quality standards (i.e. at least 45% cocoa solids content).For simplicity, use the values 45, 44.3 and 2 (instead of the percentage values) to answer the following. It wont change the meaning of your results.

(a) State the null and alternative hypothesis and explain their meaning. Is this a one-sided or two-sided test? Why?

(b) Let = 0.05. Construct a test to determined whether or not the average cocoa solids content is consistent with the desired quality standards.

(c) Based on the result of your test, provide an explanation and a recommendation to Hershey regarding the production line of their Special Dark chocolate bars. Be specific.