A manufacturer of chocolate candies uses machines to package candies as they move along a filling line

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A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the package to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that a particular sample of 50 packages, the mean amount dispersed is 8.159 ounces with a sample standard deviation of 0.051 ounces.

1. Is there evidence that the population mean amount is different from 8.17 ounces? Use an ? = 0.05 level of significance.

a. State the null and alternative hypotheses

b. State the decision rule

c. Compute the test statistic

d. State the decision

2. Determine the p-value and interpret its meaning

3. Based on your findings, what conclusions do you reach? How is this data useful for effective managerial decision-making?