The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces. Every box of cereal is not expected to contain exactly the targeted weight, but the average of all boxes filled should. At the end of every shift (eight hours), 16 boxes are selected at random and the mean and standard deviation of the sample are computed. Based on these sample results, the production control manager determines whether the filling machine needs to be readjusted or whether it remains all right to operate. Use α = 0.05.
a. Establish the appropriate null and alternative hypotheses to be tested for boxes that are supposed to have an average of 24 ounces.
b. At the end of a particular shift during which the machine was filling 24-ounce boxes of Mini-Oats, the sample mean of 16 boxes was 24.32 ounces, with a standard deviation of 0.70 ounce. Assist the production control manager in determining if the machine is achieving its targeted average.
c. Why do you suppose the production control manager would prefer to make this hypothesis test a two-tailed test? Discuss.
d. Conduct the test using a p -value.
e. Considering the result of the test, which of the two types of errors in hypothesis testing could you have made?