A manufacturer of potato chips advertises that each bag contains 10 ounces of chips. However, the production lines at the manufacturer (which produce thousands of bags of chips per day) do not always fill each bag with exactly 10 ounces. Throughout the day, quality control staff at the manufacturer select random samples of bags on a selected production line and conduct a hypothesis test with the following null and alternative hypotheses:
If enough evidence is found to reject the null hypothesis in favor of the alternative, the production line is shut down and re-calibrated.
a. Describe a Type II error in the context of the manufacturer’s hypothesis test, and identify a possible consequence of making a Type II error.
b. In a random sample of 35 bags of chips, the mean weight is 9.9 ounces with a standard deviation of 0.45 ounces. At the significance level of 0.05, should the company shut down the production line? Justify your response.