4. A production line is designed to fill cartons with detergent to a mean weight of 0.75 kg. A sample of cartons is periodically selected and weighed to determine whether under- filling or over-filling is occurring. If the sample data lead to a conclusion of under-filling or over-filling, the production line will be shut down and adjusted. Suppose a sample of n = 50 cartons yields a sample mean X = 0.743 kg. Assume the population standard deviation of carton weights is Psigma = 0.009 kg. Write the hypotheses test and compute the value of the test statistic. b. What is the p-value? c. At a = 0.01, what is your conclusion? d. What is a Type I error in this situation? What are the consequences of making this error? What is a Type ll error in this situation? What are the consequences of making this error?

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