A cement producer claims that the average weight of a bag of cement is at least 25kg. The weights of bags of cement is assumed to be normally distributed with a standard deviation of 1.2kg. The cement producer tests a random sample of bags to evaluate their claim. The decision rule they adopt is to reject the null hypothesis if the sample mean is 24kg or less.

A. Writethenullandalternativehypothesesforevaluatingtheseclaims.(1point) B. In context of this problem, what is a Type I error? What is a Type II error? (2

points)

C. If the true mean is 23.5kg, what sample size is minimally required to achieve a

power of 0.95? (4 points)

D. Basedonthesamplesizecalculatedinpart(C),whatisthesignificancelevel

associated with the decision rule the cement company has adopted? (3 points)