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Problem 5 (Type II error, P-value, Sample Size Selection). A machine is used to fill containers with a liquid product. Fill volume can be assumed to be normally distributed. You realized that you lost the manual of your machine. A random sample of ten containers is selected, and the net contents (oz) are as follows: 12.03,12.01,12.04,12.02,12.05,11.98,11.96,12.02,12.05, and 11.99. (a) Suppose that the manufacturer wants to be sure that the mean net contents are 12.00oz. Population standard deviation is known be 0.02. What conclusions can be drawn from the data? (b) Find the p value for this test (a). (Remark: We will study the concept of p-value on Sep. 20th ) (c) Suppose that the manufacturer wants to be sure that the mean net contents are 12 oz. However, the mean net contents are actully 12.02oz. You can assume that the process standard deviation is 0.02. The type I error probability is specified as =0.05. Find type II error probability ( ). (d) Like (a), if the true mean is really 12.02, what is the sample size to be used to ensure that the type II error probability () is no greater than 0.2 ? The type I error probability is still specified as =0.05 and the process standard deviation is 0.02