You test a hypothesis that μ S 60 liters. Your sample size is 16 shipments, sample mean is 68, and population standard deviation is 12. You find the critical value of 66 and reject the null. (a) Draw the density of liters. Mark up the critical value, the sample mean, the hypothesis about the population, and the probability of committing a Type I error. Indicate the non-rejection interval. Explain why you rejected the null. (b) Let's consider the probability of Type Il error if the true population mean is true = 66 liters. Convert the critical value to a CDF using the sampling distribution of the true mean. (c) Take your non-rejection Interval from (a) and find how much probability mass, (as the difference of CDFs) is in it. Draw the sampling distribution centered on the true mean. Show the probability of Type Il error on your graph.

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