Question

1. a) Suppose average monthly sales for retail locations across the United States are approximately normally distributed with variance σ^2= 5200. We took a sample of size 50 and found ̄x= 12018,  Using this, conduct a hypothesis test with α= 0.05 to test the null hypothesis that the mean is 12000 vs. the alternative hypothesis that it is not. For full credit, state the null and alternative hypothesis, the test statistic, the rejection region, and your conclusion.

b)Using the setup from part a, if we know that the true mean is 12030, what is the probability of a type II error?

c)Using the setup from part a, what would be the p-value of this test? Would you reject the null hypothesis if α= 0.01? How about if α= 0.1

d)Using the set up from part a, perform the hypothesis test again, but now use the alternative hypothesis that the mean is actually greater than 12000.

e)Using the setup from part a, if we know the true mean is 12030 and we want the probability of a type I error to be 0.05 and the probability of a type II error

to be 0.10, what is the minimum sample size required to ensure this?

Answer 1