Question

1. A simple random sample of size 19 is taken from a Normal population (given below).

11.3 12.0 10.1 10.3 13.5 10.8 13.7 12.8 11.9 10.7 11.0 11.6 10.1 11.7 10.6 12.0 11.7 13.1 11.3

a) Build a 94% confidence interval for the unknown population mean. Show your work.

b) Does the above interval provide evidence that the true mean is different from 11? Explain your answer.

2. Using the scenario in problem 1, conduct the following tests.

a) Test (at the 7.25% level) whether there is sufficient evidence to conclude that the true mean is greater than 11.25 using the rejection region approach.

b) Test (at the 12.5% level) whether there is sufficient evidence to conclude that the true mean is different than 11.5 using the p-value approach.

3. At the 2% level, use the data from problem 1 to test whether it is reasonable to believe that the true population variance is larger than 1.

4. Using the scenario from problem 3, do the following.

a) Derive the power function. Show your work.

b) Using R, graph the power function for 0.5 < sigma^2 < 3.5.

c) Pretend that the sample size was actually 56. Plot this power function on the same graph.

d) Based on the power functions graphed in c, why is the test described in part c "better" than the original test? Explain your answer using the power functions.

Answer 1