A treatment is administered to a sample of N = 16 individuals. The treatment population has unknown mean, but has a known standard deviation of = 8. The sample mean is found to be X = 33. (a) Compute a 95% confidence interval for , the mean of the treatment population. (b) Define H0 : = 30 and H1 : > 30. What is the probability of observing a sample mean X = 33 or larger if H0 is true? (c) Given the results of (a) and (b), can we reject H0 in favor of H1? Why or why not?

3. A treatment is administered to a sample of N = 25 individuals. The treatment population has unknown mean, but has a known standard deviation of = 5. The sample mean is found to be X = 44. (a) Compute a 95% confidence interval for , the mean of the treatment population. (b) Define H0 : = 40 and H1 : > 40. What is the probability of observing a sample mean X = 44 or larger if H0 is true? (c) Given the results of (a) and (b), can we reject H0 in favor of H1? Why or why not?