Question: A random sample is selected from a normal population with a mean of µ = 40 and a standard deviation of ? =10. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 42.

a. How large a sample is necessary for this sample mean to be statistically significant? Assume a two tailed test with α = .05

b. If the sample mean were M = 41, what sample size is needed to be significant for a two-tailed test with α = .05.