A random sample is selected from a normal population with a mean of m = 40 and a standard deviation of s = 10. After a treatment is administered to the individuals in the sample, the sample mean is...

A random sample is selected from a normal population with a mean of m = 40 and a standard deviation of s = 10. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 46.

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

b. If the sample mean were M = 43, what sample size is needed to be significant for a two-tailed test with a = .05?