Question: Under some circumstances a 6-point treatment effect can be very large, and in some circumstances it can be very small. Assume that a sample of n =16 individuals is selected from a population with a mean of \(\mu \) =70. A treatment is administered to the sample and, after treatment, the sample mean is found to be M =76. Notice that the treatment appears to have increased scores by an average of 6 points.

a. If the population standard deviation \(\sigma =\) 20, is the 6-point effect large enough to be statistically significant? Use a two-tailed test with \(\alpha \) = .05.

b. If the population standard deviation is \(\sigma =\) 8, is the 6-point effect large enough to be statistically significant? Use a two-tailed test with a = .05.