For each of the following samples that were given an experimental treatment, test whether they represent populations that score significantly higher than the general population:
(a) A sample of 100 with a mean of 82.
(b) A sample of 10 with a mean of 84. The general population of individuals has a mean of 81, a standard deviation of 8, and follows a normal curve. For each sample, carry out a Z test using the five steps of hypothesis testing with a one-tailed test at the .01 significance level, and make a drawing of the distributions involved.
(c) Figure the 99% confidence interval for parts (a) and (b).