A researcher conducts an experiment on the IQ of one hundred randomly selected only children and finds that their average IQ is 145. Test the hypothesis that the IQ of only children is below 150 at a level of significance of 5 percent. A previous study concluded that the population variance is 81 points.
a. Construct the power curve of this test at u=148, u=146 and u= 144.
b. What is the probability of a Type II error if the true value of only children IQ's is 144.
c. If you require that the Type II error at u=144 and the Type I error be equal, then what sample size should you use to conduct any subsequent test?