Twenty-five women between the ages of 70 and 80 were randomly selected from the general population of women their age to take part in a special program to decrease reaction time (speed). After the course, the women had an average reaction time of 1.5 seconds. Assume that the mean reaction time for the general population of women of this age group is 1.8, with a standard deviation of .5 seconds. (Also assume that the population is approximately normal.) What should you conclude about the effectiveness of the course?
(a) Carry out a Z test using the five steps of hypothesis testing (use the .01 level).
(b) Make a drawing of the distributions involved.
(c) Explain your answer to someone who is familiar with the general logic of hypothesis testing, the normal curve, Z scores, and probability, but not with the idea of a distribution of means.
(d) Figure the 99% confidence interval and explain your answer to someone who is familiar with the general logic of hypothesis testing, the normal curve, Z scores, probability, and the idea of a distribution of means, but has not heard of confidence intervals.