An instructor has decided to introduce a greater component of independent study into an intermediate microeconomics course as a way of motivating students to work independently and think more carefully about the course material. A colleague cautions that a possible consequence may be increased variability in student performance. However, the instructor responds that she would expect less variability. From her records she found that in the past, student scores on the final exam for this course followed a normal distribution with standard deviation 18.2 points. For a class of 25 students using the new approach, the standard deviation of scores on the final exam was 15.3 points.
Assuming that these 25 students can be viewed as a random sample of all those who might be subjected to the new approach, test the null hypothesis that the population standard deviation is at least 18.2 points against the alternative that it is lower.