A Midwest college admissions committee recently conducted a study to determine the relative debt incurred by students receiving their degrees in four years versus those taking more than four years. Some on the committee speculated a four-year student would likely be attending full time, whereas one taking more than four years could have a part-time job. However, average total debt provides only part of the information. Since the average, or mean, is affected by both large and small values, the committee also needed some way to determine the relative variances for the two groups. Samples of size 20 produced standard deviations of 2,636 for four-year graduates and 1,513 for those taking more than four years.
Conduct a test of hypothesis to determine if the standard deviation of the debt for four-year graduates is larger than those taking more than four years. Use a significance level of 0.05.