The Graduate Management Admission Council reported a shift in the job-hunting strategies among second-year masters of business administration (MBA) candidates. Even though their prospective base salary has increased from $81,900 to $93,770 from 2002 to 2005, it appears that MBA candidates are submitting fewer job applications. Data obtained from online surveys of 1,442 MBA candidates at 30 business school programs indicate that in 2002 the average number of job applications per candidate was 38.9 and 2.0 in 2005. The sample variances were 64 and 0.32, respectively.
a. Examine the sample variances. Conjecture whether this sample evidence indicates that the two population variances are equal to each other. Support your assertion.
b. On the basis of your answer in part a, construct a 99% confidence interval for the difference in the average number of job applications submitted by MBA candidates between 2002 and 2005.
c. Using your result in part b, is it plausible that the difference in the average number of job applications submitted is 36.5? Is it plausible that the difference in the average number of job applications submitted is 37? Are your answers to these two questions contradictory? Explain.