A firm has just developed a new cost-reducing technology for producing a certain replacement part for automobiles. Since a replacement part must be produced within close specifications in order for it to be acceptable to customers, the new technology's specifications must not deviate drastically from the older version. Suppose the sample variance for 15 parts produced using the older version is s1 2 = 0.35, while the sample variance for 15 parts produced using the new technology is s 2 2 = 0.48. Assume that the two samples are drawn independently from normally distributed populations.
a. Develop the hypotheses to test whether the population variances differ.
b. Calculate the value of the test statistic.
c. Using the critical value approach, determine the decision rule at the 5% significance level.
d. Can you conclude that the variances are different? Given that all other criteria are satisfied, should the company adopt the new technology?