A design engineer at Sperling Manufacturing, a supplier of high-quality ball bearings, claims a new machining process can result in a higher daily output rate. Accordingly, the production group is conducting an experiment to determine if this claim can be substantiated. The mean and standard deviation of bearings in a sample of 8 days' output using the new process equal 2,613.63 and 90.78, respectively. A similar sample of 10 days' output using the old process yield the mean and standard deviation of 2,485.10 and 148.22, respectively.
a. Set up the hypotheses to test whether the mean output rate of the new process exceeds that of the old process. Assume normal populations and equal population variances for each process. Use the critical value approach for the analysis.
b. Compute the value of the test statistic.
c. At the 5% significance level, what is the conclusion of the experiment?
d. At the 1% significance level, what is the conclusion of the experiment?