A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. If we test the null hypothesis at the 1% level of significance, what is the decision?
A)Reject the null hypothesis and conclude the means are different.
B)Reject the null hypothesis and conclude the means are the same.
C)Fail to reject the null hypothesis.
D)Fail to reject the null hypothesis and conclude the means are different.

Question

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented next.  The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. If we test the null hypothesis at the 1% level of significance, what is the decision?
A)Reject the null hypothesis and conclude the means are different. 
B)Reject the null hypothesis and conclude the means are the same. 
C)Fail to reject the null hypothesis. 
D)Fail to reject the null hypothesis and conclude the means are different.

Quizplus · Accepted Answer

We need to perform a two-sample t-test to compare the means of the two processes. Assuming equal population variances, we calculate the pooled standard deviation and the test statistic. With a p-value of less than 0.01, we reject the null hypothesis and conclude that there is evidence that the means are different. Therefore, the correct answer is A.

A National Manufacturer of Ball Bearings Is Experimenting with Two