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 calculated.The results are presented below. The researcher is interested in determining whether there is evidence that the two processes yield different average errors.Assume that the population standard deviations are 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 and conclude the means are the same.
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 calculated.The results are presented below.  The researcher is interested in determining whether there is evidence that the two processes yield different average errors.Assume that the population standard deviations are 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 and conclude the means are the same. 
D)Fail to reject the null hypothesis and conclude the means are different.

Quizplus · Accepted Answer

Since we are testing whether there is evidence that the two processes yield different average errors, this corresponds to a two-sample t-test with equal population standard deviations. We can calculate the test statistic and p-value using statistical software or a t-table. If we set the significance level at 1%, we reject the null hypothesis if the p-value is less than 0.01. The calculated p-value turns out to be less than 0.01, so we reject the null hypothesis and conclude that the means are different. Therefore, the best choice is A.

A National Manufacturer of Ball Bearings Is Experimenting with Two