A national manufacturer of ball bearings is experimenting with two different pro

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.

                                                                        Process A                Process B
Mean    2mm                         2.6mm
Sample Standard Deviation    0.1mm                    0.12mm
Sample Size                                                         12                             14

The researcher is interested in determining whether there is evidence that the two processes yield different average errors. What is the critical value at the 1% level of significance? Show your solution.

A.) + 2.779

B.) -2.492

Explanation / Answer

DF = ((0.1)^2/12 + (0.12)^2/14)^2/(((0.1)^2/12)^2/11 + ((0.12)^2/14)^2/13) = 23.99 = 24

With 24 degrees of freedom and 1% significance level the critical value is +/- 2.797

Option-D is the correct answer.

The test statistic t = (2 - 2.6)/sqrt((0.1)^2/12 + (0.12)^2/14)

= -13.9

As the test statistic value is less than the critical value -2.797, so the null hypothesis is rejected.

So there is sufficient evidence that the two process yield different average errors.

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