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 here. Process A Process B Sample mean 2.0 3.0 Standard deviation 1.0 0.5 Sample size 12 14 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. This example is what type of test

A researcher is interested in determining if the two process yield different average errors and we have to identify which type of test will be used here. Following are the points to look for in order to decide for the right statistical test:

Do we know the value of Population Standard Deviation or not?

If the value of Population standard deviations is known, then Two sample z-test is used, else we use t-tests. Since, the value of population standard deviations is unknown, we will move to t-tests. We have two options in t-test.

t-test for 2 population means with equal variance
t-test for 2 population means with unequal variance

Since it is mentioned in the statement that population standard deviations are assumed to be equal, this means population variances (which are square of the standard deviations) will also be equal.

Therefore, the test which must be used is:

t-test for difference in 2 population means with Equal Variance.