# Conduct a two-tailed hypothesis test given the information below

ABC 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.

Process A Process B

Sample Mean 2 3

Standard Deviation 1 0.5

Sample Size 12 14

A. What are the assumptions used for this test?

B. 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 assumed equal. What is the critical t value at the 10% level of significance?

C. 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 5% level of significance, what is the decision?

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#### Solution Preview

A)

Assumptions:

-the two samples are not dependent

-Both populations are normally distributed

-population standard deviations are unknown, but are equal

B)

df = 12+14-2 ...

#### Solution Summary

Step-by-step computations are shown.