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Intervals & Tests
The following is an excerpt from The Quality Engineering Handbook by Thomas Pyzdek, © QA Publishing, LLC.
The variance of machine X output, based on a sample of n = 25 taken from a stable process, is 100. Machine Y variance, based on a sample of 10, is 50. The manufacturing representative from the supplier of machine X contends that the result is a mere "statistical fluke." Assuming that a "statistical fluke" is something that has less than 1 chance in 100, test the hypothesis that both variances are actually equal.
The test statistic used to test for equality of two sample variances is the F statistic, which is calculated by the equation
For this data, F = 100/50 = 2.0
Using Table 8 in the Appendix for F.99 we find that for 24 df in the numerator and 9 df in the denominator F = 4.73. Based on this we conclude that the manufacturer of machine X could be right, the result could be a statistical fluke. This example demonstrates the volatile nature of the sampling error of sample variances and standard deviations.