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https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=A+business+major+wants+to+determine+whether+the+variation+in+advertising+costs+of+hair+salons+is+different+from+the+variation+in+advertising+costs+of+nail+salons.+He+surveys+several+businesses+and+finds+the+standard+deviation+in+monthly+advertising+costs+is+%2423+for+12+hair+salons%2C+and+%2443+for+8+nail+salons.+At+the+0.05+level+of+significance%2C+what+is+the+critical+value%3F

Solution

The test statistic is
F = 43^2 / 23^2 = 3.50 rounded to two places
the degrees of freedom are 12-1 = 11 and 8 - 1 = 7
The critical value for alpha = .05 for these df\'s is between 3.28 and 3.35 (from a table)
Since 3.50 is greater than the critical value, yes the results are significant. We have found evidence of a difference in standard deviations.