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I'm working through Koosis:Statistics: A Self Teaching Guide, 4th edition. In Chapter 5, Koosis describes how to use a function which goes by the name of F.INV.RT(probability,deg_freedom1,deg_freedom2) in Excel 2010 to find the critical region for a given significance level, for a statistical test where the alternative hypothesis is that the standard deviation of the numerator population isgreaterthan that of the denominator population. I've tried this on the example in the book, in section 16, and get the same result.

I've now come to sections 5.19-22 where he introduces the idea of a statistical test for the alternative that the standard deviations of a pair of populations are not equal.

In 5.19 he says the method is the same, except that "you double the probabilities when you use the F table." When I try this on the example in 5.20, I get a different result from the book. In this example, the size of both samples is 10. The significance level is 2%. In Excel 2010, I get F.INV.RT(0.04,9,9) = 3.438684. In Mathematica, I get InverseCDF[FRatioDistribution[9, 9], 1 - .04] = 3.43868. (This function in Mathematica produces the same results as the book for the one-tailed case.) The book's answer is 5.35; the critical region is the region greater than or equal to 3.35.

Is 5.35 a typo, or am I making a mistake? If the latter, how do I find the correct result in Excel and Mathematica?

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# Two-tailed inverse CDF of F distribution

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