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Math Help - Confidence Interval Using F

  1. #1
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    Angry Confidence Interval Using F

    Stat Question.pdf

    Verify that {F}_{\alpha,n,m} = \frac{1}{{F}_{ \alpha,n,m } }

    I am very frustrated with this verification. Attached is a PDF of the question because I don't know how to really work the formatting on this site. Please Help!
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  2. #2
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    An F distribution is equal in distribution to a ratio of chi-squares divided by their degrees of freedom. Hence, the distribution of 1/F is equal is also equal in distribution to a ratio of chi-squares divided by their degrees of freedom; you just end up switching the degrees of freedom. Use that fact to get the result.
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  3. #3
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    First, use [tex] ... latex here ... [/tex] tags to post latex. Second, do you know what the value F_{\alpha, n, m} indicates? I'll give you a hint: it's a certain percentile of the F distribution. With that in hand, think about what percentage of the F distribution alpha and 1-alpha are specifying, and see how they relate according to the provided equality. Your proof will derive from that understanding.
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  4. #4
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    To Clarify,
    does
    <br />
F_{\alpha,n,m} = (1-\alpha) 100?<br />
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  5. #5
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    No. F_{\alpha, n, m} is the number such that if X has an F distribution with n and m degrees of freedom, then

    P(X \ge F_{\alpha, n, m})= \alpha.
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