Unformatted text preview: n 21) S 2 2 σ 2 2 , then Z 1 and Z 2 are independent random variables with Z i ∈ χ 2 ( n i ). If F = Z 1 / ( n 11) Z 2 / ( n 22) = ( n 11) S 2 1 σ 2 1 ( n 11) ( n 21) S 2 2 σ 2 2 ( n 21) = S 2 1 /σ 2 1 S 2 2 /σ 2 2 = S 2 1 σ 2 2 S 2 2 σ 2 1 , then F has the Fdistribution with ( n 11) numerator degreesoffreedom and ( n 21) denominator degreesoffreedom. This is written as F ∈ F ( n 11 ,n 21). Problem #10 on page 28 asks you to verify this fact....
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 Fall '08
 MichaelKozdron
 Statistics, FDistribution, Probability, Null hypothesis, Statistical hypothesis testing, Statistical significance, Fisher's method, n1, Likelihood principle

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