09_25_09 - STAT 409 Fall 2009 Examples for If U and V are...

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STAT 409 Examples for 09/25/2009 Fall 2009 If U and V are independent χ 2 ( r 1 ) and χ 2 ( r 2 ) random variables, respectively, then F = 2 1 r r V U has an F distribution with r 1 and r 2 degrees of freedom. X 1 , … , X n ~ 2 , X X N σ μ , Y 1 , … , Y m ~ 2 , Y Y N σ μ , 2 2 2 2 X X Y Y S S σ σ = ( ( 29 ( 29 ( 29 1 1 1 1 2 2 2 2 - - - - n n m m X X Y Y S S σ σ ~ F ( m – 1, n – 1 ) . 100 ( 1 – α ) % confidence interval for 2 2 Y X σ σ ( 29 ( 29 - - - - 1 , 1 α , 1 , 1 α 1 2 2 2 2 2 2 y x F y x F s s n m s s m n 1. A manufacturer of electronic components believes that the variance of the lifetime distribution of components he manufactures is equal to that of his major competitor;
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