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# TA13 - ECO2121 Methods of Economic Statistics TA13 8 April...

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ECO2121: Methods of Economic Statistics TA13 8 April 2009 There is a supplement TA13a. 1. Hypothesis Testing (Two populations) (continued) What is F distribution? F stands for Sir Ronald Fisher. Definition : Suppose W ~ χ 2 ( k w ) and V ~ χ 2 ( k v ) independently , then the ratio = ~ ( , ) . So we see the random variable (1/ F ) ~ F ( k v , k w ). Suppose X ~ N ( μ X , σ X 2 ) and Y ~ N ( μ Y , σ Y 2 ) independently , their samples are with size n X and n Y respectively. Recall ( n X 1) S X 2 / σ X 2 ~ χ 2 ( n X 1) and ( n Y 1) S Y 2 / σ Y 2 ~ χ 2 ( n Y 1) independently , so [( 1) ] [ 1] [( 1) ] [ 1] = ~ ( 1, 1) For H 0 : σ X 2 = σ Y 2 vs. H 1 : σ X 2 σ Y 2 , under H 0 , the test statistic F 0 = S X 2 / S Y 2 ~ F ( n X 1, n Y 1). If F 0 > F α /2 ( n X 1, n Y 1) or F 0 < F 1- α /2 ( n X 1, n Y 1), H 0 is rejected. In the textbook, if S X 2 > S Y 2 , we always put the larger in the numerator, then only F > F α /2 ( n X 1, n Y 1) is used as the rejection rule.

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TA13 - ECO2121 Methods of Economic Statistics TA13 8 April...

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