TA13 - ECO2121: Methods of Economic Statistics TA13 – 8...

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Unformatted text preview: 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 = ¡ ¢ £ ⁄ ¤ ¥ ¦ ⁄ ~ § ( ¨ © , ª « ) . 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) ® ¯ ° ± ² ³ ⁄ ] [ ´ µ − 1] ⁄ [( ¶ · − 1) ¸ ¹ º » ¼ ½ ⁄ ] [ ¾ ¿ − 1] ⁄ = À Á Â Ã Ä Å ⁄ Æ Ç È É Ê Ë ⁄ ~ Ì ( Í Î − 1, Ï Ð − 1) For H : σ X 2 = σ Y 2 vs. H 1 : σ X 2 ≠ σ Y 2 , under H , the test statistic F = S X 2 / S Y 2 ~ F ( n X – 1, n Y – 1). If F > F α /2 ( n X – 1, n Y – 1) or F < F 1- α...
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This note was uploaded on 11/16/2009 for the course ECO 2121 taught by Professor Professorwen during the Fall '08 term at Al Ahliyya Amman University.

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TA13 - ECO2121: Methods of Economic Statistics TA13 – 8...

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