Lecture17 - AMS 312 Lecture Notes ( April 23 , 2010 )...

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Unformatted text preview: AMS 312 Lecture Notes ( April 23 , 2010 ) Inference on two population proportions with two large independent samples. Data: Sample 1 (population proportion -- 1 ): 1 n , 1 X Sample 2 (population proportion -- 2 ): 2 n , 2 X 1. Derivation of the Pivotal Quantity: Parameter of Interest: 1 2 - 1 1 1 1 1 1 1 2 2 2 2 2 2 2 (1 ) ~ ( , ) (1 ) ~ ( , ) X N n n X N n n - =- = & & Point Estimator of 1 2 ( ) - is: 1 2 ( ) - Pivotal Quantity (P.Q.) for 1 2 ( ) - : 1 1 2 2 1 2 1 2 1 2 (1 ) (1 ) ~ ( , ) N n n ---- + & 1 2 1 2 1 1 2 2 1 2 ( ) ~ (0,1) (1 ) (1 ) N n n ----- + & The above is not a P.Q. because 1 , 2 are used in 1 1 2 2 1 2 (1 ) (1 ) n n -- + However the following is a P.Q.: 1 2 1 2 1 1 2 2 1 2 ( ) ~ (0,1) (1 ) (1 ) Z N n n --- =-- + & 2. The 100(1- )% CI for 1 2 - 2 2 ( ) 1 P Z Z Z - - B We can follow the same procedure as before to arrive at the following formula for the...
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This note was uploaded on 11/14/2010 for the course AMS 312 taught by Professor Zhu,w during the Spring '08 term at SUNY Stony Brook.

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Lecture17 - AMS 312 Lecture Notes ( April 23 , 2010 )...

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