Chapter9.3 lecture notes

Chapter9.3 lecture notes - Handout on Chapter 9.3 . 9.3....

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Handout on Chapter 9.3 . 9.3. Hypotheses Concerning several proportions. H 0 : p 1 = p 2 =……p j …. p k = p p j =P(A|B j ) (independence of A and B) H 1 : At least one of these p j p i Data: n j observations from population j and X j = frequency of event A in the sample from population j and n j -X 2 denotes the frequency of A in the sample from population j for j=1,2,….k. Sample 1 Sample 2 Sample j ….. ….. Sample k Total Success X 1 X 2 X J X k X Failure n 1 -X 1 n 2 -X 2 n J -X j n k -X k n-X Total n 1 n 2 n j n k n Special Case: k=2. H 0 : p 1 = p 2 = p and H 1 : p 1 > p 2 OR H 1 : p 1 < p 2 OR H 1 : p 1 p 2 Sample 1 Sample 2 Total Success X 1 X 2 X Failure n 1 -X 1 n 2 -X 2 n-X Total n 1 n 2 n 1 ˆ p = X i /n i = X i /n i for j=1,2. p ˆ = n x = n X X 2 1 + . Test statistic is ) 1 1 )( ˆ 1 ( ˆ ˆ ˆ 2 ` 1 2 1 n n p p p p Z + - - = . H 1 Reject at α level if P value p 1 < p 2 Z< -z α Φ (z) p 1 > p 2 z> z α 1- Φ (z) = Φ (-z) p 1 p 2 |z|> z α /2 2 Φ (-|z|) Example: We have a vote on whether a chemical plant should be constructed. We wish to see if the percentage approving within the
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Chapter9.3 lecture notes - Handout on Chapter 9.3 . 9.3....

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