UASTAT141Ch22 - Ch. 22 - Two Population Proportions for...

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Ch. 22 - Two Population Proportions for Large Samples Def’n: Two samples drawn from two populations are independent if the selection of one sample from one population does not affect the selection of the second sample from the second population. Otherwise, the samples are dependent . Notation: Two samples require appropriate subscripts. e.g. p 1 and p 2 , n 1 and n 2 Properties of the Sampling Distribution of 2 1 ˆ ˆ p p : If the random samples on which 1 ˆ p and 2 ˆ p are based are selected independently of one another, then 1. 2 1 ˆ ˆ 2 1 p p p p = µ 2. 2 2 2 1 1 1 2 ˆ 2 ˆ 2 ˆ ˆ ) 1 ( ) 1 ( 2 1 2 1 n p p n p p p p p p + = + = σ and 2 ˆ ˆ ˆ ˆ 2 1 2 1 p p p p = 3. If both n 1 & n 2 are large (i.e. if n 1 p 1 15, n 1 (1 – p 1 ) 15, n 2 p 2 15, & n 2 (1 – p 2 ) 15), then 1 ˆ p and 2 ˆ p each have a sampling distribution that is (approximately) normal. This implies that the sampling distribution of 2 1 ˆ ˆ
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UASTAT141Ch22 - Ch. 22 - Two Population Proportions for...

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