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Lecture

UASTAT141Ch22.pdf

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Department
Statistics
Course
STAT141
Professor
Paul Cartledge
Semester
Winter

Description
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. Æ p a1d p , n2an1 n 2 Properties of the Sampling Distribution of p − p : 1 2 If the random samples on which p and p are based are selected independently of one 1 2 another, then 1. µ p1−p2 = p1− p 2 2. σ 2 = σ 2 + σ 2 = p1(1− p1) + p2(1− p 2) and σ = σ 2 p1− 2 p1 p2 n n p1− 2 p1−2p 1 2 3. If both n1 & n2 are large (ifn1 1 ≥ 15, n1(1 – p1) ≥ 15, n 2 2≥ 15, & n2(1 – p2) ≥ 15), then pˆ1and p2each have a sampling distribution that is (approximately) normal. Thus, the sampling distribution of p1− p ˆ2is also (approximately) normal. Assumptions (for both the interval and the test): 1. Samples are independent random samples. rd 2. The 3 property mentioned above holds when using pˆ1and p2 instead of p 1nd p .2 Confidence Interval: The (1 – α)100% CI for p – p1is 2 p (1− p ) p (1− p ) p − p ˆ ± zα/2 1 1 + 2 2 1 2 n n 1 2 Substituting p and p is p
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