09lecture20 - Lecture 20 1 Lecture 20 Inference about two...

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Lecture 20 1 Lecture 20 Inference about two population proportions Assume a claim regarding the two population proportions p 1 and p 2 is made. Then, if n 1 ˆ p 1 (1 - ˆ p 1 ) 10, n 2 ˆ p 2 (1 - ˆ p 2 ) 10, and the samples are independent and not larger than 5% of the population, we could follow the following steps to test the hypothesis: 1) Arrange the claim in one of the 3 forms: two-tailed, left-tailed or right-tailed form. 2) Compute the test statistic: z = p 1 - ˆ p 2 ) - ( p 1 - p 2 ) q p 1 (1 - p 1 ) n 1 + p 2 (1 - p 2 ) n 2 3) Compute the P -value. 4 State the conclusion. November 30, 2009
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Lecture 20 2 Remark: Usually, the common practice is to replace the unknown σ D with an estimate that takes into account our null hypothesis : H 0 : p 1 = p 2 . If these two proportions are equal then we can view the two proportions as coming from the same population, with a proportion given by the common value of p 1 and p 2 , denoted by p . So, now the pooled standard error becomes:
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09lecture20 - Lecture 20 1 Lecture 20 Inference about two...

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