Chapter 20 - STAT 2053 Elementary Statistics Chapter 20...

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STAT 2053 – Elementary Statistics Chapter 20 – Comparing Two Proportions 1
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Two Sample Proportions In Chapter 18, we discussed inference on two population means. Now, we’re going to move on to two population proportions. We often compare the proportions of two groups: How many A’s different professors give. What group is more likely to buy a product? 2
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BPS - 5th Ed. Chapter 20 3 Two-Sample Problems The goal of inference is to compare the responses to two treatments or to compare the characteristics of two populations. We have a separate sample from each treatment or each population. The units are not matched, and the samples can be of differing sizes.
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Two Sample Proportions We’ll consider two populations, each with it’s own population proportion, and take random samples from each population. Like in Ch. 18, the samples must be independent. 4
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Two Sample Proportions The notation we’ll use for these problems is as follows: 5 Populati on Populati on Proporti on Sample Size Sample Proporti on 1 p 1 n 1 2 p 2 n 2 ˆ p 1 ˆ p 2
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BPS - 5th Ed. Chapter 20 6 Case Study A study is performed to test of the reliability of products produced by two machines. Machine A produced 8 defective parts in a run of 140, while machine B produced 10 defective parts in a run of 200. This is an example of when to use the two-proportion z procedures. n Defects Machine A 140 8 Machine B 200 11 Machine Reliability
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Proportions We want to compare the two population proportions, which is done by looking at the difference between them (p 1 – p 2 ). We estimate this difference by using In other words, we estimate the difference in the population proportions by using the difference in the sample proportions. 7 ˆ p 1 - ˆ p 2
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BPS - 5th Ed. Chapter 20 8 Inference about the Difference p 1 p 2 Simple Conditions When both of the samples are large, the sampling distribution of this difference is approximately Normal with mean p p and standard deviation ( 29 ( 29 2 2 2 1 1 1 1 1 n p p n p p - + -
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BPS - 5th Ed. Chapter 20 9 Inference about the Difference p 1 p 2 Sampling Distribution Again, we can’t use the standard deviation.
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BPS - 5th Ed. Chapter 20 10 Since the population proportions p 1 and p 2 are unknown, the standard deviation of the difference in sample proportions will need to be estimated by substituting for p 1 and p 2 : Standard Error 2 1 and p p ˆ ˆ ( 29 ( 29 2 2 2 1 1 1 1 1 n p p n p p SE ˆ ˆ ˆ ˆ - + - =
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This note was uploaded on 09/23/2011 for the course STAT 2053 taught by Professor Staff during the Fall '08 term at Oklahoma State.

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Chapter 20 - STAT 2053 Elementary Statistics Chapter 20...

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