Chapter_20 - Chapter 20 Comparing Two Proportions BPS 5th Ed Chapter 20 1 Two-Sample Problems The goal of inference is to compare the responses to

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BPS - 5th Ed. Chapter 20 1 Chapter 20 Comparing Two Proportions
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BPS - 5th Ed. Chapter 20 2 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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BPS - 5th Ed. Chapter 20 3 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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BPS - 5th Ed. Chapter 20 4 Inference about the Difference p 1 p 2 Simple Conditions The difference in the population proportions is estimated by the difference in the sample proportions: When both of the samples are large, the sampling distribution of this difference is approximately Normal with mean p p and 2 1 p p ˆ ˆ - ( 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 5 Inference about the Difference p 1 p 2 Sampling Distribution
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BPS - 5th Ed. Chapter 20 6 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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BPS - 5th Ed. Chapter 20 7
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BPS - 5th Ed. Chapter 20
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This note was uploaded on 08/27/2011 for the course MA 116 taught by Professor Muntheralraban during the Summer '11 term at Montgomery CC.

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Chapter_20 - Chapter 20 Comparing Two Proportions BPS 5th Ed Chapter 20 1 Two-Sample Problems The goal of inference is to compare the responses to

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