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Unformatted text preview: Chapter 9 Section 3 Confidence Intervals about a Population Proportion Fall 2008 1 Confidence Intervals for Proportions Learning objectives Get a point estimate for the population proportion Construct and interpret a confidence interval for the population proportion Determine the sample size necessary for estimating a population proportion within a specified margin of error Fall 2008 2 Confidence Intervals for Proportions In Section 1, we calculated confidence intervals for the mean, assuming that we knew In Section 2, we calculated confidence intervals for the mean, assuming that we did not know In this section, we construct confidence intervals for situations when we are analyzing a population proportion The issues and methods are quite similar Fall 2008 3 Confidence Intervals for Proportions When we analyze the population mean, we use the sample mean as the point estimate The sample mean is our best guess for the population mean When we analyze the population mean, we use the sample mean as the point estimate The sample mean is our best guess for the population mean When we analyze the population proportion, we use the sample proportion as the point estimate The sample proportion is our best guess for the population proportion Fall 2008 4 Confidence Intervals for Proportions Confidence intervals for the population mean are Centered at the sample mean Plus and minus z /2 times the standard deviation of the sample mean (the standard error from the sampling distribution) Confidence intervals for the population mean are Centered at the sample mean Plus and minus z /2 times the standard deviation of the sample mean (the standard error from the sampling distribution) Similarly, confidence intervals for the population proportion will be Centered at the sample proportion Plus and minus z /2 times the standard deviation of the sample proportion Fall 2008 5 Confidence Intervals for Proportions We have already studied the distribution of the sample proportion is approximately normal with under most conditions We use this to construct confidence intervals for the population proportion n p p p ) ( 1 p p Fall 2008 6 Confidence Intervals for Proportions The (1 ) 100% confidence interval for the population proportion is from to where z /2 is the critical value for the normal distribution n p p z p ) ( / 1 2 n p p z p ) ( / 1 2 Fall 2008 7 Confidence Intervals for Proportions As for confidence intervals for population means, the quantity is called the margin of error n p p z ) ( / 1 2 Fall 2008 8 Confidence Intervals for Proportions Example #1 We polled n = 500 voters When asked about a ballot question, x = 235 of them were in favor Obtain a 99% confidence interval for the population proportion in favor of this ballot question ( = 0.01) Note: Manual solution will be shown in class....
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This note was uploaded on 02/14/2011 for the course STAT 250 taught by Professor Sims during the Spring '08 term at George Mason.
 Spring '08
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