The Practice of Statistics Third Edition Chapter 10.3 (12.1): Estimating a Population Proportion Copyright © 2008 by W. H. Freeman & Company Daniel S. Yates

Essential Questions What are the three conditions for constructing a confidence interval for an unknown population proportion? How do you construct a confidence interval for the population proportion, using the four step procedure? How do you determine the sample size needed to construct a level C confidence interval with a specified margin of error?

We use z procedures for constructing a confidence interval. estimate ± z*·SE estimate

Conditions Necessary for Constructing a Confidence Interval for Population Proportion

Example – Will Smoking Shorten Your Life? The Harris Poll addressed smoking in a sample survey conducted by telephone in January Because Harris called residential telephone numbers at random, the sample (ignoring practical problems) was an SRS of smokers living in the United States in households with telephone service. The sample size was n = The two findings of the survey are: Do you believe that smoking will probabiilty shorten your life or not? 848 of 1010 said yes. Have you ever tried to give up smoking? 707 of 1010 said yes. Construct 95% confidence interval for the population of all American smokers who think that smoking will probably shorten their lives.

Solution

Solution Continued Step 4 Interpretation. We are 95% confident that the proportion of all smokers that believe that smoking will shorten their lives is between 82% and 86% Note. The margin of error of is the variation due to chance in choosing a random sample. It does not include the effects of non-responses and other error sources.

Sample size for a specific C level and a specific Margin of Error