9.3 C ONFIDENCE I NTERVALS About a Population Proportion Obj: Use a formula or a calculator to create a confidence interval.

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9.3 C ONFIDENCE I NTERVALS About a Population Proportion Obj: Use a formula or a calculator to create a confidence interval

R EVIEW Interpret: In a poll conducted by the Gallup Organization in early December, 2004, a random sample of 1004 Americans resulted in 84% of the respondents stating that they are satisfied with the way things are going in their personal lives. The poll had a margin of error of + 3% with 95% confidence.

P OPULATION P ROPORTIONS To obtain a point estimate of the population proportion, use the formula as before: where x is the number of individuals in the sample with the specified characteristic and n is the sample size.

C ONSTRUCTING A CONFIDENCE INTERVAL To construct a (1 – α)100% confidence interval, take the point estimate + the margin of error. Make sure that and n <.05N.

T O USE THE CALCULATOR … STAT TESTS 1-PropZInt… Enter the x and n values and the confidence level. Example: A study of 74 patients with ulcers was conducted in which they were prescribed 40 mg of Pepcid. After 8 weeks, 58 reported ulcer healing. 1. Obtain a point estimate for the proportion. 2. Construct a 99% confidence interval.

S AMPLE S IZE If we need to know the sample size needed to estimate the population proportion, there are two options. Both would be rounded up to the next integer.

E XAMPLE An economist wishes to estimate the proportion of Americans who own their house. What size sample should be obtained if he wishes the estimate to be within 0.02 with 90% confidence? If he uses an estimate of from 2000? If he does not use any prior estimates?

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