# Confidence Interval & Sample Size: Population Proportion

6. Read the following statement and answer the questions that follow.

'The Environmental Protection Agency (EPA) is interested in determining the proportion of Americans who live in neighborhoods with acceptable levels of carbon monoxide. The EPA took a random sample of 1201 Americans and discovered that 1139 of them lived in neighborhoods with acceptable levels of carbon monoxide.'

(a) Describe the population of interest and calculate the numerical value of the statistic that that the EPA will use to estimate p.

(b) Construct a 95% confidence interval for the proportion of Americans who live in neighborhoods with acceptable levels of carbon monoxide.

(c) Construct a 99% confidence interval for the proportion of Americans who live in neighborhoods with acceptable levels of carbon monoxide.

(d) Describe the relationship between the confidence level and the size of the confidence interval.

(e) Suppose you wish to conduct your own study to determine the proportion of Americans who live in neighborhoods with acceptable levels of carbon monoxide. Using your estimate for p, what sample size would be needed for the estimate to be within 1.5 percentage points with 90% confidence?

(f) Suppose you wish to conduct your own study to determine the proportion of Americans who live in neighborhoods with acceptable levels of carbon monoxide. Without having a prior estimate for p, what sample size would be needed for the estimate to be within 1.5 percentage points with 99% confidence?

(g) Describe the relationship between the confidence level and the size of the sample needed to estimate p within 1.5 percentage points.

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#### Solution Summary

The solution provides step by step method for the calculation of confidence interval and sample size for population proportion. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.