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# Confidence Interval & Sample Size: Population Proportion

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'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.