Q19.) A pollster wants to construct a 95% confidence interval for the proportion

Question

Q19.) A pollster wants to construct a 95% confidence interval for the proportion of adults who believe that economic conditions are getting better. A Gallup poll taken in July 2010 estimates this proportion to be 0.33. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.067? Write only an integer as your answer. Q20.) A researcher wants to construct a 99% confidence interval for the proportion of people who changed jobs in the past year. What sample size is needed so that the confidence interval will have a margin of error of 0.027 Write only an integer as your answer.

Explanation / Answer

19) At 95% confidence interval the critical value is z0.025 = 1.96

Margin of error = 0.067

or, z0.025 * sqrt(p(1 - p)/n) = 0.067

or, 1.96 * sqrt(0.33 * (1 - 0.33)/n) = 0.067

or, n = (1.96 * sqrt(0.33 * (1 - 0.33))/0.067)^2

or, n = 190

20) At 99% confidence interval the critical value is z0.005 = 2.58

Margin of error = 0.027

or, z0.005 * sqrt(p(1 - p)/n) = 0.027

or, 2.58 * sqrt(0.5 * (1 - 0.5)/n) = 0.027

or, n = (2.58 * sqrt(0.5 * (1 - 0.5))/0.027)^2

or, n = 2283

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