A researcher wishes o estimate with 99% confidence, the population proportion ad

Question

A researcher wishes o estimate with 99% confidence, the population proportion adults who th nk he res er o ther count y can con ro the Pnce of gasoil e e estimate must be accurate within 5% of the true proportion. a) No preliminary estimate is available. Find the minimum sample size needed. b) Find the minimum sample size needed, using a prior study that found that 32% of the respondents said they think their president can control the price of gasoline c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available? n(Round up to the nearest whole number as needed.) b) What is the minimum sample size needed using a prior study that found that 32% of the respondents said they think their president can control the price of n(Round up to the nearest whole number as needed.) (c) How do the results from (a) and (b) compare? O A. O B. ° C. Having an estimate of the population proportion has no effect on the minimum sample size needed. Having an estimate of the population proportion reduces the minimum sample size needed. Having an estimate of the population proportion raises the minimum sample size needed.

Explanation / Answer

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

Margin of error = 0.05

or, z0.005 * sqrt(p(1 - p)/n) = 0.05

or, 2.58 * sqrt(0.5 * 0.5/n) = 0.05

or, sqrt(n) = 2.58 * sqrt(0.5 * 0.5)/0.05

or, n = (2.58 * sqrt(0.5 * 0.5)/0.05)^2

or, n = 666

b) Margin of error = 0.05

or, z0.005 * sqrt(p(1 - p)/n) = 0.05

or, 2.58 * sqrt(0.32 * 0.68/n) = 0.05

or, sqrt(n) = 2.58 * sqrt(0.32 * 0.68)/0.05

or, n = (2.58 * sqrt(0.32 * 0.68)/0.05)^2

or, n = 580

c) Option - B

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