A researcher wishes to estimate, with 90% confidence, the population proportion

Question

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who say chocolate is their favorite ice cream flavor. Her estimate must be accurate within 5% the population 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 46% of the respondents said their favorite flavor of ice cream is chocolate. (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 46% of the respondents said their favorite ice cream flavor is chocolate? n = (Round up to the nearest whole number as needed.) (c) How do the results from (a) and (b) compare? A. Having an estimate of the population proportion reduces the minimum sample size needed. B. Having an estimate of the population proportion has no effect on the minimum sample size needed. C. Having an estimate of the population proportion raises the minimum sample size needed.

Explanation / Answer

a) when no estimate is available

n = z^2 /(4e^2)

here z = 1.645 for 90 % confidence ,

e = 0.05

hence n = 1.645^2 /(4 * 0.05^2)

= 270.6025

hence n = 271

b) when p^ = 0.46

n = z^2 * p*q /e^2

n = 1.645^2 * 0.46 *0.54/0.05^2

= 268.870644

hence n = 269

c) option A) is correct as 269 < 271

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