A researcher wishes to estimate with 99% confidence the population proportion of

Question

A researcher wishes to estimate with 99% confidence the population proportion of adults who are confident with their country's banking system. His estimate must be accurate within 5% of 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 22% of the respondents said they are confident with their country's banking system. (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 22% of the respondents said they are confident with their country's banking system. n = (round up to the nearest whole number as needed.) (c) How do 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 raises the minimum sample size needed. A. Having an estimate of the population proportion has no effect on the minimum sample size needed.

Explanation / Answer

99% , z = 2.576 .e = 0.05

a) if estimate not available

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

= 2.576^2 /(4 *0.05^2)

= 663.5776

n = 664

b) when p^ = 0.22

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

= 2.576^2 * 0.22*0.78 /0.05^2

= 455.479664

n = 456

c)

option A) is correct

as 456 < 664

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