Question

A researcher wishes to? estimate, with 95?% ?confidence, the population proportion of adults who are confident with their? country's banking system. His estimate must be accurate within 3?% 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? nequals nothing ?(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? nequals nothing ?(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 has no effect on the minimum sample size needed. B. Having an estimate of the population proportion reduces the minimum sample size needed. C. Having an estimate of the population proportion raises the minimum sample size needed.

Answer 1

Sample size = Z²/2 * p(1-p) / E² , Where E is margin of error.

a)

When no prior estimate for proportion is available, then p = 0.50

Sample size n = 1.96² * 0.5 * 0.5 / 0.03²

= 1067.11

Sample size n = 1068 (Rounded up to nearest integer)

b)

Given, p = 0.22

Sample size n = 1.96² * 0.22 * 0.78 / 0.03²

= 732.47

Sample size n = 733 (Rounded up to nearest integer)

c)

Comparing parts a and b,

Having estimate of the population proportion reduces the minimum sample size needed.