Question

# A researcher wishes to​ estimate, with 99​% ​confidence, the population proportion of adults who are confident...

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 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 26​% of the respondents said they are confident with their​ country's banking system. ​(c) Compare the results from parts ​(a) and ​(b).

c = 99%

z- score for 99% is 2.58

E = 3% (0.03)

n = (z/E)^2 * p(1 - p)

(a) p = 1 - p = 0.5

n = (2.58/0.03)^2 * (0.5 * 0.5) = 1844

(b) p = 0.26

n = (2.58/0.03)^2 * 0.26(1 - 0.26) = 1419

(c) With no estimate of the population proportion available, we make a conservative estimate of the sample size. This will always be greater than the sample size estimate made with a prior knowledge about the population proportion.

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