A researcher wishes to estimate, with 95% confidence, the population proportion

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 2% of the population proportion. (a) No estimate is available. Find minimum sample (b) Find the minimum sample size needed, using a prior study that found that 25% 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 =

Explanation / Answer

a) For no preliminary estimate, use p =0.5

The critical z-value for 95% confidence is +/-1.96
z*sqrt{ p*(1-p)/n} =0.02
square both sides and multiply both by n,
z^2*p/(1-p)=0.0004n
1.96^2*(0.5/0.5) = 0.0004n
n = 9604

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