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 are confident with their country's banking system. His estimate must be accurate within 33% 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 28% 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? (b) What is the minimum sample size needed using a prior study that found that 28% of the respondents said they are confident with their country's banking system? (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 raises the minimum sample size needed. C. Having an estimate of the population proportion reduces the minimum sample size needed.

Explanation / Answer

a) for 90% CI ; critical value of z=1.645

for no prior estimate: p=0.5

(note here margin of error is 33% or 3% cause in practice it should be 3% . I m considering 3% please revert if it is 33% and I will update the solution)

margin of error E =0.03

hence required sample size n=p*(1-p)*(z/E)2 =~752

b)

for prior estimate p=0.28

required sample size n=p*(1-p)*(z/E)2 =~607

c)

opion C is correct

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

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