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

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 44% 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 24% of the respondents said they are confident with their country's banking system. (c) Compare the results from parts (a) and (b).

Explanation / Answer

I am confused with if it is with in 44% or 4% . Cause 44% is too much for margin of error I am considering it to be 4%. PLease revert on this.

a) here margin of error E =0.04

for no prior estimate p=0.5

for 99% CI; z=2.5758

therefore sample size n=p(1-p)*(Z/E)2 =~1037

b) for p=0.24

therefore sample size n=p(1-p)*(Z/E)2 =~757

c) we can see in part a) for no  preliminary estimate sample size requirement is higher.

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