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

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 2% of the population proportion. No preliminary estimate is available Find the minimum sample size needed Find the minimum sample size needed, using a prior study that found that 38% of the respondents said they are confident with their country's banking system Compare the results from parts (a) and (b) (a) What is the minimum sample size needed assuming that no prior information is available? n = (Round up, to the nearest whole number as needed.)

Explanation / Answer

a.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.576
Sample Proportion = 0.5
ME = 0.02
n = ( 2.576 / 0.02 )^2 * 0.5*0.5
= 4147.36 ~ 4148

b.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.576
Sample Proportion = 0.38
ME = 0.02
n = ( 2.576 / 0.02 )^2 * 0.38*0.62
= 3908.472 ~ 3909

c.
result in part A is larger

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