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 5% of the population proportion. 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 34% of the respondents said they are confident with their country's banking system. (c) Compare the results from parts (a) and (b). What is the minimum sample size needed assuming that no prior information is available? n= (Round up to the nearest whole number as needed.) (b) What is the minimum sample size needed using a prior study that found that 34% of the respondents said they are confident with their country's banking system? n= (Round up to the nearest whole number as needed.)

Explanation / Answer

a) In this Z=1.645 for 90%

when no prior information available

p=1/2

1-p=1/2

E=5%=0.05

therefor sample size=n=0.5(1-0.5)(1.645/0.05)2

   =270.60

as sample size cant have decimal places

n=271(rounding off to nearest integer).

b)

)34% confident that they are confident with countrys banking system.

p=38%=34/100=0.34

1-p=1-.34=0.66

E=5%=5/100=0.05

sample size=(0.34)(0.66)(1.645/0.05)2

   =242.89

rounding off to nearest integer

min sample size=n=243

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