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home / study / questions and answers / math / statistics and probability / a researcher wishes to estimate, with 99% confidence, ... Question A researcher wishes to estimate, with 99% confidence, the percentage of adults who support abolishing the penny. His estimate must be accurate within 3% of the true proportion. a) Find the minimum sample needed, using a prior study that found that 58% of the respondents said they support abolishing the penny. b) No preliminary estimate is available. Find the minimum sample size needed.

Solution

a)
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.576
Samle Proportion = 0.58
ME = 0.03
n = ( 2.576 / 0.03 )^2 * 0.58*0.42
= 1796.083 ~ 1797
b)
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.576
Samle Proportion = 0.5
ME = 0.03
n = ( 2.576 / 0.03 )^2 * 0.5*0.5
= 1843.271 ~ 1844