A researcher wishes to estimate the percentage of adults who

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 5 percentage points with 99% confidence if:

a. he uses a previous estimate of 0.34?_____ (Round answer to the nearest integer)

b. he does not use any prior estimates?_____(Round answer to the nearest integer)

Solution

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A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with 99% confidence if (a) he uses a previous estimate of 34%? (b) he does not use any prior estimates? (a) n= ______(Round up to the nearest integer.)

Answer

a.
proportion,p = 0.34
error,E = 0.02
alpha,a = 1-0.99 = 0.01
.
Za/2 = Z0.005 = 2.575
sample size,n >= [Za/2 / E]^2 * p(1-p)
n >= [2.575 / 0.02]^2 * 0.34(1-0.34)
n >= 3719.78
n = 3720

b.
without any prior estimate use p=0.50
proportion,p = 0.5
error,E = 0.02
alpha,a = 0.01
.
Za/2 = Z0.005 = 2.575
sample size,n >= [Za/2 / E]^2 * p(1-p)
n >= [2.575 / 0.02]^2 * 0.5(1-0.5)
n >= 4144.14
n = 4145