Question

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 equals nothing ​(Round up to the nearest​ integer.) ​(b) n equals nothing ​(Round up to the nearest​ integer.)

Answer 1

SOLLUTION:-

Margin of error = +0.02

Critical value for 99% confidence is +2.575

P = 0.34

Std Error = sqrt[P * (1 - P) / N] = sqrt[0.34 * (1 - 0.34) / N] = sqrt[0.2244/N]

Margin of error = Critica value * Std Error

0.02 = 2.575 * sqrt[0.2244/N]

N = 3719.78 = 3720

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b) No prior estimates

We use P = 0.5

Std Error = sqrt[P * (1 - P) / N] = sqrt[0.5 * (1 - 0.5) / N] = sqrt[0.25/N]

Margin of error = Critica value * Std Error

0.02 = 2.575 * sqrt[0.25/N]

N = 4144.14 = 4144