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 95% confidence if ​

(a) he uses a previous estimate of 34%? ​

(b) he does not use any prior​ estimates?

Answer 1

Solution:

Part a

We are given

p = 34% = 0.34

q = 1 – p = 1 – 0.34 = 0.66

Margin of error = E = 2% = 0.02

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

The sample size formula is given as below:

n = p*q*(Z/E)^2

n = 0.34*0.66*(1.96/0.02)^2

n = 2155.138

n = 2156

Required sample size = 2156

Part b

Here, we do not know the estimate for p

So, we take p = 0.5, q = 0.5

Confidence level = 95%

Critical Z value = 1.96

Margin of error = E = 2% = 0.02

The sample size formula is given as below:

n = p*q*(Z/E)^2

n = 0.5*0.5*(1.96/0.02)^2

n = 2401

Required sample size = 2401