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Complete Question
A magazine company is planning to survey customers to determine the proportion who will renew their subscription for the coming year. The magazine wants to estimate the population proportion with 95% confidence and a margin of error equal to ±0.02. What sample size is required?
Answer:
2401
Explanation:
Margin of Error Formula For Proportion =
Margin of Error = z × √p(1 - p)/n
We are to find n
p = 0.5
z = z score of 95% confidence interval = 1.96
We are told: a margin of error equal to ±0.02 = ± 2%
0.02 = 1.96 × √0.5(1 - 0.5)/n
We square both sides
0.02² =( 1.96 × √[0.5(1 - 0.5)/n])²
0.0004 = 1.96² × 0.5 × 0.5/n
Cross Multiply
0.0004 × n = 1.96² × 0.5 × 0.5
Divide bother side by 0.0004
n = 1.96²× 0.5 × 0.5/0.0004
n = 3.8416 × 0.25/0.0004
n = 2401
Sample size required is 2401