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 % confidence and a margin of error equal to . What sample size is required?

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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?

2401

Step-by-step 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

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