Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.37. You would like to be 98% confident that your estimate is within 3% of the true population proportion. How large of a sample size is required?

Answer 1

Formula for sample size to estimate a population proportion

pg : Believed to be  population proportion = 0.37

Confidence level = 98%

for 98% confidence level = (100-98)/100 =0.02

/2 = 0.02/2=0.01

Z/2 = Z0.01 = 2.3263

Estimate to be within 3% of the true population proportion i.e Margin of error : E = 3/100 =0.03

Sample size required = 1402