Statistics: Confidence Intervals

Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 70%. You would like to be 90% confident that your estimate is within 4.5% of the true population proportion. How large of a sample size is required? 

n=?

Answer 1

Margin of Error = z√[p(1-p)/n]

0.045 = 1.645√[(0.70)(1-0.70)/n] <-- Recall the critical value for 90% confidence is 1.645

(0.045/1.645)² = (0.70)(0.30)/n

n = 0.21/(0.045/1.645)²

n ≈ 281

Therefore, you would need a sample size of 281

Hope this helped!