Figuring out Sample Size

Question

Find the sample size needed if a 98% confidence interval has a ‘margin of error’ of 4% if … 

1. You feel safe using an estimate for p of .13
2. You are going to play it as safe as possible and use p of .50

Answer 1

sample size (n) = phat * (1-phat) * (z-critical/margin of error)^2

For part 1 use phat = 0.13. For part 2 use phat = 0.5

z-critical for 98% confidence it z-score at 99 percentile = 2.33

margin of error percent (4%) converted to probability between 0 and 1 (0.04).