Interval Estimates for the mean when the variance is known

Question

Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E. that corresponds to a sample of size 214 with 49 successes at a confidence level of 99.9%.

M.E. = % 

(report answer accurate to one decimal place; answer should be reported as a percent, not a decimal—though do not type the percent sign)

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

So your estimate for p is 49/219 ≈ 0.2237. We'll use this in the Margin of Error formula for sample proportions

M.E. = Z_α/2•√(p•(1-p)/n)

= 3.291•√(0.2237•0.7743/219)

= 0.092554

Rounding to 3 decimal places, the margin of error is about 9.3%.