Assume that a sample is used to estimate a population proportion p.

Question

Find the margin of error M.E. that corresponds to a sample of size 223 with 62.8% successes at a confidence level of 99.9%.

M.E. = %

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

Answer 1

Write MOE = ±z^*√[p_hat(1 − p_hat) ÷ n].

I have a program for Casio Calculator which returns a proportion of area under the standard normal curve as 0.99900026 (equivalent to 99.9%) for -3.2905999 ≤ z^* ≤ 3.2905999.

Place values to obtain Margin Of Error = ±3.2905999√[(0.628)(1 −0.628) ÷ 223], which simplifies to ±0.1065059675 equivalent to ±10.7%.