Find the margin of error for the 95% confidence interval used to estimate the population proportion.?

Question

n = 169, x = 107

Answer 1

55.6 % - 70.5 %

Based on simulations:

A two-sided 95% test for the hypothesis p = 55.5% would be rejected for >= 107 out of 169.

A two-sided 95% test for the hypothesis p = 70.6% would be rejected for <= 107 out of 169.

But between 55.6 % - 70.5 % would not be rejected.

Answer 2

... so to build on first answer (55.6 % - 70.5 %), the margin of error is 1/2 the width of the confidence interval. Subtract 55.6 fr4om 70.5 and divide it in half.