If n=110 and ˆ p (p-hat) =0.91, find the margin of error at a 95% confidence level

Answer 1

If p hat is 0.91,then q hat is 1.00 - 0.91,or 0.09. n x p hat and n x q hat are both > 5, so can assume a normal distribution. For confidence level of 95%, z_c = 1.96.

Margin of error (E) is z_c x sqrt[(p hat x q hat)/n] 1.96 x sqrt[(0.91 x 0.09)/110] ≈ 0.053

Left endpoint: 0.91 - 0.053 = 0.857 Right endpoint: 0.91 + 0.053 = 0.963

With 95% confidence, you can say that the population proportion is between 85.7% and 96.3%.