Answer to Question #184147 in Statistics and Probability for Jii

Question

Calculate the confidence interval to estimate the population proportion, given the following data: a. n=400; p ̂ = 0.70; confidence level : 95% and b. n=700; p ̂ = 0.45; confidence level : 99%. 

Answer 1

a.) $p = 0.70$

$n = 400$

We know confidence interval can be given as,

$CI = p \pm z \sqrt{\dfrac{p(1-p)}{n}}$

$z= 1.96$ for 95% Confidence level.

$CI = 0.70 \pm 1.96 \sqrt{\dfrac{0.70\times 0.30}{400}}$

$CI = 0.70 \pm 0.045$

b.) $z= 2.57$ for 99% confidence interval.

$n= 700$

$p = 0.45$

$CI = 0.45 \pm 2.57\sqrt{\dfrac{0.45 \times 0.55}{700}}$

$CI= 0.45 \pm 0.048$