Question

Construct a confidence interval of the population proportion at the given level of confidence.

X= 240 N= 300 99% confidence

Answer 1

Confidence interval for population proportion is
sample proportion +/- confidence coefficient*standard error of p
Sample proportion = p = x/n = 180/300 = 0.6
Confidence coefficient is the critical value of z for 95% confidence level = 1.96
Standard error of p = sqrt [p*(1-p)/n]
= sqrt [0.6*0.4/300]
= 0.0283
The CI is
0.6 +/- 1.96*0.0283
0.6 +/- 0.055
lower boundary is 0.6-0.055 = 0.545
upper boundary is 0.6+0.055 = 0.655
The CI is (0.545, 0.655)