Question

construct a ​99% confidence interval of the population proportion using the given information. x=240 n=300

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)