Use the given degree of confidence and sample data to constr

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Round to three decimal places. n= 144, x=52; 90% confidence

Solution

Given a=1-0.9= 0.1, Z(0.05) = 1.645 (from standard normal table)

p=52/144 = 0.3611111

So the lower bound is

p - Z*sqrt(p*(1-p)/n) =0.3611111 - 1.645*sqrt(0.3611111*(1-0.3611111)/144) =0.295

So the upper bound is

p + Z*sqrt(p*(1-p)/n) =0.3611111 + 1.645*sqrt(0.3611111*(1-0.3611111)/144) =0.427