Question

A particular poll tracks daily the percentage of citizens from a certain country who approve or disapprove of the job the President is doing. Daily results are based on telephone interviews with approximately 1500 national adults. The poll reported that 43​% of adults approve of the President doing his job. A media outlet claimed the true proportion to be 44​%.

Find the 99% confidence interval _______________, ________________ (round to 3 decimal points)

Please show the math and not just the equation

Answer 1

At 99% confidence interval the critical value is z_0.005 = 2.58

The 99% confidence interval is

$\widehat p$+/- z_0.005 * sqrt($\widehat p$(1 - $\widehat p$)/n)

= 0.43 +/- 2.58 * sqrt(0.43 * (1 - 0.43)/1500)

= 0.43 +/- 0.033

= 0.397, 0.463