Question

In a survey of

30833083

​adults,

14201420

say they have started paying bills online in the last year.

Construct a​ 99% confidence interval for the population proportion. Interpret the results.

A​ 99% confidence interval for the population proportion is

left parenthesis nothing comma nothing right parenthesis,.

​(Round to three decimal places as​ needed.)

Answer 1

n = 3083

p = 1420 / 3083 = 0.4606

Z for 99% confidence interval = Z_0.005 = 2.576

confidence interval = (p + Z_0.005 * sqrt(p * (1 - p) / n))

                               = (0.4606 + 2.576 * sqrt(0.4606 * (1 - 0.4606) / 3083))

                               = (0.4606 + 0.023)

                               = (0.437 , 0.484)