Question

In a survey of 2548 ​adults, 1413 say they have started paying bills online in the last year. Construct a​ 99% confidence interval for the population proportion. Interpret the results.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 1413 / 2548 = 0.555

1 - = 1 - 0.555 = 0.445

Z_/2 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.555 * 0.445) / 2548)

= 0.025

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.555 - 0.025 < p < 0.555 + 0.025

0.530 < p < 0.580

The 99% confidence interval for the population proportion p is : 0.530 , 0.580