Question

In a survey of 2957 adults, 1455 say hey have started paying bills online in the least year construct a 99% confidence interval for the population proportion

Answer 1

Answer: 0.49 ± 0.0237

Step-by-step explanation: A interval of a 99% confidence interval for the population proportion can be found by:

$p_{hat}$ ± z.$\sqrt{\frac{p_{hat}(1-p_{hat})}{n} }$

$p_{hat}$ is the proportion:

$p_{hat}$ = $\frac{1455}{2957}$

$p_{hat}$ = 0.49

For a 99% confidence interval, z = 2.576:

0.49 ± 2.576.$\sqrt{\frac{0.49(1-0.49)}{2957} }$

0.49 ± 2.576.$\sqrt{\frac{0.49*0.51}{2957} }$

0.49 ± 2.576.(0.0092)

0.49 ± 0.0237

For a 99% confidence interval, the proportion will be between 0.4663 and 0.5137 or 0.49 ± 0.0237