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{(p_(hat)(1-p_(hat)))/(n) }`

`p_(hat)` is the proportion:

`p_(hat)` =
`(1455)/(2957)`

`p_(hat)` = 0.49

For a 99% confidence interval, z = 2.576:

0.49 ± 2.576.
`\sqrt{(0.49(1-0.49))/(2957) }`

0.49 ± 2.576.
`\sqrt{(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