Question

in a survey of 2767 adults ,1422 say they have started paying bills online in the last year constuct a confidence interval for the population proportion interpret the results. A 99% confidence interval for the population proportion is

Answer 1

In order to find the confidence interval, follow these steps:

1. calculate the "p-hat" value, we can calculate it by dividing the number of people that said they have started paying bills online by the total number of people, like this:

p-hat = 1422/2767 = 0.51

2. Calculate the margin of error.

The margin of error "ME" is given by the following formula:

`ME=z\sqrt[]{(p-hat(1-p-hat))/(n)}`

Where n is the sample size (2767 in this case) and z is the z-score value. The z-score is tabulated and it depends on the value of the confidence percentage, in this case we have a 99% confidence and the z-score is 2.5758 for this value, then we get:

`ME=2.5758\sqrt[]{(0.51(1-0.51))/(2767)}=0.024`

3. Add and subtract the ME from the p-hat value, like this:

The confidence interval is determined by subtracting and adding the ME to the p-hat, then we get:

CI = (0.51 - 0.024, 0.51 + 0.024) = (0.486, 0.534)

Then, a 99% confidence interval for the population proportion is ​(0.486, 0.534)