Question

Alice wants to estimate the percentage of people who plan

on voting yes for the upcoming school levy. She surveys
380 individuals and finds that 260 plan on voting yes.
Identify the values needed to calculate a confidence interval
at the 90% confidence level. Then find the confidence interval.
zo10 z0.05 zo.025 zo01 z0.005
1.282 1.645 1.960 2.326 2.576
Use the table of common z-scores above.

Answer 1

"
`0.6450 < p < 0.723`" is the right solution.

Explanation:

Given:

n = 380

x = 260

Point estimate,

`\hat p = (x)/(n)`

`=(260)/(380)`

`=0.6842`

Critical value,

`Zc = 1.645`

Standard error will be:

`S.E = \sqrt{(0.6842(1-0.6842))/(380) }`

`=0.0238`

Margin of error will be:

`E = Zc* S.E`

`=1.645* 0.0238`

`=0.0392`

hence,

Confidence level will be:

=
`\hat p \pm E`

=
`0.6842 \pm 0.0392`

=
`0.6450 < p < 0.723`