Question

A magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie. Among the 1500 ​respondents, 12​% chose chocolate​ pie, and the margin of error was given as plus or minus5 percentage points. What values do ModifyingAbove p with caret​, ModifyingAbove q with caret​, ​n, E, and p​ represent? If the confidence level is 99​%, what is the value of alpha​?

Answer 1

Answer with explanation:

The confidence interval for population proportion is given by :_

`p\pm z_(\alpha/2)\sqrt{(p(1-p))/(n)}`

Where :
`\sqrt{(p(1-p))/(n)}=E` is the margin of error , n is the sample size , p is the sample proportion of success and
`\alpha` is the significance level.

Given : Confidence level :
`0.99`

Then , Significance level :
`\alpha: 1-0.99=0.01`

Sample size :
`n= 1500`

Sample proportion of ​respondents chose chocolate​ pie:
`p=0.12`

Margin of error :
`E=\pm0.05`