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 :_

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

Where : $\sqrt{\dfrac{p(1-p)}{n}}=E$ 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 : $E=\pm0.05$