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 ±3 percentage points. what values do $hat{p}$, $hat{q}$, n, e, and p represent? if the confidence level is 99%, what is the value of $alpha$? the value of $hat{p}$ is the value of $hat{q}$ is the value of n is the value of e is the value of p is

Explanation:

Step1: Define $\hat{p}$

$\hat{p}$ is the sample proportion. Given 12% chose chocolate - pie, so $\hat{p}=0.12$.

Step2: Calculate $\hat{q}$

$\hat{q}=1 - \hat{p}$. Substitute $\hat{p}=0.12$, then $\hat{q}=1 - 0.12 = 0.88$.

Step3: Identify $n$

$n$ is the sample size. Here, $n = 1500$.

Step4: Determine $E$

$E$ is the margin of error. Given margin of error is $\pm3$ percentage points, so $E = 0.03$.

Step5: Calculate $\alpha$

The confidence - level is $C=0.99$. We know that $\alpha=1 - C$. So $\alpha=1 - 0.99=0.01$.

Answer:

The value of $\hat{p}$ is $0.12$
The value of $\hat{q}$ is $0.88$
The value of $n$ is $1500$
The value of $E$ is $0.03$
The value of $\alpha$ is $0.01$