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A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 respondents, $12 \%$ chose chocolate pie, and the margin of error was given as \pm 3 percentage points. What values do $\hat{p}$, $\hat{q}, n, E$, and $p$ represent? If the confidence level is $95 \%$, 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
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Step 1 ：In this problem, we are given a poll of 1000 adults where 12% chose chocolate pie. The margin of error is given as ±3 percentage points. We are asked to identify the values of \(\hat{p}\), \(\hat{q}\), \(n\), \(E\), and \(p\).

Step 2 ：\(\hat{p}\) represents the sample proportion, which in this case is the proportion of adults who chose chocolate pie. So, \(\hat{p}\) = 0.12

Step 3 ：\(\hat{q}\) represents the complement of the sample proportion, which is the proportion of adults who did not choose chocolate pie. So, \(\hat{q}\) = 1 - \(\hat{p}\) = 1 - 0.12 = 0.88

Step 4 ：\(n\) represents the sample size, which is the total number of adults polled. So, \(n\) = 1000

Step 5 ：\(E\) represents the margin of error, which is the range within which the true population proportion is likely to fall. So, \(E\) = 0.03

Step 6 ：\(p\) represents the population proportion, which is the true proportion of all adults who would choose chocolate pie. However, this value is unknown in this problem.

Step 7 ：The confidence level is 95%, so \(\alpha\) would be 1 - 0.95 = 0.05, representing the probability that the true population proportion falls outside the confidence interval.

Step 8 ：Final Answer: The value of \(\hat{p}\) is \(\boxed{0.12}\), The value of \(\hat{q}\) is \(\boxed{0.88}\), The value of \(n\) is \(\boxed{1000}\), The value of \(E\) is \(\boxed{0.03}\), The value of \(p\) is unknown, The value of \(\alpha\) is \(\boxed{0.05}\)