Question

a magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. among the 1000 respondents, 11% chose chocolate pie, and the margin of error was given as ±5 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

Explanation:

Step1: Find the value of \(\hat{p}\)

\(\hat{p}\) is the sample proportion. Given that 11% chose chocolate pie, so \(\hat{p}=0.11\)

Step2: Find the value of \(\hat{q}\)

We know that \(\hat{q} = 1-\hat{p}\). Substituting \(\hat{p}=0.11\), we get \(\hat{q}=1 - 0.11=0.89\)

Step3: Find the value of \(n\)

\(n\) is the sample size. The problem states there are 1000 respondents, so \(n = 1000\)

Step4: Find the value of \(E\)

\(E\) is the margin of error. Given as ±5 percentage points, so \(E=0.05\)

Step5: Find the value of \(\alpha\)

The confidence level \(C = 0.95\). Using the formula \(\alpha=1 - C\), we substitute \(C = 0.95\) and get \(\alpha=1- 0.95 = 0.05\)

Answer:

The value of \(\hat{p}\) is \(0.11\).
The value of \(\hat{q}\) is \(0.89\).
The value of \(n\) is \(1000\).
The value of \(E\) is \(0.05\).
The value of \(\alpha\) is \(0.05\).