Question

a magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie. among the 1500 respondents, 11% chose chocolate pie, and the margin of error was given as ±5 percentage points. what values do p, q, n, e, and p represent? if the confidence level is 99%, what is the value of a? the value of p is the value of q is the value of n is the value of e is the value of p is

Explanation:

Step1: Identify the sample proportion \(\hat{p}\)

The sample proportion \(\hat{p}\) is the proportion of respondents who chose chocolate pie. Given that \(11\%\) of the \(1500\) respondents chose chocolate pie, \(\hat{p}=0.11\).

Step2: Calculate \(\hat{q}\)

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

Step3: Identify the sample size \(n\)

The sample size \(n\) is the number of respondents in the poll. Here, \(n = 1500\).

Step4: Identify the margin of error \(E\)

The margin of error \(E\) is given as \(5\%\) or \(E = 0.05\) (since \(5\%=\frac{5}{100}=0.05\)).

Step5: Calculate \(\alpha\)

The confidence level \(C = 99\%\) or \(C=0.99\). We use the formula \(\alpha=1 - C\). Substituting \(C = 0.99\) into the formula, we get \(\alpha=1 - 0.99 = 0.01\).

Answer:

The value of \(\hat{p}\) is \(0.11\), the value of \(\hat{q}\) is \(0.89\), the value of \(n\) is \(1500\), the value of \(E\) is \(0.05\), and the value of \(\alpha\) is \(0.01\).