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 sample size. the margin of error. the population proportion. found from evaluating (1 - hat{p}). the sample proportion. the value of (p) is

Explanation:

• $\hat{p}$ represents the sample proportion. Given that 11% of the respondents chose chocolate pie, so $\hat{p}=0.11$.
• $\hat{q}$ is calculated as $1 - \hat{p}$. Substituting $\hat{p}=0.11$, we get $\hat{q}=1 - 0.11 = 0.89$.
• $n$ is the sample size. Here, $n = 1000$.
• $E$ is the margin of error. The margin of error is given as ±5 percentage points, so $E = 0.05$.
• $p$ is the population proportion. Since we don't have information about the population proportion (it is what we are trying to estimate), we don't have a numerical value for it from the given data.
• For a confidence level of $C = 95\%=0.95$, we use the formula $\alpha=1 - C$. Substituting $C = 0.95$, we 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 $p$ is (unknown, population proportion).
• The value of $\alpha$ is $0.05$.