Question

a magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. among th respondents, 14% chose chocolate pie, and the margin of error was given as ±4 percentage points. what val (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 margin of error. the value of (hat{q}) is the value of n is the value of e is the value of p is the sample proportion. the margin of error. the population proportion. found from evaluating (1-hat{p}). the sample size.

Explanation:

Step1: Determine the value of $\hat{p}$

$\hat{p}$ represents the sample proportion. Given that 14% of the respondents chose chocolate pie, so $\hat{p}=0.14$.

Step2: Determine the value of $\hat{q}$

$\hat{q}$ is found from evaluating $1 - \hat{p}$. So $\hat{q}=1 - 0.14 = 0.86$.

Step3: Determine the value of $n$

$n$ represents the sample size. Here, $n = 2000$.

Step4: Determine the value of $E$

$E$ represents the margin of error. Given as $\pm4$ percentage points, so $E = 0.04$.

Step5: Determine the value of $p$

$p$ represents the population proportion (unknown in this context as we only have sample - based estimates).

Step6: Determine the value of $\alpha$

The confidence level is $C=0.95$. Using the formula $\alpha=1 - C$. So $\alpha=1 - 0.95=0.05$.

Answer:

$\hat{p}=0.14$, $\hat{q}=0.86$, $n = 2000$, $E = 0.04$, $p$ is the population proportion (unknown), $\alpha=0.05$