a magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie. among…

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 ±4 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 $alpha$?\nthe value of $hat{p}$ is\nthe value of $hat{q}$ is\nthe value of n is\nthe value of e is\nthe value of p is

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 ±4 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 $alpha$?\nthe value of $hat{p}$ is\nthe value of $hat{q}$ is\nthe value of n is\nthe value of e is\nthe value of p is

Answer

Explanation:

Step1: Define $\hat{p}$

$\hat{p}$ is the sample - proportion. Given that 11% of respondents chose chocolate pie, so $\hat{p}=0.11$.

Step2: Define $\hat{q}$

$\hat{q}=1 - \hat{p}$. Substituting $\hat{p}=0.11$, we get $\hat{q}=1 - 0.11 = 0.89$.

Step3: Define $n$

$n$ is the sample - size. Here, $n = 1500$.

Step4: Define $E$

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

Step5: Define $p$

$p$ is the population - proportion. Since we don't know the true population proportion, we have no information to determine its value. In a confidence - interval context, we are trying to estimate $p$ using $\hat{p}$.

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 $0.04$ The value of $p$ is unknown