a magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. among…

a magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. among the 2000 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 99%, 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

a magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. among the 2000 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 99%, 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

Answer

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})

(\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. Here, (n = 2000)

Step4: Find the value of (E)

(E) is the margin of error. Given as (\pm5) percentage points, so (E = 0.05)

Step5: Find the value of (\alpha)

The confidence level (C=0.99). Using the formula (\alpha=1 - C), we substitute (C = 0.99) and 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 (2000) The value of (E) is (0.05) The value of (\alpha) is (0.01)