Question

magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the ​respondents, ​% chose chocolate​ pie, and the margin of error was given as percentage points. What values do ​, ​, ​n, E, and p​ represent? If the confidence level is ​%, what is the value of ​?

Answer 1

Complete Question

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 ​respondents, 12 ​% chose chocolate​ pie, and the margin of error was given as plus or minus 5 percentage points.What values do ​ $\r p , \ \r q$, ​n, E, and p​ represent? If the confidence level is 90​%, what is the value of $\alpha$ ​?

Answer:

a

   $\r p$ is the sample proportion   $\r p = 0.12$

   $n$ is the  sample size is  $n = 500$

   $E$ is the  margin of error is $E = 0.05$

   $\r q$ represents the proportion of those that did not chose chocolate​ pie i.e                        $\r q = 1- \r p$

b

   $\alpha = 10\%$

Step-by-step explanation:

Here

    $\r p$ is the sample proportion   $\r p = 0.12$

   $n$ is the  sample size is  $n = 500$

    $\r q$ represents the proportion of those that did not chose chocolate​ pie i.e  

      $\r q = 1- \r p$

      $\r q = 1- 0.12$

      $\r q = 0.88$

     $E$ is the  margin of error is $E = 0.05$

Generally $\alpha$ is the level of significance and it value is mathematically evaluated as

     $\alpha = ( 100 - C )\%$

Where  $C$ is the confidence level which is given in this question as  $C = 90 \%$

So  

    $\alpha = ( 100 - 90 )\%$

    $\alpha = 10\%$