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\%`

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\%`