Question

A magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie. among the 1500 ​respondents, 12​% chose chocolate​ pie, and the margin of error was given as plus or minus3 percentage points. what values do modifyingabove p with caret​, modifyingabove q with caret​, ​n, e, and p​ represent? if the confidence level is 99​%, what is the value of alpha​? the value of modifyingabove p with caret is ▼ the value of modifyingabove q with caret is ▼ the sample size. found from evaluating 1 minus modifyingabove p with caret . the population proportion. the margin of error. the sample proportion. the value of n is ▼ the population proportion. the margin of error. the sample size. found from evaluating 1 minus modifyingabove p with caret . the sample proportion. the value of e is ▼ the margin of error. the sample proportion. the sample size. the population proportion. found from evaluating 1 minus modifyingabove p with caret .

Answer 1

The value of
`\hat p` will be the same as the percentage of the 1500 respondents who like chocolate pie. And that percentage as per the data in the question is 12%. Therefore,
`\hat p`=0.12.

The value of
`\hat q` simply is
`\hat q=1-\hat p`, therefore,
`\hat q=1-0.12=0.88`.

The sample size is 1500. Therefore,
`n=1500`

The margin of error is given as
`\pm 3`%. Therefore,
`E=0.03`.

The value of
`\alpha` is calculated as
`\alpha`=1-Confidence Level

`\alpha=1-0.99=0.01`

Answer 2

0.01 is alpha level

Explanation:

Given that a survey of a magazine of 1500 adults revealed that 12% chose chocolate pie.

i.e. p = proportion of people who like chocolate pie = 0.12

Margin of error = ±0.03

The value of q =1-\hat p , =1-0.12 = 0.88

The sample size n is given as 1500. Therefore, n=1500

The confidence level is given as 99%

Hence alpha = 1- confidence level

=1-0.99=0.01

Hence answer is 0.01