Question

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 14% chose chocolate pie, and the margin of error was given as + or - 5 percentage points. What values do p, q, n, E, and p represent(The sample proportion, found from evaluating 1-p, the sample size, margin of error, and population of proportion)? If the confidence level is 99%, what is the value of a?

Answer 1

• p = 0.12

,

• q = 0.88

,

• n = 500

,

• E = 0.05

,

• p =, ,population proportion

,

• α = 0.01

Step-by-step explanation

Given

• Sample: 500 adults

,

• Proportion of chocolate pie: 0.14

,

• Margin of error: ±0.05

,

• We are asked for the values that ,p​, q​, ​n, E, ,and, p​ ,represent.

Procedure

Assuming that p is the estimated proportion of the sample that chose chocolate, this would be 0.12, while q would be the estimated proportion of the sample that did not choose chocolate:

`q=1-p=1-0.12=0.88`

Additionally, the letter n represents the sample size, which in our case is 500, and E is the given margin of error 0.05. Finally, the last p represented as the population proportion with a confidence interval of:

`\hat{p}\pm z_{(\alpha)/(2)}*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

where the value of α is:

`\alpha=1-0.99=0.01`

and the value of α/2 is:

`(\alpha)/(2)=0.005`

Additionally, E is also:

`E=z_{(\alpha)/(2)}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`