Advanced Placement (AP) Middle School

8. Candidate A and Candidate B are running for president. You are planning a survey to determine what proportion of registered voters plan to vote for Candidate A (p). You will contact a random sample of registered voters. You want to estimate p with 99% confidence and a margin of error no greater than 0.01. What is the minimum number of registered voters you will need to survey in order to meet these requirements?
(A)97
(B)166
(C)6,766
(D)9,604
(E)16,590​

Answers

Answer 1

Answer:

The correct answer is (E).

Answer 2

The minimum sample size of registered voters that are needs to be surveyed in order to meet these requirements is 16590 registered voters.

What is the required sample size?

The sample size, n, can be calculated using the formula below:

[tex]n = \frac{z^{2}×p(1-p)}{(\frac{ε}{2}) ^{2}}[/tex]

where:

z = is the z scoreε is the margin of errorpis the population proportion

For the data provided:

z for 99% confidence = 2.58

ε/2 = 0.005

p = 0.5

Substituting the values:

[tex]n = \frac{2.58^{2}×0.5(1-0.5)}{0.005^{2}} = 16641[/tex]

Therefore, the minimum sample size of registered voters that are needs to be surveyed in order to meet these requirements is 16590 registered voters.

Learn more about sample size at: https://brainly.com/question/24084761

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