Question

a political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate wants a 4% margin of error at a 99% confidence level, what sample size is needed? use technology to find the z - score and do not round between steps. make sure you use the correct rounding rule for samples size, and give your answer in whole people. check answer

Explanation:

Step1: Find the z - score

For a 99% confidence level, the z - score \(z\) is \(z = 2.576\) (using standard normal distribution tables or technology).

Step2: Use the formula for sample size in proportion

The formula for the sample size \(n\) when estimating a proportion is \(n=\frac{z^{2}\cdot p(1 - p)}{E^{2}}\). When no prior estimate of the proportion \(p\) is available, we use \(p=0.5\) (this gives the maximum variance and thus maximum sample size required). The margin of error \(E = 0.04\).
Substitute the values into the formula:

$$
LATEXBLOCK0
$$

Step3: Round the sample size

Since we cannot have a fraction of a person and we want to ensure the margin of error is met or exceeded, we round up.

Answer:

\(1037\)