A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 4% margin of error at a 99% confidence level, what size of sample is needed? Give your answer in whole people.
To achieve a 4% margin of error at a 99% confidence level, a sample size of 1037 people is required. The calculation uses the formula for sample size estimation focused on proportions. This includes determining the Z-value for 99% confidence, estimating the population proportion, and setting the desired margin of error.
To determine the necessary sample size to achieve a 4% margin of error at a 99% confidence level, we can use the formula for sample size estimation in proportion studies. The formula is given by:
n = (Z^2 p (1 - p)) / E^2
Where:
1. Identifying Z-value: For a 99% confidence level, the Z-value is approximately 2.576.
2. Estimating p: Assuming p = 0.5 (which provides the maximum sample size as it yields the largest product of p(1-p)).
3. Setting margin of error (E): The desired margin of error is 0.04 (4%).
Plug these values into the formula:
n = (2.576^2 0.5 (1 - 0.5)) / 0.04^2
Calculating further:
n = (6.635776 0.5 0.5) / 0.0016
n = (6.635776 * 0.25) / 0.0016
n = 1.658944 / 0.0016
n = 1036.84
Since we can’t have a fraction of a person, we round up to the nearest whole number. Thus, the required sample size is 1037 people for a 4% margin of error at a 99% confidence level.
https://brainly.com/question/39045727