Question

A political candidate has asked his/her assistant to conduct a poll to determine the percentage of people in the community that supports him/her. if the candidate wants a 3% margin of error at a 99% confidence level, what size of sample is needed? be sure to round accordingly. the candidate would need to survey people in the community in order to be within a 3% margin of error at a 99% confidence level.

Answer 1

To calculate the sample size needed for a political candidate to achieve a 3% margin of error at a 99% confidence level, one can use the formula involving the Z-score, the estimated population proportion (often taken as 0.5 for maximum variability), and the desired margin of error. This calculation will determine the minimum number of people in the community that the candidate needs to survey.

Step-by-step explanation:

To determine the sample size needed for a 3% margin of error at a 99% confidence level, it's essential to understand the concepts of sampling error and confidence intervals in polling. The margin of error indicates the range within which we can expect the true proportion of the population's opinion to lie. The confidence level indicates the degree of certainty with which we can expect the sample proportion to fall within the margin of error of the true population proportion.

If a political candidate wants a 3% margin of error at a 99% confidence level, without the population proportion or standard deviation, we can use the maximum variability assumption where the population proportion (p) is 0.5, since this value will provide the largest sample size. The formula for determining sample size is:

n = (Z^2 * p * (1-p)) / E^2

Where:

• n is the sample size
• Z is the Z-score corresponding to the desired confidence level
• p is the estimated proportion of the population
• E is the margin of error

Using standard Z-scores for common confidence levels (Z is approximately 2.58 for a 99% confidence level) and a margin of error (E) of 0.03, the formula would look like this:

n = (2.58^2 * 0.5 * 0.5) / 0.03^2

After calculating, we obtain a sample size that must be rounded up to the nearest whole number to ensure the margin of error is not exceeded.

To reduce the margin of error or increase the confidence level, one can increase the sample size. However, other factors not covered by the margin of error, such as non-sampling errors, question wording, and the timing of the poll, can also affect the survey's outcome.