find the margin of error for the sample proportion, given a sample size of n=1400. Round to the nearest percent.
To find the margin of error for the sample proportion, you need to know the sample size (n). The formula for the margin of error for a sample proportion is:
Margin of Error = Z * sqrt((p * (1 - p)) / n)
where:
- Z is the z-score associated with the desired level of confidence
- p is the estimated proportion of the population
Since you haven't provided the estimated proportion or the desired level of confidence, I cannot calculate the exact margin of error. However, I can walk you through the steps to calculate it once you have these values.
First, you need to determine the desired level of confidence. Typically, common levels of confidence are 90%, 95%, or 99%. Let's assume a confidence level of 95% for the purpose of this explanation.
Second, you need to determine the estimated proportion of the population. This can be based on previous data or an initial estimate. Let's assume an estimated proportion of 0.5 (50%) for simplicity.
With these values, you can calculate the margin of error:
1. Determine the z-score associated with a 95% confidence level. The z-score for a 95% confidence level is approximately 1.96.
2. Plug the values into the formula:
Margin of Error = 1.96 * sqrt((0.5 * (1 - 0.5)) / 1400)
3. Calculate the expression inside the square root:
= sqrt((0.5 * 0.5) / 1400)
= sqrt(0.25 / 1400)
= sqrt(0.0001785714)
4. Plug the result into the original formula:
Margin of Error = 1.96 * 0.01334
= 0.0261 (rounded to four decimal places)
Finally, round the margin of error to the nearest percent:
= 3% (rounded to the nearest percent)
Therefore, the margin of error for a sample proportion with a sample size of n = 1400, assuming a 95% confidence level and an estimated proportion of 0.5 (50%), is approximately 3% rounded to the nearest percent.