How is the margin of error in a survey calculated?

The margin of error in a survey is calculated using the formula that includes the critical value (z), the population standard deviation (σ), and the sample size (n). The correct formula, which is represented in the chosen answer, calculates the margin of error as the product of the z-score, which corresponds to the desired confidence level (for instance, 1.96 for a 95% confidence interval), and the standard error of the mean, which is (σ/√n).

This relationship is significant because it quantifies the uncertainty in estimating a population parameter based on a sample. The standard deviation measures the variability within the population, and dividing it by the square root of the sample size provides a measure of how much the sample mean is expected to vary from the true population mean. As the sample size increases, the standard error decreases, leading to a smaller margin of error. In contexts where accurate data estimation is crucial, such as in surveys, this formula is essential for ensuring that the results are statistically sound and that conclusions can be drawn with a specified degree of confidence.

The other formulas do not accurately represent the margin of error as they either misplace the z-score or incorrectly arrange the components involving standard deviation and sample size.