In the context of confidence intervals, what does the margin of error account for?

• A. The bias introduced by measurement errors
• B. The difference between the sample mean $𝑛$ and the population median
• C. The variability due to random sampling from the population
• D. The total population size $N$

Answer: (C)

Verified step by step guidance

1. Understand that the margin of error in a confidence interval quantifies the amount of uncertainty or variability in the estimate due to random sampling.
2. Recognize that it does not account for systematic errors like bias from measurement errors, but rather the natural fluctuations that occur when different samples are taken from the same population.
3. Recall that the margin of error is typically calculated using the standard error of the estimate and a critical value from a probability distribution (such as the z-distribution or t-distribution).
4. Express the margin of error formula as \(\text{Margin of Error} = z^* \times SE\), where \(z^*\) is the critical value and \(SE\) is the standard error representing sampling variability.
5. Conclude that the margin of error reflects the variability due to random sampling from the population, which helps to create a range (confidence interval) that likely contains the true population parameter.