In the context of probability and statistics, what does the error (accuracy of a poll) expressed as a $\pm$ percentage most commonly represent?

• A. The likelihood that the sample was randomly selected
• B. The probability that the sample mean $ṅ$ equals the population mean $\mu$
• C. The margin of error, which indicates the range within which the true population parameter is likely to fall
• D. The standard deviation of the population $\sigma$

Answer: (C)

Verified step by step guidance

1. Understand that in the context of polls and surveys, the plus-or-minus percentage often refers to the margin of error.
2. Recognize that the margin of error quantifies the uncertainty or potential error in the estimate derived from a sample compared to the true population parameter.
3. Know that the margin of error is typically calculated based on the standard error of the sample statistic and a critical value from a probability distribution (often the normal 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 of the estimate.
5. Interpret the margin of error as the range around the sample estimate within which the true population parameter is likely to lie with a certain confidence level (e.g., 95%).