How is the margin of error (ME) calculated?

• A. ME = SE / CV
• B. ME = CV + SE
• C. ME = Critical Value × Standard Error
• D. ME = CV − SE

Answer: (C)

Margin of error tells you how wide your confidence interval around the estimate will be. It is determined by scaling the standard error by a critical value from the appropriate sampling distribution. The standard error shows how much the estimate would vary from one sample to another, and the critical value adjusts that variability to match the desired confidence level (for example, about 1.96 for a 95% interval under a normal approximation, or a t-value for small samples). Multiplying these two pieces gives ME = Critical Value × Standard Error. That product captures both the variability of the estimate and the level of certainty you want. The other forms—adding, subtracting, or dividing by the coefficient of variation—do not align with how a confidence interval’s width is defined.