In a confidence interval, the range of values above and below the sample statistic is called:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → margin of error
A confidence interval is written as
\( \displaystyle \text{sample statistic}\pm\text{margin of error} \)
For a mean, for example, it is \( \bar{x}\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} \). The amount added to and subtracted from the sample statistic, \( z_{\alpha/2}\frac{\sigma}{\sqrt{n}} \), which fixes the range of values above and below it, is the margin of error.
Why the other options are incorrect
Option (1) degree of freedom — Incorrect. The degrees of freedom (such as n − 1) decide which t-distribution is used; they are not a range of values.
Option (2) critical value — Incorrect. The critical value (such as \( z_{\alpha/2} \)) is only one factor of the margin of error.
Option (4) standard deviation — Incorrect. The standard deviation measures the spread of the data; divided by \( \sqrt{n} \) and multiplied by the critical value, it gives the margin of error.