Question

The is the standard deviation of the sampling distribution of the mean or proportion.

• A. standard error
• B. standardized variate
• C. variance
• D. standard deviation

Hint:

SE = SD of a sampling distribution. SD describes spread of data; SE describes precision of an estimator.

Answer 1

The Correct Option is A

Step 1: Definition.
The standard error (SE) is the standard deviation of a sampling distribution.
For a mean: $\mathrm{SE}(\bar X)=\sigma/\sqrt{n}$ (or $s/\sqrt{n}$ when $\sigma$ unknown).
For a proportion: $\mathrm{SE}(\hat p)=\sqrt{\dfrac{p(1-p)}{n}}$ (or with $\hat p$).
Step 2: Eliminate distractors.
(b) A standardized variate is $(X-\mu)/\sigma$.
(c) Variance is the square of a standard deviation.
(d) “Standard deviation” without qualification refers to a population/sample spread, not specifically the spread of the sampling distribution.
\[ \boxed{(a)} \]