How does increasing the sample size affect the standard error of an estimated mean?
Correct Answer
C) It decreases the standard error of the estimate
Why this is correct: Increasing the sample size decreases the standard error of the estimate. Standard error measures the precision of an estimate (like a mean); a larger sample reduces variability and provides a more precise estimate, as the original explanation notes. Why the other choices are wrong: It does not have no effect. It does not increase the standard error. It does not convert the standard error into a variance; variance is a different measure. Exam tip: Standard Error = Standard Deviation / sqrt(n). As n (sample size) increases, the standard error decreases, improving estimate precision.
Why This Is the Correct Answer
The standard error of a mean decreases as sample size increases, in proportion to the square root of the sample size, narrowing the confidence interval around the estimate.
Why the Other Options Are Wrong
Option A: It has no effect on the standard error at all
Sample size is the principal determinant of the standard error alongside underlying variability. It has a substantial effect.
Option B: It increases the standard error proportionally
The relationship runs in the opposite direction. Larger samples reduce rather than increase the standard error.
Option D: It converts the standard error into a variance
Variance is a separate measure of dispersion. Increasing sample size does not convert one statistic into another.
Square Root of n
Square Root of n. Four times the sample for half the error β precision gets expensive.
How to use: Tighten the market area as well as enlarging the sample. Lower variability helps at every sample size.
Exam Tip
Do not confuse standard error with standard deviation. One describes the estimate's precision, the other the data's spread.
Common Mistakes to Avoid
- -Confusing standard error with standard deviation
- -Expecting linear improvement from larger samples
- -Ignoring underlying variability as the other lever
Concept Deep Dive
Analysis
The standard error of an estimated mean measures how much that estimate would vary across repeated samples from the same population, and it falls as sample size grows β specifically in proportion to the square root of the sample size. That square root relationship is what makes the practical point: quadrupling the sample halves the standard error, so improvements come at increasing cost. Reducing the standard error narrows the confidence interval around the estimate, which is what allows an appraiser to say a market's mean price per square foot is known within a useful band rather than a wide one. The other lever is the underlying variability: a homogeneous market produces a smaller standard error at any sample size than a heterogeneous one, which is part of why tightly defined market areas support better statistics. The distractors misstate the direction, deny an effect, or confuse the standard error with the variance, which is a different measure entirely.
Background Knowledge
The standard error of a mean equals the standard deviation divided by the square root of the sample size. It decreases with larger samples and with lower underlying variability, narrowing confidence intervals.
Real-World Application
An appraiser expands a sample from 15 to 60 sales, halving the standard error of the mean price per square foot and reporting a materially tighter interval.
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