3. Cholesterol levels are measured for a random sample of 1,000 persons. The survey
is repeated for the same population, but with the sample size tripled to 3,000. Which
one of the following is true?
a. The two sample standard deviations will be approximately equal
b. The new sample standard deviation will be smaller than the first
c. The new sample standard deviation will be larger than the first
d. This cannot be answered without knowing the sample means

Cholesterol Sample Standard Deviation: Sample Size Effect Explained

Sample standard deviation measures data spread within a cholesterol sample and remains approximately equal regardless of tripling sample size from 1,000 to 3,000, as it estimates population variability independently of n.​

Correct Answer

Option a holds true. Both samples from the same population yield standard deviations close to the population value, with larger n providing a more stable but not systematically different estimate.​

Option Analysis

• a. The two sample standard deviations will be approximately equal: Correct. Sample SD estimates population SD without dependence on sample size; simulations confirm near-identical values (e.g., 40.61 for n=1,000 vs. 38.90 for n=3,000 from normal population).​

• b. The new sample standard deviation will be smaller than the first: Incorrect. No systematic decrease occurs; any difference arises from sampling variability, not size.​

• c. The new sample standard deviation will be larger than the first: Incorrect. Larger samples do not inflate SD; they better approximate the population value.​

• d. This cannot be answered without knowing the sample means: Incorrect. SD calculation uses deviations from the sample mean, independent of mean values.​

Key Statistical Concepts

Sample standard deviation s=∑(xi−xˉ)2n−1s=n−1∑(xi−xˉ)2 depends on data dispersion, not n directly. Contrast with standard error SE=snSE=ns, which shrinks with larger n for mean precision.​