When determining sample size, the conventional approach would NOT be ________.

Question

BlackTom AI · Accepted Answer

Sample size is determined by desired confidence level, margin of error, population variability, and (when necessary) finite-population correction—not by an arbitrary fixed percentage of the population.

1) Relevant concepts
- Key inputs: confidence level (Z), acceptable margin of error (E), estimated proportion or variability (p), and population size (N). 
- Basic formula for a proportion (large population): n0 = (Z^2 * p * (1 − p)) / E^2. 
- For finite populations, apply the correction: n = n0 / [1 + (n0 − 1)/N].

2) Step-by-step reasoning
- A conventional approach is to compute n from the desired precision (E) and confidence (Z). Using heuristics from prior studies or reported sample sizes is also common practice when formal calculation is impractical. Choosing “5% of the population” is an arbitrary rule that ignores precision, confidence, and variability, so it is not a conventional statistical approach.

3) Example calculation (intermediate steps shown)
- Suppose 95% confidence (Z = 1.96), worst-case p = 0.5, margin E = 0.05:
  n0 = (1.96^2 * 0.5 * 0.5) / 0.05^2
  = (3.8416 * 0.25) / 0.0025
  = 0.9604 / 0.0025
  = 384.16 → n ≈ 385.
- If population N = 10,000, finite correction:
  n = 384.16 / [1 + (384.16 − 1)/10,000]
  = 384.16 / [1 + 0.038316]
  = 384.16 / 1.038316 ≈ 370.
- These results show sample size depends on E and Z, not a flat 5% rule (5% of 10,000 = 500, which may be larger or smaller than required depending on precision).

4) Why the correct answer is correct
- Option A (“five percent of the entire population”) is not conventional because it ignores the statistical determinants of sample size. A fixed percentage is arbitrary and can under- or over-estimate the needed sample for a given precision/confidence.

5) Why the other options are incorrect
- B, C, D are conventional heuristics: using averages of sample sizes of similar studies, previous surveys, or reported sample sizes in the literature are commonly used practical guides when formal calculation is not done.

6) Conclusion
- Therefore the unconventional choice is A) five percent of the entire population, which matches the provided correct answer.

When determining sample size, the conventional approach would NOT be ________.单项选择题

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