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A researcher happens to use a very small number of replications during a Monte Carlo study. Which of the following statements will be true in this scenario?
I. Standard errors of the estimated quantities may be too large and quite unacceptable II. The process may yield a statistic that's imprecise III. The results of the process may be affected by unrepresentative combinations of random draws
A
All the above
B
I and II only
C
II only
D
II and III only
Explanation:
When using a very small number of replications in a Monte Carlo study:
Standard errors will be too large: With few replications, the estimated standard errors of quantities will be large and unreliable because they are based on insufficient data.
Statistics will be imprecise: The estimates produced will have high variance and low precision due to the small sample size.
Results may be affected by unrepresentative combinations: With few random draws, there's a higher chance of getting unusual or atypical combinations that don't represent the true underlying distribution.
All three statements (I, II, and III) are correct, making option A the correct answer. This is a fundamental issue in Monte Carlo simulation where increasing the number of replications reduces sampling error and improves the reliability of estimates.