medium · FRM Part 1 Quantitative Analysis
For a very large sample (n > 1000), an analyst finds that the sample variance s^2 is 1.1 times the hypothesized variance σ_0^2. Even though the difference is small, the Chi-square test rejects the null hypothesis. Why?
- Because variance tests generally lose statistical reliability once the sample becomes very large.
- Because the mean of the Chi-square sampling distribution steadily decreases as n grows larger.
- Because a variance ratio of 1.1 is always considered a statistically significant deviation.
- Because the test becomes highly powerful with a large sample size, detecting even small deviations.
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