medium · FRM Part 1

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?

1. Because variance tests are not reliable for large samples.
2. Because the Chi-square distribution mean decreases with n.
3. Because 1.1 is always a significant ratio.
4. Because the test becomes highly powerful with a large sample size, detecting even small deviations.

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