FRM Part I · FRM Exam Part I · Hypothesis Testing
Which statement about chi-square and F tests for variances is correct?
Both the chi-square test for a single variance and the F-test for two variances are sensitive to non-normality, so fat-tailed return data can distort results. They also cannot be negative, and the F-test assumes independent samples.
- ABoth are sensitive to departures from normality in the underlying dataCorrect
- BThe chi-square variance test is robust to non-normality when the sample is small
- CThe F-test requires the two samples to be positively correlated
- DA chi-square variable can take negative values when the sample variance is below the hypothesized variance
Explanation
Both tests assume normal populations and can be misleading if the data are fat-tailed. The F-test requires independent samples, and chi-square and F variables are never negative because they are built from sums of squares or ratios of variances.
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