FRM Part I · FRM Exam Part I · Hypothesis Testing
An analyst tests whether the variance of monthly returns on a fund equals 16 (%^2) using a sample of 25 monthly observations with a sample variance of 24 (%^2). Assuming returns are normally distributed, what is the chi-square test statistic for H0: sigma^2 = 16?
The chi-square statistic equals (n-1) times the sample variance divided by the hypothesized variance: 24 x 24 / 16 = 36.0, with 24 degrees of freedom. It uses n-1 because one degree of freedom is lost estimating the sample mean.
- A36.0Correct
- B16.0
- C24.0
- D38.4
Explanation
The statistic is (n-1)s^2/sigma0^2 = 24 x 24 / 16 = 36.0. Using n instead of n-1 gives 25 x 24/16 = 37.5, and the simple ratio 24/16 = 1.5 omits the degrees-of-freedom factor. The statistic has 24 degrees of freedom.
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