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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

A risk analyst tests whether the mean daily return of a portfolio is zero using 25 independent, normally distributed daily returns. The sample mean is 0.30% and the sample standard deviation is 1.00%. The population variance is unknown. What is the t-statistic and its degrees of freedom?

The t-statistic is 1.50 with 24 degrees of freedom. The standard error is 1.00%/√25 = 0.20%, so t = 0.30%/0.20% = 1.50, and the degrees of freedom equal the sample size minus one, which is 24.

  1. At = 1.50 with 24 degrees of freedomCorrect
  2. Bt = 1.50 with 25 degrees of freedom
  3. Ct = 0.30 with 24 degrees of freedom
  4. Dt = 7.50 with 24 degrees of freedom

Explanation

t = (0.30 - 0)/(1.00/√25) = 0.30/0.20 = 1.50. Degrees of freedom are n-1 = 24. Option 7.50 uses 1.00/25 as the standard error, which wrongly omits the square root; option 0.30 ignores the standard error entirely.

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