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FRM Part I · FRM Exam Part I · Hypothesis Testing

An analyst samples 25 monthly returns of a fund. The sample mean is 1.4% and the sample standard deviation is 3.0%. She tests H0: mean = 0.5% against a two-sided alternative. Population variance is unknown and returns are assumed normal. What is the test statistic and its distribution?

The statistic is t = 1.50 with 24 degrees of freedom. The standard error is 3.0 divided by the square root of 25, or 0.6, and the difference of 0.9 divided by 0.6 gives 1.50. Unknown population variance requires a t distribution with n minus 1 degrees of freedom.

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

Explanation

Standard error = 3.0/sqrt(25) = 0.6. The statistic = (1.4 - 0.5)/0.6 = 1.50. With unknown variance, use t with n-1 = 24 degrees of freedom. Using 25 df miscounts df; 0.30 forgets to divide by sqrt(n) properly (uses 3.0/... as 3 only); 7.50 divides by 0.12.

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