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FRM Part I · FRM Exam Part I · Hypothesis Testing

A portfolio manager tests H0: mu = 0.50% against H1: mu ≠ 0.50% for mean monthly return using a sample of 36 observations. The sample mean is 0.80% and the sample standard deviation is 1.20%. What is the t-statistic, and is H0 rejected at the 5% two-tailed level (critical t with 35 degrees of freedom is approximately 2.03)?

The standard error is 1.20% divided by the square root of 36, which is 0.20%. The t-statistic is (0.80 − 0.50)/0.20 = 1.50. This is smaller than the critical value of about 2.03, so the analyst fails to reject the null hypothesis.

  1. At = 1.50; fail to reject H0Correct
  2. Bt = 1.50; reject H0
  3. Ct = 9.00; reject H0
  4. Dt = 0.25; fail to reject H0

Explanation

Standard error = 1.20/sqrt(36) = 0.20. t = (0.80 − 0.50)/0.20 = 1.50, which is below 2.03 in absolute value, so H0 is not rejected. Using 1.20 without dividing by sqrt(n) gives 0.25, and multiplying by sqrt(n) instead gives 9.00, both being errors.

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