FRM Part I · FRM Exam Part I · Hypothesis Testing
A researcher tests H0: mean return ≤ 0 versus H1: mean return > 0 using 36 observations, sample mean 0.9% and sample standard deviation 3.6%. The critical t (35 df, one-sided 5%) is about 1.69. Which conclusion is correct?
The t statistic is 1.50, from a standard error of 3.6 divided by 6, or 0.6, and a mean of 0.9. It falls short of the one-sided 5% critical value of about 1.69, so the researcher fails to reject the null that the mean return is nonpositive.
- At = 1.50; fail to reject H0Correct
- Bt = 1.50; reject H0
- Ct = 0.25; fail to reject H0
- Dt = 9.0; reject H0
Explanation
SE = 3.6/6 = 0.6, so t = 0.9/0.6 = 1.50. This is below the one-sided critical value of 1.69, so H0 is not rejected. Rejection would require a larger statistic.
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