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CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing

An analyst wants to test whether the median monthly return of a small-cap fund differs from zero. The return sample is small and strongly skewed with extreme outliers. Which type of test is most appropriate?

A nonparametric test is most appropriate. The sample is small and strongly skewed with outliers, so the normality assumption behind t-tests and z-tests is violated. Nonparametric tests make few or no distributional assumptions, so they remain valid for such data and a hypothesis about the median.

  1. AA nonparametric test, because it does not rely on a normal distributionCorrect
  2. BA parametric z-test, because the population variance is unknown
  3. CA parametric t-test, because the sample is small

Explanation

Parametric tests such as the t-test assume the data come from a particular distribution, usually normal. With a small, skewed sample containing outliers that assumption fails, so a nonparametric test, such as a sign test, is more suitable. The t-test is not rescued by small sample size; a small sample makes the normality assumption more important.

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