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Chartered Financial Analyst Level 1

Chartered Financial Analyst Level 1

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An analyst evaluates 30 paired monthly returns for two stock indices to determine if the mean difference of the returns is zero. The number of degrees of freedom for the t-test in this scenario is:

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Explanation:

The correct answer is B (29).

Explanation:

  • For a paired comparisons test, the t-statistic has n−1n - 1n−1 degrees of freedom, where nnn is the number of paired observations.
  • Here, n=30n = 30n=30, so the degrees of freedom are 30−1=2930 - 1 = 2930−1=29.

Why not A or C?

  • A (28) is incorrect because it assumes n−2n - 2n−2 degrees of freedom, which is not applicable for a paired test.
  • C (58) is incorrect because it represents the degrees of freedom for a hypothesis test concerning the equality of means of two independent samples, calculated as n1+n2−2n_1 + n_2 - 2n1​+n2​−2.
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