CFA Level 1: Hypothesis Testing - Two-Tailed vs. One-Tailed Tests

Hypothesis Testing: Two-Tailed vs. One-Tailed Tests

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Question

Which of the following is/are true?

I. It is harder to reject the null under a two-tailed test than under a one-tailed test.

II. To test the hypothesis: Ho: X = 0, H1: X < 0, you have to employ a left-tailed test.

III. The acceptance region under a right tailed test extends from zero to positive infinity.

IV. The critical z-statistics in one-tailed tests are always lower than the z-statistics in the corresponding two-tailed test.

Answers

Explanations

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A. B. C. D. E.

D

Under a two-tailed test, values on either side of the null can contribute to a rejection. Hence, the critical values under a two-tailed test have to be higher than under a one-tailed test for a given level of significance. This makes it harder to reject the null under a two-tailed test. This makes intuitive sense. In a one-tailed test, you are specifying a stricter alternative than under a completely general, two-tailed alternative (in the current example, you are claiming that X is less than zero as an alternative which is a stronger statement than the claim that X is non-zero). The rejection region in a right-tailed regression extends from the critical t-value associated with the given significance level and positive infinity. This critical value is greater than zero.