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Answer: Construct a two-tailed test with Hₐ: m ≠ 0
C is correct. Since the objective is to test if the mean return is zero, this would be a two-tailed test with the assumed true null hypothesis that the mean is equal to 0. The alternative hypothesis would be that the mean return is not equal to zero. A, B, and D are Incorrect. These go against the correct formulation of the hypothesis test as explained in C above. **Learning Objective:** Differentiate between a one-sided and a two-sided test and identify when to use each test. **Reference:** Global Association of Risk Professionals. Quantitative Analysis. New York, NY: Pearson, Chapter 6, Hypothesis Testing [QA-6].
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An Investor is testing the hypothesis that the mean return generated by an equity fund is zero and collects return data on the fund over the past 250 trading days. The Investor calculates the sample daily mean return and the sample standard deviation as 0.2% and 0.35%, respectively. In performing the hypothesis test, which of the following is the most appropriate construction of the alternative hypothesis for testing the true mean, m?
A
Construct a one-tailed test with Hₐ: m > 0
B
Construct a one-tailed test with Hₐ: m < 0.2
C
Construct a two-tailed test with Hₐ: m ≠ 0
D
Construct a two-tailed test with Hₐ: m ≥ 0.2