Financial Risk Manager Part 1
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If a researcher wants to test that the mean return of 50 small-cap stocks from the Singapore Exchange is greater than 14%, which of the following would be the alternative hypothesis for the test?
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NNikitesh
A
H₁: μ ≠ 14%
B
H₁: μ > 14%
C
H₁: μ < 14%
D
H₀: μ < 14%
Explanation:
The correct answer is B: H₁: μ > 14%.
Explanation:
In hypothesis testing:
- The null hypothesis (H₀) is typically a statement of no effect or no difference, or the status quo that we want to test against.
- The alternative hypothesis (H₁) is what the researcher wants to prove or find evidence for.
In this case, the researcher wants to test that the mean return is greater than 14%. Therefore:
- The null hypothesis would be H₀: μ ≤ 14% (mean is less than or equal to 14%)
- The alternative hypothesis would be H₁: μ > 14% (mean is greater than 14%)
This is a one-tailed test (specifically, a right-tailed test) because we're only interested in whether the mean is greater than 14%, not whether it's different in either direction.
Why the other options are incorrect:
- A (H₁: μ ≠ 14%): This would be for a two-tailed test where we want to test if the mean is different from 14% in either direction.
- C (H₁: μ < 14%): This would be for testing if the mean is less than 14% (left-tailed test).
- D (H₀: μ < 14%): This is a null hypothesis statement, not an alternative hypothesis, and it's for testing if the mean is less than 14%.
The text confirms: "Since the researcher wants to test that if the mean of 50 small-cap stocks is greater than 14%, the null hypothesis is H₀: μ ≤ 14% and the alternative hypothesis is H₁: μ > 14%."
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