Financial Risk Manager Part 1
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During a statistical test to determine if the mean return on an asset is different from zero, an FRM Part 1 candidate obtains a p-value of 1.4%. With a significance level of 1%, she would:
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NNikitesh
A
Reject the null hypothesis
B
Fail to reject the null hypothesis
C
Conclude that the mean return is different from zero
D
Conclude that the mean return is negative (loss)
Explanation:
Explanation
In hypothesis testing:
- p-value = 1.4% (0.014)
- Significance level (α) = 1% (0.01)
The decision rule is:
- If p-value ≤ α → Reject the null hypothesis
- If p-value > α → Fail to reject the null hypothesis
Here: 1.4% > 1% (0.014 > 0.01), so we fail to reject the null hypothesis.
Key Points:
- The p-value (1.4%) represents the probability of observing the test results (or more extreme results) assuming the null hypothesis is true.
- The significance level (1%) is the threshold we set for rejecting the null hypothesis.
- Since the p-value is greater than the significance level, we don't have sufficient evidence to reject the null hypothesis.
- The null hypothesis in this case would be: "The mean return is equal to zero."
Why not the other options:
- A: Incorrect because p-value > α
- C: Incorrect because we fail to reject the null hypothesis, so we cannot conclude the mean is different from zero
- D: Incorrect - we cannot determine the direction (positive or negative) from this test alone; this would require a one-tailed test
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