Financial Risk Manager Part 1
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A two-tailed hypothesis test at the 95% significance level has a p-value of 2.14%. This means that:
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NNikitesh
A
At a 3% significance level, we cannot reject the null hypothesis
B
At a 2% significance level, we can reject the null hypothesis
C
At a 3% significance level, we can reject the null hypothesis
D
We have insufficient information to provide any kind of conclusion
Explanation:
The p-value of 2.14% is the smallest significance level at which we can reject the null hypothesis.
Key concepts:
- P-value definition: The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true.
- Decision rule: If p-value ≤ significance level (α), reject the null hypothesis. If p-value > significance level, fail to reject the null hypothesis.
Analysis:
- At 3% significance level (α = 0.03): p-value (0.0214) < α (0.03) → Reject H₀
- At 2% significance level (α = 0.02): p-value (0.0214) > α (0.02) → Fail to reject H₀
Therefore, option C is correct because at a 3% significance level, we can reject the null hypothesis since 2.14% < 3%.
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