Explanation:
There is a direct relationship between a confidence interval and a two-sided hypothesis test. If the null hypothesized value () falls within the specified confidence interval at the confidence level, then we will fail to reject the null hypothesis at the significance level.
In this case, Sarah's 95% confidence interval is . Because the hypothesized value of 0.01 falls inside this interval ($0.0066 \le 0.01 \le 0.0334H_0$) at the 5% significance level.
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Q.41 Sarah, a risk manager at a global investment bank, is reviewing the performance of a Value-at-Risk (VaR) model in anticipation of a regulatory audit. The bank's current model estimates a 99% VaR of $25 million. To validate this model, Sarah compares the actual daily losses that exceed the VaR estimate (VaR exceptions) with the expected number of exceptions. For a one-year period (250 trading days), she observes 5 VaR exceptions. Sarah constructs a 95% confidence interval for the true probability of a VaR exception and finds it to be [0.0066, 0.0334]. She then conducts a hypothesis test with: H₀: p = 0.01 (model is correctly calibrated) H₁: p ≠ 0.01 (model is not correctly calibrated) Using the same data and at the same significance level as her confidence interval, which of the following statements is correct regarding the relationship between Sarah's hypothesis test and confidence interval?
A
Sarah will reject H₀ because 0.01 falls outside her 95% confidence interval
B
Sarah will fail to reject H₀ because 0.01 falls within her 95% confidence interval
C
Sarah will reject H₀ because 0.01 falls within her 95% confidence interval
D
Sarah will fail to reject H₀ because 0.01 falls outside her 95% confidence interval
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