Financial Risk Manager Part 1
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An analyst obtained the following linear regression relationship between 2 variables, X and Y: Y = α + β₁X where α = 0.45 and β = 0.8823
He proceeded to construct a 2-sided 95% confidence interval for the slope coefficient (β₁) and obtained the following interval: β = 0.8823 ± 0.2147
Suppose the analyst decided to test the hypothesis H₀: β₁ = 1 vs Hₐ: β₁ ≠ 1 at 5% significance, what would be the inference?
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NNikitesh
A
Reject H₀
B
Do not reject H₀
C
The slope coefficient is statistically different than "1"
D
Cannot tell from the information provided
Explanation:
The 95% confidence interval for β₁ is 0.8823 ± 0.2147, which gives us the interval (0.6676, 1.0970). Since this interval contains the value 1, we cannot reject the null hypothesis H₀: β₁ = 1 at the 5% significance level. In hypothesis testing, if the hypothesized value (1 in this case) falls within the confidence interval, we fail to reject the null hypothesis. Option C is incorrect because it states the opposite conclusion. Option D is incorrect because we have sufficient information from the confidence interval to make the inference.
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