
Answer-first summary for fast verification
Answer: Do not reject $H_0$
## Explanation The 95% confidence interval for the slope coefficient is: $$\beta_1 = 0.8823 \pm 0.2147$$ This gives us the interval: - Lower bound: 0.8823 - 0.2147 = 0.6676 - Upper bound: 0.8823 + 0.2147 = 1.0970 The interval [0.6676, 1.0970] contains the value 1. **Key Concept**: When testing a hypothesis at significance level α, if the (1-α)% confidence interval contains the hypothesized value, we **fail to reject** the null hypothesis. - Significance level: 5% - Confidence level: 95% - Hypothesized value: β₁ = 1 - Since 1 is within the 95% confidence interval [0.6676, 1.0970], we **do not reject** H₀ This means there is insufficient evidence to conclude that the slope coefficient is statistically different from 1 at the 5% significance level.
Author: Tanishq Prabhu
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An analyst obtained the following linear regression relationship between 2 variables, X and Y:
where and . He proceeded to construct a 2-sided 95% confidence interval for the slope coefficient () and obtained the following interval:
Suppose the analyst decided to test the hypothesis vs at 5% significance, what would be the inference?
A
Reject
B
Do not reject
C
The slope coefficient is statistically different than "1"
D
Cannot tell from the information provided
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