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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
Explanation:
The 95% confidence interval for the slope coefficient is:
This gives us the interval:
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.
This means there is insufficient evidence to conclude that the slope coefficient is statistically different from 1 at the 5% significance level._