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Degrees of Freedom for Slope T-Test

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In a linear regression analysis of the relationship between fertilizer amount and corn yield, a t-test is conducted for the slope of the regression line. If the degrees of freedom are incorrectly calculated as n−1n-1 instead of the correct n−2n-2, what is the most likely effect on the resulting p-value?

A

The slope estimate would become biased upward and the p-value would be inflated, reducing the chance of rejecting H0H_0.

B

The miscalculation would affect only the width of the confidence interval, leaving the p-value and t-test results unchanged.

C

There would be no effect on the p-value or conclusions since the difference between n−1n-1 and n−2n-2 is negligible.

D

Using n−1n-1 degrees of freedom instead of n−2n-2 would overestimate the degrees of freedom, likely resulting in a smaller p-value and an increased risk of a Type I error.

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