APFIVE In an experiment studying the effect of fertilizer amount (x, in grams) on corn yield (y, in bushels), a linear regression is performed and the estimated slope with its standard error is used to conduct a t-test for the slope. What would happen if the degrees of freedom were mistakenly calculated as $$n-1$$ instead of the correct $$n-2$$, particularly affecting the p-value of the t-test?
The miscalculation would affect only the width of the confidence interval, leaving the p-value and t-test results unchanged.
The slope estimate would become biased upward and the p-value would be inflated, reducing the chance of rejecting $$H_0$$.
There would be no effect on the p-value or conclusions since the difference between $$n-1$$ and $$n-2$$ is negligible.
Using $$n-1$$ degrees of freedom instead of $$n-2$$ would overestimate the degrees of freedom, likely resulting in a smaller p-value and an increased risk of a Type I error.
Question Leaderboard
Not enough data yet to show leaderboard.