APFIVE In a laboratory setting where researchers study the link between enzyme concentration (x) and reaction time (y, in seconds), a linear regression produces an estimated slope $$b$$ and its standard error $$s_b$$, which are then used to perform a t-test. What would happen if the population variance of reaction time increased significantly while the variability in enzyme concentration remained constant, especially regarding $$s_b$$ and the corresponding t-distribution?
A higher reaction time variance would unexpectedly decrease $$s_b$$ by normalizing the error term, leading to a narrower confidence interval.
An increase in the reaction time variance would raise the residual standard error, thereby increasing $$s_b$$ and widening the confidence interval, even though the degrees of freedom stay the same.
The increased variance in reaction time would have no effect on $$s_b$$ since it depends solely on the spread of $$x$$.
The t-distribution would adjust for the increased variance, leaving the standard error and confidence interval unchanged.
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