APFIVE In an experiment where researchers analyze the impact of the number of study sessions per week (x) on improvement in test scores (y, in points), a regression model is applied yielding the t-statistic computed as $$t=\frac{b-\beta}{s_b}$$. What would happen if the sample residuals were not normally distributed, particularly affecting the validity of the t-test and the resulting confidence interval for the slope?
Non-normal residuals will lead to a slight change in the numerical value of the t-statistic but not enough to impact conclusions drawn from the test.
The t-test remains valid regardless of the residual distribution because the central limit theorem fully compensates for non-normal errors.
Non-normally distributed residuals weaken the validity of the t-test and confidence intervals because the assumed t-distribution of the statistic is no longer appropriate.
A departure from normality in residuals would affect only the intercept estimation, leaving the slope test unaffected.
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