A dataset of 9 observations shows a strong sample slope but a residual plot reveals a curved pattern. Evaluate whether t-based inference about beta is appropriate and justify your recommendation.

• A. Not appropriate: t-based inference assumes linearity of the conditional mean. A curved residual pattern indicates model misspecification; fit a nonlinear model or transform variables and reassess assumptions before performing t-based slope inference.
• B. Appropriate only if n > 30; with n = 9 you should always use nonparametric methods regardless of residual patterns.
• C. Not appropriate because small samples never allow any inference; you must have at least 50 observations for t-methods to be considered.
• D. Appropriate because a strong sample slope guarantees the t-procedures work even if residuals show curvature, since t-tests are robust to model misspecification.

Answer: (A)