In reply to Ksharp.

Hi KSharp, Thanks for noticing that I switched the null and alternative hypotheses in that sentence! I have corrected the text. The null hypothesis for these tests is always that the REDUCED model is better (in this case, beta1=0). When the p-value is large, there is no evidence to reject H0, so you should use the reduced model.

This example does not have a small p-value, but if a p-value is small you reject H0 and use the alternative (which is the full model).