11.65 Compare the means.

Regression on a single indicator variable compares the mean responses in two groups. It is, in fact, equivalent to the pooled $t$ test for comparing two means (Chapter 7, page 389). Use the pooled $t$ test to compare the mean price of the homes that have three or more bedrooms with the mean price of those that do not. Verify that the test statistic, degrees of freedom, and $P$-value agree with the $t$ test for the coefficient of Bed3 in Example 11.21.