Show that for the birthweight data in Section 5.

6.6.2 there is no significant decrease in birthweight for smoking mothers. [Hint: create a new variable nonsmoke \(=1\)-smoke, which reverses the encoding for the smoking and non-smoking mothers. Then, the parameter \(\beta_{1}+\) \(\beta_{3}\) in the original model is the same as the parameter \(\beta_{1}\) in the model

\[ \mathrm{Bwt}=\beta_{0}+\beta_{1} \text { age }+\beta_{2} \text { nonsmoke }+\beta_{3} \text { age } \times \text { nonsmoke }+\varepsilon \]

Now find a \(95 \%\) for \(\beta_{3}\) and see if it contains zero.]