After estimating the model \(y=\beta_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+e\) with \(N=203\) observations, we obtain the following information: \(\sum_{i=1}^{N}\left(x_{i 2}-\bar{x}_{2}\right)^{2}=1780.7, \sum_{i=1}^{N}\left(x_{i 3}-\bar{x}_{3}\right)^{2}=3453.3, b_{2}=0.7176, b_{3}=1.0516\), \(S S E=6800.0\), and \(r_{23}=0.7087\).

a. What are the standard errors of the least squares estimates \(b_{2}\) and \(b_{3}\) ?

b. Using a \(5 \%\) significance level, test the hypothesis \(H_{0}: \beta_{2}=0\) against the alternative \(H_{1}: \beta_{2} eq 0\).

c. Using a \(10 \%\) significance level, test the hypothesis \(H_{0}: \beta_{3} \leq 0.9\) against the alternative \(H_{1}: \beta_{3}>0.9\).

d. Given that \(\widehat{\operatorname{cov}}\left(b_{2}, b_{3}\right)=-0.019521\), use a \(1 \%\) significance level to test the hypothesis \(H_{0}: \beta_{2}=\beta_{3}\) against the alternative \(H_{1}: \beta_{2} eq \beta_{3}\).