Results from a regression model analysis are shown below. The numbers below the coefficient estimates are the sample standard errors of the coefficient estimates.

a$.$ Compute two$-$sided $95\%$ confidence intervals for the three regression slope coefficients.

b$.$ For each of the slope coefficients, test the hypothesis $H_0$:${}_j=0$ against the appropriate one$-$sided alternative. Use $=0\mathrm{.}05.$

hat$(y)=-24\mathrm{.}50+15\mathrm{.}4x_1-1\mathrm{.}7x_2-35\mathrm{.}1x_3$

$R^2=0\mathrm{.}75$

$(8\mathrm{.}1)$

$n=21$

Click the icon to view a table of critical values for the Student's $t$ distribution.

a$.$ What is the $95\%$ confidence interval for the coefficient of $x_1?$

$($Round to one decimal place as needed.$)$