Given the simple regression model $Y={}_0+{}_{1}x$ and the regression results that follow, test the null hypothesis that the slope coefficient is $0$ versus the alternative hypothesis of greater than zero using probability of Type I error equal to $0\mathrm{.}05,$ and determine the two$-$sided $95\%$ and $99\%$ confidence intervals.

a$.$ A random sample of size $n=35$ with $b_1=6$ and $s_{b_1}=1\mathrm{.}9$

b$.$ A random sample of size $n=48$ with $b_1=6\mathrm{.}2$ and $s_{b_1}=1\mathrm{.}9$

c$.$ A random sample of size $n=35$ with $b_1=3\mathrm{.}8$ and $s_{b_1}=1\mathrm{.}49$

d$.$ A random sample of size $n=31$ with $b_1=9\mathrm{.}5$ and $s_{b_1}=1\mathrm{.}4$

a$.$ Test the null hypothesis that the slope coefficient is $0$ versus the alternative hypothesis of greater than zero using probability of Type I error equal to $0\mathrm{.}05.H_0.$ There is evidence that the slope coefficient is greater than zero.

Determine the two$-$sided $95\%$ confidence interval.

$(2\mathrm{.}12,($Round to two decimal places as needed.$)$

Determine the two$-$sided $99\%$ confidence interval.

$($Round to two decimal places as needed.$)$