(Solved): For the data and sample regression equation shown below, do the following. a. Decide, at the 10% si ...

For the data and sample regression equation shown below, do the following. a. Decide, at the $10\%$ significance level, whether the data provide sufficient evidence to conclude that $\mathrm{x}$ is useful for predicting $\mathrm{y}$. b. Find a $90\%$ confidence interval for the slope of the population regression line. $\hat{y}=1.255+1.266x$ $\begin{array}{l}{?}_{{\mathrm{s}}_{\mathrm{e}}}=1.4911\end{array}$ Click here to view the critical t-values page $1^2$ Click here to view the critical t-values page $2^3$ a. What are the hypotheses for the test? A. ${\mathrm{H}}_0:{?}_1=0$ and ${\mathrm{H}}_{\mathrm{a}}:{?}_1?=0$ B. ${\mathrm{H}}_0:{?}_1=0$ and ${\mathrm{H}}_{\mathrm{a}}:{?}_1>0$ C. ${\mathrm{H}}_0:{?}_1?=0$ and ${\mathrm{H}}_{\mathrm{a}}:{?}_1=0$ D. ${\mathrm{H}}_0:{?}_1=0$ and ${\mathrm{H}}_{\mathrm{a}}:{?}_1<0$ What is the test statistic? $\mathrm{t}=$ (Round to two decimal places as needed.) The critical value(s) is(are) (Use a comma to separate answers as needed. Round to three decimal places as needed.) Which of the following is the correct conclusion for the hypothesis test? A. Do not reject ${\mathrm{H}}_0$; the data do not provide sufficient evidence to conclude that $\mathrm{x}$ is useful for predicting $\mathrm{y}$. B. Reject ${\mathrm{H}}_0$; the data do not provide sufficient evidence to conclude that $\mathrm{x}$ is useful for predicting $\mathrm{y}$. C. Do not reject ${\mathrm{H}}_0$; the data provide sufficient evidence to conclude that $\mathrm{x}$ is useful for predicting $\mathrm{y}$. D. Reject ${\mathrm{H}}_0$; the data provide sufficient evidence to conclude that $\mathrm{x}$ is useful for predicting $\mathrm{y}$. b. Find a $90\%$ confidence interval for the slope of the population regression line. The $90\%$ confidence interval for ${?}_1$ is from to (Round to three decimal places as needed.)