(Solved): 6. For the data and sample regression equation shown below, do the following. a. Decide, at the 5% ...

6. For the data and sample regression equation shown below, do the following. a. Decide, at the $5\%$ significance level, whether the data provide sufficient evidence to conclude that $\mathrm{x}$ is useful for predicting $\mathrm{y}$. b. Find a $95\%$ confidence interval for the slope of the population regression line. $\hat{y}=2.074+1.148x,?x_i=11,?x_i^2=35,b_1=1.148,\text{ and }{s}_e=1.7285$ 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? $t=$ (Round to two decimal places as needed.) Find the P-value. P-value $=$ (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 provide sufficient evidence to conclude that $\mathrm{x}$ is useful for predicting $\mathrm{y}$. B. Do not reject ${\mathrm{H}}_0$; the data do not provide sufficient evidence to conclude that $\mathrm{x}$ is useful for predicting $\mathrm{y}$. C. Reject ${\mathrm{H}}_0$; the data do not 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 $95\%$ confidence interval for the slope of the population regression line. The $95\%$ confidence interval for ${?}_1$ is from to (Round to three decimal places as needed.)