(Solved): The amounts of a chemical compound \( y \) that dissolved in 100 grams of water at various tempera ...

The amounts of a chemical compound \( y \) that dissolved in 100 grams of water at various temperatures \( x \) were recorded. The data were coded and recorded in the accompanying table. Use this information to answer parts \( \mathbf{a} \) and \( \mathbf{b} \). Click here to view the table of chemical compounds. Click here for page 1 of the table of critical values of the t-distribution. Click here for page 2 of the table of critical values of the t-distribution. a) Construct a \( 99 \% \) confidence interval for the average amount of chemical that will dissolve in 100 grams of water at \( 50^{\circ} \mathrm{C} \). \( <\mu_{Y \mid 50}<\quad \) (Round to three decimal places as needed.) Chemical compound data fitted linear regression equation \[ \begin{array}{c} \hat{y}=5.3175+0.7086 x \\ s^{2}=6.94 \\ \bar{x}=37.5 \\ S_{x x}=11812.50 \end{array} \]