A nutritionist randomly assigned $65$ students to receive either a regular ($150\text{ mL}$) or extra-large ($300\text{ mL}$) smoothie before class. After class, the nutritionist measured how much smoothie each student drank. The $32$ students with the regular smoothie drank an average of $92.4\text{ mL}$ with a standard deviation of $18.2\text{ mL}$. The $33$ students with the extra-large smoothie drank an average of $121.7\text{ mL}$ with a standard deviation of $15.5\text{ mL}$. Construct a $95\%$ confidence interval for the difference in mean smoothie consumption between the two groups.