Melatonin is a hormone in the body that is commonly known to affect sleep. Researchers studying the effects of synthetic melatonin on sleep measured the amount of time (in minutes) it took $7$ subjects to fall asleep after taking a specified dosage of melatonin as well as after taking a placebo. Their data is shown in the table below: Subject | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ :-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:| Placebo | $14.2$ | $12.0$ | $15.3$ | $8.5$ | $8.9$ | $11.6$ | $17.8$ Melatonin | $13.1$ | $9.2$ | $11.9$ | $7.2$ | $7.0$ | $8.1$ | $13.5$ **Assuming that all the necessary conditions are met, construct a $95\%$ confidence interval for the true average difference (placebo - melatonin) in time needed to fall asleep for subjects like these.** *Round your answer to the nearest hundredth.* [[☃ math-keypad 1]] to [[☃ math-keypad 2]] *minutes*