Two Means - Matched Pairs (Dependent Samples): Videos & Practice Problems

A nutritionist wants to determine if a new supplement increases the number of hours athletes sleep. She selects $12$ athletes and records their sleep hours with and without the supplement. The mean of the differences $\bar{d}$ is $0.7$ hours, and the standard deviation of the differences $s_d$ is $0.5$ hours. Construct a $90\%$ confidence interval for ${\mu }_d$, the mean difference in sleep hours. Assume the differences are normally distributed.