QuestionDark Chocolate for Good Health A study ${ }^{1}$ examines chocolate's effects on blood vessel function in healthy people. In the randomized, double-blind, placebo-controlled study, 11 people received 46 grams ( 1.6 ounces) of dark chocolate (which is naturally flavonoid-rich) every day for two weeks, while a control group of 10 people received a placebo consisting of dark chocolate with low flavonoid content. Participants had their vascular health measured (by means of flow-mediated dilation) before and after the two-week study. The increase over the two-week period was measured, with larger numbers indicating greater vascular health. For the group getting the good dark chocolate, the mean . increase was 1.3 with a standard deviation of 2.32 , while the control group had a mean change of -0.96 with a standard deviation of 1.58. ${ }^{1}$ Engler, M., et. al., "Flavonoid-rich dark chocolate improves endothelial function and increases plasma epicatechin concentrations in healthy adults," Journal of the American College of Nutrition, 2004 Jun; 23(3): 197-204.
Part 1 (a) Find a $95 \%$ confidence interval for the difference in means between the two groups $\mu_{C}-\mu_{N}$, where $\mu_{C}$ represents the mean increase in flow-mediated dilation for people eating dark chocolate every day and $\mu_{N}$ represents the mean increase in flowmediated dilation for people eating a dark chocolate substitute each day. You may assume that neither sample shows significant departures from normality.
Round your answers to two decimal places. The 95\% confidence interval is $\square$ to i .