Dark Chocolate & Health Flavonoids are compound in plants that are thought to have antioxidant effects. They are commonly found in foods such as tea, chocolate, leafy greens, broccoli, citrus and purple fruits and vegetables. One study examined the effect of flavonoids on blood vessel function in healthy people. In a randomized, double-blind, placebo-controlled study, one group received 46 grams (1.6 ounces) of dark chocolate that is naturally flavonoid-rich every data for two weeks, while a control group received a placebo consisting of dark chocolate with low flavonoid content. Participants had their vascular health measured (by means of the flow-mediated dilation (FMD) before and after the two-week study. The increase (measured in percent changeover the two-week period was measured, with larger numbers indicating greater vascular health. If flavonoids increased blood vessel function, we would expect higher changes in in those that had higher flavonoid chocolate. * Based on Engler et al 2004 3.2. State the null and alternative hypotheses in symbolic and sentence form. 3.4. assess the conditions for conducting the appropriate test in the contacts of the problem. you may need to run code to get some of the answers but you must show the code and the justification within this document. 3.5. perform an appropriate hypothesis test using the 't.test()' function then provide your test statistic, degrees of freedom(Welch's approximation), and p-value. 3.6. Interpret your p-value in the context of the problem. 3.7. Using the t.test() function, calculate and interpret the 99% confidence interval for the difference in change in FMO for those that had higher flavonoid chocolate or that had lower flavonoid chocolate 3.8. True or false? The confidence interval does not include zero which suggests that there is a significant difference in the change in FMD from high flavonoid and from low flavonoid consumption . Data: Group Dilation High 0.1 High -2.5 High. 3.9 High 2.8 High 1.7 High 3.8 High 1.1 High. 3.7 High 5.0 High -1.2 High. 0.4 High -1.2 High -0.5 High 1.6 High. 2.4 High 1.5 High -2.9 High -1.0 High 0.2 High 0.0 High 3.8 High 4.8 High 2.0 Low -1.0 Low -4.1 Low. -1.6 Low -1.1 Low -1.0 Low 0.2 Low 0.4 Low -3.8 Low. -1.0 Low 1.1 Low 0.1 Low. -2.6 Low -0.8 Low 2.1 Low. -0.7 Low 0.3 Low 1.2 Low -3.1 Low -2.5 Low. -2.2 Low. -0.7 Low -0.9