Hello! I need help with this problem, I am puzzled by this: A study used a cross-over trial experiment to dissect whether eating oat bran lowered serum cholesterol levels. Twelve individuals were randomly assigned a diet that included either oat bran or cornflakes. After two weeks on the initial diet, serum cholesterol (mmol/L) was measured & then participants were "crossed-over" to the other diet. After two weeks on the second diet, cholesterol levels were measured again. 1) Using a 5% significance level, test the claim that a diet that includes oat bran decreases serum cholesterol using an R function only (no by-hand not needed). [be sure to follow all steps for hypothesis testing for this part] (1 hypothesis, 1 R output, 1 reporting required numbers, 1 decision, 1 interpretation in context) 2) Construct an appropriate confidence interval equivalent to the test in part (1) only using an R function. Explain the choice of the interval, then report and interpret the interval. 3) In the context of this problem, what does it mean if a Type 1 error was committed? Are there any significant consequences if a Type 1 error was made? Any help is appreciated; thanks!