For all the hypothesis testing problems in this and future assignments, please state the null and alternative hypotheses, calculate the value of the test statistic, determine if the results are statistically significant (using rejection region or p-value approaches), and then state your conclusion in terms of the problem (do not just say reject or fail to reject HO). For the problems done using R, do not pad the assignment with tons of R output. Please only provide the relevant output. Copy and paste the R code and output into word. You do not need to submit your R log le. A crossover study was conducted to investigate whether oat bran cereal helps to lower serum cholesterol in hypercholesterolemic males. Fourteen such individuals were randomly placed on a diet that included either oat bran or corn flakes; after two weeks, their low-density lipoprotein (LDL) cholesterol levels were recorded. Each man was then switched to the alternative diet. After a second two-week period, the LDL cholesterol level of each individual was again recorded. The data from this study are shown below: Subject Corn flakes Oat bran 1 4.61 3.84 2 6.42 5.57 3 5.4 5.85 4 4.54 4.8 5 3.98 3.68 6 3.82 2.96 7 5.01 4.41 8 4.34 3.72 9 3.8 3.49 10 4.56 3.84 11 5.35 5.26 12 3.89 3.73 13 2.25 1.84 14 4.24 4.14 a. Are the two samples of data paired or independent? b. What are the appropriate null and alternative hypotheses for a one-sided test? c. Conduct the test at the 0.05 significance level. What is the p-value? d. What do you conclude?2. Use the rejection region approach to make the decision in parta). Calculate the approximate p-value in part b) to confirm your decision in parta). An experiment was conducted to compare the mean lengths of time required for the bodily absorption of two drugs A and B. Ten people were randomly selected, with five people assigned to receive one drug and the remaining five assigned to receive the other drug. The length of time (in minutes) for the drug to reach a specified level in the blood was recorded, and the data summary is given in the table: Drug A Drug B X1 = 27.2 X2 = 33.5 $7 = 16.36 $7 = 18.92 a. Do the data provide sufficient evidence to indicate a difference in mean times to absorption for the two drugs? Find the rejection region and draw the conclusion using a = 0.05. b. Find the approximatep-value for the test. Does this value confirm your conclusions? c. Find a 95% confidence interval for the difference in mean times to absorption. Does the interval confirm your conclusions in part a