please use R code

Several neurosurgeons wanted to determine whether a dynamic system (Z-plate) has different operative time relative to a static system (ALPS plate). The operative times, in minutes, for 14 dynamic replica- tions of the operation and 6 static replications were obtained and are given below. The neurosurgeons believe the collection of all operative times with either device would be roughly normally distributed. Dynamic: 370, 330, 510, 445, 295, 315, 490, 345, 450, 505, 335, 230, 325, 500 Static: 430, 445, 455, 455, 490, 535 The data can also be found in opt ime . csv. Here are the numeric summaries of the samples: Sample 3': Sample Median s 71, Dynamic 394.64 365 84.75 14 Static 468.33 455 38.166 6 (a) Graph the data as you see t. Why did you choose the graph(s) you did? How do those graphs align with the assumption that the populations of operative times are approximately normal? (b) Perform a two independent sample t test for means at the 5% level allowing the population variances to differ. As part of this test, specify your hypotheses, calculate a test statistic and p value by hand and make a conclusion in the context of the question. Check your computations with t.test() in R. (c) The data made us less condent in the surgeons assumptions that the populations of procedure times were close to normally distributed. So, perform a bootstrap hypothesis test of the hypotheses H0 1 denamic _ lgillsta'iic : 0 VBI'SUS HA : lgu-dy'.I'.I;c1.rr.~.1ic _ Hetatic 7 0 and compare the assumptions, test statistic, p value, and conclusions of this test to the Welchs you performed in part (b). The urinary uoride concentration (ppm) was measured both for a sample of livestock that had been grazing in an area previously exposed to ouride pollution and for a similar sample that had grazed in an unpolluted region. Due to the smaller sample sizes and some evidence of nonnormality seen in the samples, the researchers plan to perform a one-sided Wilcoxon Rank Sum Test. Polluted: 21.3, 13.7, 23.0, 17.1, 15.3, 20.9, 19.7 Unpolluted: 142,133, 17.2, 18.4, 20.0 The hypotheses to be tested are: H0 : The distributions of the polluted and unpolluted groups are identical. H A : The distribution of the polluted group is shifted to the right of the unpolluted group. (a) What assumptions must be made for a Wilcoxon Rank Sum Test to be reasonable? Check these assumptions for this data. (b) Rank all of the data from lowest to highest, and nd R, the sum of all the ranks from the polluted group. Also nd Rmm, the minimum possible sum of the ranks from the polluted group. (c) Find U553, the test statistic for this data. (d) Complete the test with the wilcox.test function in R, using a = 0.05. You will need to set the alternative argument to perform a one-sided test