Ignore parts within questions that require R, do it instead only by hand.

4. Several neurosurgeons wanted to determine whether a dynamic system (Z-plate) reduced operative time relative to a static system (ALPS plate). The operative times, in minutes, for 14 dynamic replications of the operation and 6 static replications were obtained and are given below: Dynamic: 370, 360, 510, 445, 295, 315, 490, 345, 450, 505, 335, 280, 325, 500 Static: 430, 445, 455, 455, 490, 535 (a) Graph the data as you see fit. Why did you choose the graph(s) you did and what does it (do they) tell you? Also calculate summary statistics relevant to the research question. (b) Perform a two population t test for means at the 5% level not assuming equal variance and justify why the assumptions of the test are reasonably met (or describe what assumptions we are assuming are met). As part of this test, specify your hypotheses, calculate a test statistic and p value and make a conclusion in the context of the question. Check your computations with t.test() in R. (c) Construct and interpret a 95% confidence interval for the true difference in means (by hand and then again in R) applying the same assumptions as in part b. Describe how this confidence interval relates to your findings in part b. (d) Perform a bootstrap hypothesis test of the hypotheses from (b) and compare the findings of the two tests. (e) Construct a 95% bootstrap t confidence interval for the true difference in means. Compare your findings to that in part (c). 2 (f) Suppose after the data collected it comes to your attention that Surgeon D performed all the Dynamic system operations and Surgeon S performed all of the Static operations. What, if any, concerns do you have about this method of data collection