Question 8 [6 marks] a) In both permutation testing and in bootstrapping we use the R function sample() to draw resamples from the original data. What is the main difference between the way in which this sampling is done in permutation testing compared to bootstrapping? b) In a permutation test we sample (approximately) from the data distribution that satisfies the null hypothesis. Which data distribution do we (approximately) sample from in bootstrapping? c) Outline a general method for calculating a 95% confidence interval for a median based on the bootstrap distribution. d) Below you are shown the bootstrap distribution of the median obtained from N = 10000 resampling of the Tactix goals scored data. Median goals scored 43 48 49 51 52 54 58 61 Number of occurrences in the bootstrap 1 38 185 5788 1842 1907 208 31 Provide your best estimate, including interpretation, of the 95% confidence interval for the median. If the interval is not exactly a 95% confidence interval, indicate what the exact level of confidence is