Below is the questio

2. (14 points) A study was conducted on arthritis patients, with the goal of identifying an "unusually young" age to get arthritis. Their perferred statistic for this measurement was two standard deviations below the mean (i.e, 0 = M - 20, where u represents the population mean, o the population standard deviation). Call this value the cutoff (you may refer to it as such in the rest of the problem). A distribution of the original data (n = 84) and a bootstrap distribution of 0 for 10000 bootstraps follow: Age of arthritis patients Bootstrap distribution 2500 2000 1500 10 Frequency Frequency 1000 500 O 20 30 40 50 60 70 20 25 30 35 years years (a) (4 points) What characteristic of either the bootstrap distribution, or the distribution of the sample data, may suggest what bootstrap confidence interval is appropriate to use? Specific which distribution you are discussing, and the characteristic. (b) (4 points) If the sample mean and standard deviation (respectively) are: 53.357, 12.769, and the bootstrap estimates for the expected value and standard error are: 27.977, 2.844, find the bootstrap estimate of the bias and the MSE. (c) (3 points) Based on your answers from (b), what is the bias-corrected estimate for the value of 0? d) (3 points) The BCA 95% bootstrap confidence interval for 0 is : (22.187, 33.204). Interpret this interval in terms of the