IV. (15 points) An experiment was conducted to investigate if the impact of the carcinogen DMBA could be delayed by treatment with a potential beta-blocker. Fifty mature rats of the same general health were given the beta-blocker and then were injected with DMBA. The times in days, after exposure, at which the carcinoma was diagnosed for the rats are given below. From past studies, 150 days after exposure, a carcinoma was detected in untreated rats. 10 12 13 16 37 42 43 45 55 63 66 82 99 100 100 101 107 117 122 135 138 140 142 149 150 151 154 165 170 183 194 214 218 219 224 229 232 247 268 268 298 299 325 332 379 400 434 464 499 537 Does a Weibull Distribution appear to provide an adequate fit to the data? Justify your answer using both a GOF test and a graphical plot. V. (25 Points ) A major problem in the Gulf of Mexico is the excessive capture of game fish by shrimpers. A random sample of the catch of 50 shrimpers yield the following data concerning the catch per unit effort (CPUE) of Red Snappers, a highly sought game fish. Let C; be the CPUE for the ith shrimper. The data, Ci, C2, ..., Cso is given next. 0.6 0.7 1.1 1.3 1.8 2.0 2.3 2.7 2.9 3.1 3.9 4.3 4.4 4.9 5.2 5.4 6.1 6.8 7.1 8.0 9.4 10.3 12.9 15.9 16.0 22.0 22.2 22.5 23.0 23.1 23.9 26.5 26.7 28.4 28.5 32.2 40.2 42.5 47.2 48.3 55.8 57.2 64.9 67.6 71.3 79.5 114.5 128.6 293.5 1. CPUE data is often modeled using a Log-Normal distribution. Does the above data appear to be from a Log-Normal distribution? Explain your answer with both a normal reference distribution plot and a GOF test. 2. Use the Box-Cox transformation of the CPUE data to determine the most appropriate power trans- formation to transform the CPUE distribution to Normality. How does the fit from the Box-Cox transformation compare to the fit for the log transformation? 3. Use the R program from Handout 10 (or any other program of your choice) to draw 10,000 bootstrap samples from the CPUE data. From the 10,000 samples, estimate the standard error of the sample mean for the Y, = log(C;), data. Compare this estimate to the usual estimate SK, where Sy is the sample standard deviation computed from the n = 50 values of Yi = log (Ci). 4. Use your bootstrap samples to estimate the mean and standard deviation of the following sample statistics for Y = log(C) a. The sample median, Qr (.5)