P1. ( 50 points) A researcher is studying the relative brain weights (brain weight divided by body weight) for 51 species of mammals whose litter size is 1 and for 44 species of mammals Whose average litter size is greater than or equal to 2. The researcher was interested in determining what evidence that brain sizes tend to be different for the two groups. (Data from The Statistical Sleuth by Fred Ramsey and Daniel Sehafer}. 0.42 1.73 3.18 5.59 10.32 14.27 0.94 2.58 5.39 8.96 21.00 RELATIVE BRAIN HEIGHTS - SHALL LITTER SIZE 0.86 0.88 1.11 1.34 1.38 1.42 1.47 1.63 2.17 2.42 2.48 2.74 2.74 2.79 2.90 3.12 3.27 3.30 3.61 3.63 4.13 4.40 5.00 5.20 7.04 7.15 7.25 7.75 8.00 8.84 9.30 9.68 10.41 10.48 11.29 12.30 12.53 12.69 14.14 14.15 14.56 15.84 18.55 19.73 20.00 RELATIVE BRAIN HEIGHTS - LARGE LITTER SIZE 1.26 1.44 1.49 1.63 1.80 2.00 2.00 2.56 3.24 3.39 3.53 3.77 4.36 4.41 4.60 4.67 6.25 7.02 7.89 7.97 8.00 8.28 8.83 8.91 9.92 11.36 12.15 14.40 16.00 18.61 18.75 19.05 21.41 23.27 24.71 25.00 28.75 30.23 35.45 1. For the Small Litter Size mammals, answer the following questions: The data is given in the le: Brain W'eight Data.txt in Canvas 8.. Compute a 10% trimmed mean, and compare it to the untrimmed sample mean. Dore this comparison suggest any extreme values in the data? . The researcher suggested a Weibull distribution to model the data for the Small Litter Size mammals. Assuming that the Weibnll distribution is an appropriate model for the Small Litter Size data. obtain the MLE estimates of the Weibull parameters for the Small Litter Size data. . Estimate the probability that a randomly selected mammal with a litter size of 1 will have a relative brain weight greater than 15, rst using the Weibull model and secondly using a distribution-free estimate. . Compare the MLE estimates of y and 0 based on the Weibull model to the distribution-free estimates of n and a' for the Small Litter Size data. . Compare the MLE estimates of median and IQR based on the Weibull model to the distribution-free estimates of median and [QR for the Small Litter Size data. 2. W'ithout any assumed model, estimate the mean and standard deviation of the relative brain weights for both Large and Small litter sizes. 3. Estimate the median and MAD of the relative brain weights for both Large and Small litter sizes. 4. Based on your plots from Assignment #3, which pair of estimates of the center and spread in the two data sets best represents the center and spread in the two populations of relative brain weights? 5. Using your answers from the previous three questions, suggest- a relationship (if any) between litter size and relative brain weights