Master of Applied Statistics Applied Statistics Comprehensive Exam Computer Output January 2018

Question 1a output Master of Applied Statistics Applied Statistics Comprehensive Exam Computer Output January 2018 Question 1f output Basic Statistical Measures Location Variability Mean -2.32429 Std Deviation 3.85208 Median -3.11000 Variance 14.83852 Mode. Range 10.34000 Interquartile Range 7.16000 Tests for Location: Mu0=0 Test Statistic p Value Student's t t -2.25766 Pr > t 0.0418 Sign M -1 Pr >= M 0.7905 Signed Rank S -28.5 Pr >= S 0.0785 Page 1 of 9

Question 3 Output The SAS System Dependent Variable: WebCAPE DF Sum of Squares Mean Square F Value Pr > F Model 2 1.28178188 0.64089094 2.91 0.0600 Error 87 19.18809056 0.22055277 Corrected Total 89 20.46987244 R-Square Coeff Var Root MSE WebCAPE Mean 0.062618 14.40838 0.469630 3.259426 DF Type I SS Mean Square F Value Pr > F Level 2 1.28178188 0.64089094 2.91 0.0600 DF Type III SS Mean Square F Value Pr > F Level 2 1.28178188 0.64089094 2.91 0.0600 Level Least Squares Means Adjustment for Multiple Comparisons: Tukey-Kramer WebCAPE LSMEAN LSMEAN Number Elementary 3.26824698 1 Intermediate 2.93572528 2 Novice 3.34057118 3 Least Squares Means for effect Level Pr > t for H0: LSMean(i)=LSMean(j) Dependent Variable: WebCAPE i/j 1 2 3 1 0.1122 0.7738 2 0.1122 0.0477 3 0.7738 0.0477 Page 2 of 9

Question 3 Output Continued Level Least Squares Means Adjustment for Multiple Comparisons: Bonferroni WebCAPE LSMEAN LSMEAN Number Elementary 3.26824698 1 Intermediate 2.93572528 2 Novice 3.34057118 3 Least Squares Means for effect Level Pr > t for H0: LSMean(i)=LSMean(j) Dependent Variable: WebCAPE i/j 1 2 3 1 0.1377 1.0000 2 0.1377 0.0550 3 1.0000 0.0550 Level Least Squares Means Adjustment for Multiple Comparisons: Scheffe WebCAPE LSMEAN LSMEAN Number Elementary 3.26824698 1 Intermediate 2.93572528 2 Novice 3.34057118 3 Least Squares Means for effect Level Pr > t for H0: LSMean(i)=LSMean(j) Dependent Variable: WebCAPE i/j 1 2 3 1 0.1348 0.7923 2 0.1348 0.0609 3 0.7923 0.0609 Page 3 of 9

Question 4 Output DATA crop_yield; INPUT variety $ fertilizer $ yield @@; CARDS; var_a fert_1 519.3 var_a fert_2 314.6 var_a fert_1 468.1 var_a fert_2 280.6 var_a fert_1 475.8 var_a fert_2 373.9 var_b fert_1 564.1 var_b fert_2 348.1 var_b fert_1 554.4 var_b fert_2 351.4 var_b fert_1 531.8 var_b fert_2 372.6 var_c fert_1 612.9 var_c fert_2 391.0 var_c fert_1 569.7 var_c fert_2 401.5 var_c fert_1 585.3 var_c fert_2 389.4 ; PROC GLM DATA=crop_yield ORDER=DATA; CLASS variety fertilizer; MODEL yield = variety fertilizer variety*fertilizer; RUN; Dependent Variable: yield DF Sum of Squares Mean Square F Value Pr > F Model 5 176067.3983 35213.4797 53.29 <.0001 Error 12 7929.8867 660.8239 Corrected Total 17 183997.2850 R-Square Coeff Var Root MSE yield Mean 0.956902 5.709383 25.70650 450.2500 DF Type I SS Mean Square F Value Pr > F variety 2 22426.3900 11213.1950 16.97 0.0003 fertilizer 1 152775.4939 152775.4939 231.19 <.0001 variety*fertilizer 2 865.5144 432.7572 0.65 0.5371 DF Type III SS Mean Square F Value Pr > F variety 2 22426.3900 11213.1950 16.97 0.0003 fertilizer 1 152775.4939 152775.4939 231.19 <.0001 variety*fertilizer 2 865.5144 432.7572 0.65 0.5371 Page 4 of 9

Question 4 Output Continued RANDOM fertilizer variety*fertilizer; Type III Expected Mean Square variety Var(Error) + 3 Var(variety*fertilizer) + Q(variety) fertilizer Var(Error) + 3 Var(variety*fertilizer) + 9 Var(fertilizer) variety*fertilizer Var(Error) + 3 Var(variety*fertilizer) RANDOM variety variety*fertilizer; Type III Expected Mean Square variety Var(Error) + 3 Var(variety*fertilizer) + 6 Var(variety) fertilizer Var(Error) + 3 Var(variety*fertilizer) + Q(fertilizer) variety*fertilizer Var(Error) + 3 Var(variety*fertilizer) RANDOM variety fertilizer variety*fertilizer; Type III Expected Mean Square variety Var(Error) + 3 Var(variety*fertilizer) + 6 Var(variety) fertilizer Var(Error) + 3 Var(variety*fertilizer) + 9 Var(fertilizer) variety*fertilizer Var(Error) + 3 Var(variety*fertilizer) Page 5 of 9

Question 5 Output DATA brains; INPUT logbrain logweight gest litter species $; CARDS; -0.65392647-4.07454193 24 5.0 Deer_mouse_III -0.37106368-3.72970145 24 5.0 Deer_mouse_IV -0.79850770-3.72970145 19 5.0 House_mouse -0.46203546-3.64965874 23 5.0 Deer_mouse_II -0.38566248-3.61191841 23 3.7 Deer_mouse_I -0.40047757-3.32423634 21 4.6 Hampster_I 0.13102826-3.01593498 51 1.5 Elephant_shrew_I -0.32850407-2.99573227 23 7.3 Rat_I 0.63657683-2.95651156 40 3.1 Flying_squirrel 0.31481074-2.74887220 46 1.5 Elephant_shrew_II 0.03922071-2.73336801 21 4.0 Pygmy_gerbil 0.11332869-2.04022083 16 6.3 Hampster_II 1.14740245-1.89711998 46 3.0 Tree_shrew 0.16551444-1.89711998 27 5.6 Hopping_mouse 2.05412373-1.51412773 145 2.0 Gentle_lemur 1.82937633-1.10866262 38 3.0 Tree_squirrel 0.86710049-1.07880966 21 8.0 Rat_II 1.65822808-0.84397007 110 2.0 Chinchilla 2.29253476-0.35667494 135 1.0 Bush_baby 2.29253476-0.24846136 98 1.2 Acouchis 1.25276297-0.07257069 34 4.6 Hedgehog 1.45395301-0.03045921 67 2.6 Guinea_pig 2.54944517 0.18232156 90 1.2 Slow_loris 3.44041809 0.69314718 77 1.1 Linkajou 3.09104245 0.74193734 135 1.0 Lemur 2.26176310 0.78845736 31 5.0 Aardvark 3.34638915 0.91629073 63 4.0 Domestic_cat 3.01062089 1.02961942 104 1.3 Agoutis 2.58776404 1.06471074 41 2.5 Jack_rabbit 3.34990409 1.16315081 65 4.0 Bat-eared_fox 2.86220088 1.25276297 26 1.0 Quokka 4.29045944 1.30833282 180 1.0 Ring-tail_monkey 2.48490665 1.30833282 120 4.0 Long-nose_armadillo 3.61899333 1.33500107 63 3.7 Gray_fox 3.02042489 1.33500107 225 2.4 Hyrax 4.20469262 1.52605630 195 1.0 Vervet_guenon 3.13549422 1.60943791 132 5.5 Nutria 3.72810017 1.66770682 63 3.5 Raccoon 4.62497281 1.70474809 210 1.0 White_handed_gibbon 4.18205014 1.75785792 168 1.0 Leaf_monkey 4.43793427 1.79175947 175 1.0 Rhesus_monkey_I 3.87120101 1.79175947 52 4.0 Red_fox 3.97029191 1.79175947 60 2.2 Badger 3.17805383 1.88706965 113 1.0 Porcupine_III 3.98898405 2.04122033 139 1.0 Howler_monkey 4.69134788 2.04122033 140 1.0 Spider_monkey_II 4.25134831 2.14006616 63 4.0 Dog 4.67282883 2.16332303 165 1.1 Rhesus_monkey_II 4.73619845 2.20827441 140 1.0 Spider_monkey_I 3.61091791 2.39789527 112 1.2 Porcupine_I 4.31748811 2.48490665 60 2.5 Lynx 4.53259949 2.56494936 120 1.0 Duikers 3.61091791 2.63905733 112 1.2 Porcupine_II 4.82028157 2.77258872 183 1.1 Barking_deer Page 6 of 9

Question 5 Output Continued 3.68887945 2.99573227 128 2.9 Canadian_beaver 5.20948615 3.04452244 180 1.0 Hamadryas_baboon 3.80666249 3.21887582 128 4.0 Beaver 4.33073334 3.40119738 123 3.0 Capybara 4.66343909 3.40119738 151 2.0 Domestic_goat 5.18738581 3.46573590 180 1.0 Western_baboon 5.83773045 3.61091791 270 1.0 Orangutan 5.29831737 3.66356165 180 1.0 Black_buck_antilope 5.88610403 3.80666249 230 1.0 Chimpanzee 5.28826703 3.80666249 300 1.1 Vicuna 5.05624581 3.82864140 92 2.5 Leopard 4.82831374 3.89182030 150 2.4 Domestic_sheep ; PROC GLM DATA=brains; MODEL logbrain = logweight; RUN; Dependent Variable: logbrain DF Sum of Squares Mean Square F Value Pr > F Model 1 214.0790114 214.0790114 777.13 <.0001 Error 64 17.6302634 0.2754729 Corrected Total 65 231.7092748 R-Square Coeff Var Root MSE logbrain Mean 0.923912 18.19256 0.524855 2.884999 DF Type I SS Mean Square F Value Pr > F logweight 1 214.0790114 214.0790114 777.13 <.0001 DF Type III SS Mean Square F Value Pr > F logweight 1 214.0790114 214.0790114 777.13 <.0001 Parameter Estimate Standard Error t Value Pr > t Intercept 2.336114718 0.06753891 34.59 <.0001 logweight 0.777758697 0.02789955 27.88 <.0001 Page 7 of 9

Question 5 Output Continued PROC GLM DATA=brains; MODEL logbrain = logweight litter gest; RUN; Dependent Variable: logbrain DF Sum of Squares Mean Square F Value Pr > F Model 3 220.4734130 73.4911377 405.53 <.0001 Error 62 11.2358618 0.1812236 Corrected Total 65 231.7092748 R-Square Coeff Var Root MSE logbrain Mean 0.951509 14.75576 0.425704 2.884999 DF Type I SS Mean Square F Value Pr > F logweight 1 214.0790114 214.0790114 1181.30 <.0001 litter 1 5.1876598 5.1876598 28.63 <.0001 gest 1 1.2067418 1.2067418 6.66 0.0122 DF Type III SS Mean Square F Value Pr > F logweight 1 76.56957726 76.56957726 422.51 <.0001 litter 1 2.22972727 2.22972727 12.30 0.0008 gest 1 1.20674176 1.20674176 6.66 0.0122 Parameter Estimate Standard Error t Value Pr > t Intercept 2.466735756 0.20098112 12.27 <.0001 logweight 0.656619545 0.03194427 20.56 <.0001 litter -0.139471449 0.03976187-3.51 0.0008 gest 0.003166034 0.00122692 2.58 0.0122 Page 8 of 9

Question 6 Output Parameter DF Estimate Standard Error Analysis Of Maximum Likelihood Parameter Estimates Wald 95% Confidence Limits Wald Chi-Square Pr > ChiSq Intercept 1-1.0133 1.1110-3.1910 1.1643 0.83 0.3617 Minutes 1 0.0262 0.0131 0.0005 0.0518 4.00 0.0456 Scale 0 1.0000 0.0000 1.0000 1.0000 Page 9 of 9