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Unformatted text preview: UNIVERSITY OF TORONTO Faculty of Arts and Science DECEMBER 2003 EXAMINATIONS STA 302 H1F / 1001 H1F Duration  3 hours Aids Allowed: Calculator NAME: SOLUTIONS STUDENT NUMBER: There are 22 pages including this page. The last page is a table of formulae that may be useful. Tables of the t distribution can be found on page 20 and tables of the F distribution can be found on page 21. Total marks: 90 1a 1bc 1de 1f 2ab 2cd 3ab 3cd 4ab 4cde 4fg 5abc 5de 6 1 Continued 1. Expenditures on the criminal justice system is an area of continually rising cost in the U.S. This question examines the relationship between the total number of police employed in an American state, and the total spending on the states criminal justice system (in millions of dollars US) for the 50 American states. The base 10 logarithm of each variable was taken before fitting the model. The variables are named logpol and logexp . Some output from SAS is given below. Seven of the numbers have been replaced by upper case letters. The REG Procedure Descriptive Statistics Uncorrected Standard Variable Sum Mean SS Variance Deviation Intercept 50.00000 1.00000 50.00000 logexp 129.26739 2.58535 334.94405 0.01516 0.12313 logpol 195.86603 3.91732 778.15035 0.22205 0.47122 The REG Procedure Model: MODEL1 Dependent Variable: logpol Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model (A) 1.09909 1.09909 (C) 0.0245 Error (B) 9.78122 (D) Corrected Total 49 10.88031 Root MSE 0.45141 RSquare (E) Dependent Mean 3.91732 Adj RSq 0.0823 Coeff Var 11.52356 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > t Intercept 1 0.77272 1.35553 (F) 0.5713 logexp 1 1.21632 0.52373 2.32 (G) (a) (7 marks) Find the 7 missing values (A through G) in the SAS output. A=1 B=48 C=5.393 D=0.2038 E=0.101 F=0.570 G=0.0245 2 Continued (b) (3 marks) Construct simultaneous 90% confidence intervals for the slope and intercept of the regression line. Use the Bonferroni method. Critical value: t 48; . 05 / 2 = 2 . 021 (approximating with 40 df) CI for slope: 1 . 216 2 . 021(0 . 524) = ( . 142 , 2 . 275) CI for intercept: . 773 2 . 021(1 . 356) = ( 1 . 967 , 3 . 513) (c) (4 marks) Carry out an hypothesis test to determine whether or not the data give evidence that the coefficient of logexp is greater than 1. H : 1 1 versus H a : 1 > 1 Test statistic: t obs = 1 . 216 1 . 524 = . 412 pvalue: . 3 < p < . 4 The data give no evidence that the slope is greater than one. 3 Continued (d) (5 marks) The District of Columbia (not one of the 50 states but a separate region of the U.S.) spends 1,217,000,000 (1,217 million) dollars on its criminal justice system. Predict how many police officers it has. Construct a 99% interval for your value. Express your answer as a count of the number of police....
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 Fall '04
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