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420Exam2Aans - STAT 420 Fall 2008 Version A Name ANSWERS...

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STAT 420 Fall 2008 Version A Name ANSWERS . Exam 2 Page Possible Earned 1 10 2 11 3 14 4 4 5 9 6 10 7 13 8 9 Total 80 Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. The exam is closed book and closed notes. You are allowed to use a calculator and one 8½" x 11" sheet with notes on it. ___________________________________________________________________________ Academic Integrity The University statement on your obligation to maintain academic integrity is: If you engage in an act of academic dishonesty, you become liable to severe disciplinary action. Such acts include cheating; falsification or invention of information or citation in an academic endeavor; helping or attempting to help others commit academic infractions; plagiarism; offering bribes, favors, or threats; academic interference; computer related infractions; and failure to comply with research regulations. Rule 33 of the Code of Policies and Regulations Applying to All Students gives complete details of rules governing academic integrity for all students. You are responsible for knowing and abiding by these rules.
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1. Consider the following salary data for the full professors in the Department of Philosophical Engineering at Anytown State University in thousands of dollars per month ( Y ) and x 1 ( years in rank ) . Females Males x 1 2 3 3 4 x 1 4 5 5 6 Y 2 3 5 6 Y 8 6 12 10 Consider the model Y = β 0 + β 1 x 1 + β 2 x 2 + e , where the dummy variable x 2 is the indicator for males ( i.e., x 2 = 0 for females, x 2 = 1 for males ) . Then X T X = ° ° ° ± ² ³ ³ ³ ´ µ 4 20 4 20 140 32 4 32 8 , ( X T X ) 1 = ° ° ° ± ² ³ ³ ³ ´ µ - - - - 5 . 1 5 . 0 25 . 1 5 . 0 25 . 0 75 . 0 25 . 1 75 . 0 5 . 2 , X T Y = ° ° ° ± ² ³ ³ ³ ´ µ 36 234 52 , and ° ˆ = ° ° ° ± ² ³ ³ ³ ´ µ - 2 5 . 1 5 . 0 . a) (10) Complete the ANOVA table for the “significance of the regression” test. State the null hypothesis. Is the regression significant at α = 0.05? n = 8 , p = 2 . Source SS df MS F Regression 59 p = 2 29.5 7.0238 Error (Residual) 21 n p – 1 = 5 4.2 Total 80 n – 1 = 7 H 0 : β 1 = β 2 = 0 . Critical Value: F 0.05 ( 2 , 5 ) = 5.79 . Decision: Reject H 0 .
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1. (continued) b) (6) Does there seem to be discrimination against females? Test H 0 : β 2 = 0 vs. H 1 : β 2 > 0 at a 5% level of significance. Var( 2 ° ˆ ) = C 22 × s 2 = 1.5 × 4.2 = 6.3 . Test Statistic: t = 3 . 6 0 2 - 0.79682 . Critical Value: t 0.05 ( 5 ) = 2.015 .
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