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

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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 .
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:

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## This note was uploaded on 05/09/2010 for the course MATH 420 taught by Professor Stepanov during the Spring '10 term at University of Illinois, Urbana Champaign.

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

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