HW #2 solution - STAT 420 Homework#2(10 points(due Friday...

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STAT 420 Spring 2007 Homework #2 (10 points) (due Friday, February 2, by 4:00 p.m.) From the textbook: 4.5 Prove the algebraic identity ( ) ( ) ( ) & & & & & = = = = = - + - = - J j n i j ij J j j J j n i ij Y Y Y Y n Y Y 1 1 2 1 2 1 1 2 ( ) ( ) & & & & = = = = - + - = - J j n i j j ij J j n i ij j j Y Y Y Y Y Y 1 1 2 1 1 2 = ( ) ( ) ( ) ( ) & & & & & & = = = = = = - + - - + - J j n i j J j n i j j ij J j n i j ij j j j Y Y Y Y Y Y Y Y 1 1 2 1 1 1 1 2 2 = ( ) ( ) ( ) ( ) & & & & & = = = = = - + - - + - J j j j J j n i j ij j J j n i j ij Y Y n Y Y Y Y Y Y j j 1 2 1 1 1 1 2 2 . Since ( ) & = - j n i j ij Y Y 1 = 0, j = 1, … , J , ( ) ( ) & & = = - - J j n i j ij j j Y Y Y Y 1 1 2 = 0, and ( ) ( ) ( ) & & & & & = = = = = - + - = - J j j j J j n i j ij J j n i ij Y Y n Y Y Y Y j j 1 2 1 1 2 1 1 2 . OR ( ) 2 1 1 1 1 2 1 1 2 2 1 1 2 2 2 Y Jn Y Y Y Y Y Y Y Y Y J j n i ij J j n i ij J j n i ij ij J j n i ij + - = ± ² ³ ´ µ + - = - & & & & & & & & = = = = = = = = = ( ) 2 1 1 2 2 1 1 2 2 Y Jn Y Y Jn Y Jn Y Y J j n i ij J j n i ij - = + - & & & & = = = = .
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( ) 2 1 1 2 1 2 2 1 2 2 2 Y Jn Y n Y Y n Y Y Y Y n Y Y n J j j J j j J j j j J j j + - = & ± ² ³ ´ µ + - = - = = = = = ( )
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4.6 The American Car Company is interested in the average number of cars coming off three assembly lines with obvious defects (determined by visual inspection). The number of defects per week for each of the assembly lines is recorded for several weeks. The data follow.
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HW #2 solution - STAT 420 Homework#2(10 points(due Friday...

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