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420Exam1Aans - STAT 420 Fall 2008 Version A Name ANSWERS...

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STAT 420 Fall 2008 Version A Name ANSWERS . Exam 1 Page Possible Earned 1 10 2 7 3 12 4 10 5 5 6 11 7 10 8 9 9 6 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. The number of patients in the emergency room of a local hospital during three shifts is recorded. Morning ( 7 – 3 ) Afternoon ( 3 – 11 ) Night ( 11 – 7 ) 3 2 5 7 3 1 5 8 9 6 3 5 2 3 4 2 8 5 1 y = 3.5 2 1 s = 4.7 2 y = 6.0 2 2 s = 4.8 3 y = 4.0 2 3 s = 5.2 Consider the model Y i j = μ j + ε i j , where ε i j ’s are i.i.d. N ( 0, σ 2 ) . a) (10) At α = 0.05, can one conclude that there is a difference in the average number of patients for the three shifts? H 0 : μ 1 = μ 2 = μ 3 . J = 3 . N = n 1 + n 2 + … + n J = 6 + 6 + 6 = 18 . 18 0 . 4 6 0 . 6 6 5 . 3 6 ... 2 2 1 1 + + = + + + = N n n n J J y y y y = 4.5 . SSB = ( ) ( ) ( ) 2 2 2 2 2 1 1 ... y y y y y y J J n n n - + + - + - = 6 ( 3.5 – 4.5 ) 2 + 6 ( 6.0 – 4.5 ) 2 + 6 ( 4.0 – 4.5 ) 2 = 21 . MSB = 2 21 1 SSB = - J = 10.5 . SSW = ( ) ( ) ( ) 2 2 2 2 2 1 1 1 ... 1 1 J J s n s n s n - + + - + - = 5 4.7 + 5 4.8 + 5 5.2 = 73.5 .
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