exam101a

# exam101a - Stat 501 Spring 2001 1. (a) (6 points) 4. (6...

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Stat 501 Solutions and Comments on Exam 1 Spring 2001 1. (a) (6 points) ) , N( ~ _ X n 1 ~ ~ Σ µ 4. (6 points) . ) 0 0 1 .5 - (-.5 ' ~ c where ), ~ c ' ~ c , ~ ' ~ c N( ~ Z j = Σ µ In this case 23 13 12 33 22 11 2 1 3 5 . 25 . .25 = ~ c ' ~ c and ) ( - = ~ ' ~ c σ σ σ σ σ σ Σ µ µ µ µ + + + + . 5. (8 points) Since ) p n , p ( 2 ~ ~ 1 - ~ ~ F p - n 1) - p(n ~ T = ) - _ X ( S ) - _ X n( µ µ , then ) 50 , 5 ( ~ ~ 1 - ~ ~ F (55)(50) (5)(54) ~ ) - _ X ( S ) - _ X ( µ µ ′ . 6. (10 points) Compute 1.534 ) 21 (. 1 4 55 .21 r 1 4 n r t 2 2 35 14 35 14 = = = . Since 1.534 < , we cannot reject 2 t .025 ), 54 ( 0 : H 35 14 0 = ρ at the 0.05 level of significance. 7. (10 points) Write the null hypothesis in matrix form. There is more than one way to do this correctly. One way to state the null hypothesis is . 0 0 0 0 1 - 1 0 0 0 0 1 - 1 C : H 5 4 3 2 1 ~ 0 = = µ µ µ µ µ µ Reject the null hypothesis that the difference between the post-course and pre- course means are the same for all three pre-course tests if ) 0 - _ X (C ) C (CS ) 0 - _ X 55(C = T ~ ~ 1 - ~ ~ 2 > . ), 53 , 2 ( F 53 (2)(54) α . A p-value is computed as } T (2)(53) 53 F Pr{ 2 ) 53 , 2 ( > where denotes a ) 53 , 2 ( F central F random variable with (2,53) degrees of freedom.

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8. (10 points) Use the large sample chi-square approximation. Compute
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## This note was uploaded on 12/16/2011 for the course STAT 5705 taught by Professor Staff during the Fall '09 term at FSU.

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exam101a - Stat 501 Spring 2001 1. (a) (6 points) 4. (6...

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