fin06sol - 25 1587 1 1587 1587 2 2 ˆ = − −> => Z P...

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5 ISMT111 F06 Final Exam Suggested Solution Question 1: (a) 71.5 26 / 55 . 30 06 . 2 × ± =71.5 ± 12.34 = [59.16, 83.84] (b) With 95% confidence the true mean will be enclosed in the interval. That is, if we take a large number of samples and construct the intervals as in (a) then 95% of the intervals will enclose the true mean. (c) (80.55+59.45)/2=70 (d) (80.55-59.45)/2=10.45. SE=10.55/1.96=5.33 (e) 4 . 61 8 ) 98 . 31 ( ) 96 . 1 ( 2 2 2 = n , 62 = n (f) 0.111 36 / ) 9 8 ( 9 1 96 . 1 × ± =0.111 ± 0.103 Question 2: (a) 0 : vs 0 : 1 2 1 2 0 > = p p H p p H a ( b) 645 . 1 087 . 1 0552 . 0 06 . 0 180 1 150 1 ) 330 156 1 ( 180 150 90 66 ) 44 . 0 5 . 0 ( < = = + + + , accept 0 H . that the economic outlook this year is not better than last year. (c) p-value = 0.1379 (d) 0526 . 0 } 62 . 1 { } 180 / ) 56 . 0 ( 44 . 0 44 . 0 5 . 0 { } 5 . 0 ˆ { 2 = > = > = > Z P Z P p P . Question 3: (a) Sample means have normal distribution with mean 3 and variance 1 / 25 = 0.2 , therefore 6247 . 0 } 5 . 1 5 . 0 { } 3 . 3 9 . 2 { = = z P x P (b) 0.36 = margin of error 0.36/(0.2)=1.8 = critical value 0359 . 0 2 / = α , 9282 . 0 1 = (c) t-distribution with d.f. 24, because 71 . 1 05 . 0 = t and 1 . 0 t =1.32 so the answer is 5%. (d) , 1587 . 0 } 1 { } 4 { = > = > Z P X P 2943 . 0 }
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Unformatted text preview: 25 / ) 1587 . 1 ( 1587 . 1587 . 2 . { } 2 . ˆ { = − − > = > Z P p P . Question 4: (a) -4.28+0.254 × 30=3.34 days (b) (0.254 -0.2)/0.0285=1. 895 >1. 771 reject H . (c) 0.254 ± 2.16(0.0285) (d) 3 . 1511 ) 30 87 . 37 ( 15 1 11 . 1 16 . 2 34 . 3 2 − + × ± = 3.34 ± 0.787 Question 5: (a) Larger variance of X makes the SE’s of b and 1 b smaller by the corresponding formulas. (b) If r is positive, Y will increases by Y rS . If r is negative, Y will decrease by Y rS . (c) The intercept is zero because both X ~ and Y ~ have sample means equal zero. The slope is 6 . = r because X ~ and Y ~ have s.d. equals one. Question 6: 96 . 13 ) 57 . 16 ( 11 ) 56 . 3 ( 1 2 2 2 = × × − = R 863 . 3 ) 56 . 3 ( ) 5 . 1 ( 2 2 = + , 3.863 2 . 2 × =8.50. The prediction interval is 75.62 5 . 8 ± 0...
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This note was uploaded on 02/27/2010 for the course ISOM ISOM111 taught by Professor Anthonychan during the Spring '09 term at HKUST.

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