Tuteprac3ans - contain one so it is not reasonable to suppose the standard deviations are the same 9(a ˆ p = 24 642 = 0 0374(b ˆ p ± 1 96 p ˆ

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620-202 Tutorial/Computing Labo- ratory 3. 1. 73 . 8 ± 1 . 96 × 5 / 4 = [71 . 35 , 76 . 25] 2. 2 . 09 ± 1 . 96 × 0 . 12 / 4 = [2 . 03 , 2 . 15] 3. 11 . 95 ± 2 . 028 × 11 . 8 / 37 = [8 . 016 , 15 . 884] 4. 20 . 9 ± 2 . 306 × 1 . 858 / 3 = [19 . 47 , 22 . 33] As 22 is within the confidence interval for the mean the claim is reasonable if it is interpreted to mean that the average weight of a “22-pound” wheel is 22 pounds. 5. 937 . 4 - 988 . 9 ± 1 . 96 r 784 56 + 627 57 = [ - 61 . 3 . - 41 . 7] As zero is not contained in the confidence interval it is not reasonable to suppose the mean lifetimes are the same. 6. (a) The pooled estimate of the standard deviation is s p = r 9 × 0 . 323 2 + 9 × 0 . 210 2 18 = 0 . 2724 Hence a 95% confidence interval is 2 . 548 - 1 . 564 ± 2 . 101 × 0 . 2724 r 1 10 + 1 10 = [0 . 728 , 1 . 240] (b) Yes. The confidence interval only contains positive values and does not contain zero so we are at least 95% confident the mean force required when the wedge is in place is larger than when it is not. 1
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7. " r 12 23 . 337 6 . 144 , r 12 4 . 403 6 . 144 # = [4 . 406 , 10 . 14] 8. A 90% confidence intervals for σ 2 x 2 y is ± 0 . 3821 ² . 197 2 . 318 2 ³ , 2 . 475 ² . 197 2 . 318 2 ³´ = [0 . 147 , 0 . 950] so a 90% confidence interval for σ x y is [0.383,0.975]. This interval does not
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Unformatted text preview: contain one so it is not reasonable to suppose the standard deviations are the same. 9. (a) ˆ p = 24 / 642 = 0 . 0374. (b) ˆ p ± 1 . 96 p ˆ p (1-ˆ p ) /n = [0 . 0227 , . 0521] (c) ˆ p + 1 . 96 2 / (2 n ) ± 1 . 96 p (ˆ p (1-ˆ p ) /n + 1 . 96 2 / (4 n 2 )) 1 + 1 . 96 2 /n = [0 . 0252 , . 0550] (d) ˆ p + 1 . 645 p ˆ p (1-ˆ p ) /n = 0 . 0497 10. see output 11. see output 12. The confidence interval for the ratio of the variances includes one so there is no reason to suppose they differ. 13. R computes the quadratic interval. It is quite close to the exact interval for the data of Question 9. 14. The upper line in the plot represents the upper ends of the intervals and the lower line the lower end. The straight line is the true value (zero).You should have noticed about 95% of the intervals contain zero. 2...
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This note was uploaded on 10/05/2009 for the course STATS 620-202 taught by Professor R during the One '09 term at University of Melbourne.

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Tuteprac3ans - contain one so it is not reasonable to suppose the standard deviations are the same 9(a ˆ p = 24 642 = 0 0374(b ˆ p ± 1 96 p ˆ

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