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tuteprac3ans

# tuteprac3ans - contain one so it is not reasonable to...

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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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tuteprac3ans - contain one so it is not reasonable to...

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