ch8 - 8-1 CHAPTER 8 Section 8-28-1a The confidence level...

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Unformatted text preview: 8-1 CHAPTER 8 Section 8-28-1a.) The confidence level for nxnx/14.2/14.2σμσ+≤≤-is determined by the by the value of z0 which is 2.14. From Table II, we find Φ(2.14) = P(Z<2.14) = 0.9838 and the confidence level is 100(1-.032354) = 96.76%. b.) The confidence level for nxnx/49.2/49.2σμσ+≤≤-is determined by the by the value of z0 which is 2.14. From Table II, we find Φ(2.49) = P(Z<2.49) = 0.9936 and the confidence level is is 100(1-.012774) = 98.72%. c.) The confidence level for nxnx/85.1/85.1σμσ+≤≤-is determined by the by the value of z0 which is 2.14. From Table II, we find Φ(1.85) = P(Z<1.85) = 0.9678 and the confidence level is 93.56%. 8-2 a.) A zα= 2.33 would give result in a 98% two-sided confidence interval. b.) A zα= 1.29 would give result in a 80% two-sided confidence interval. c.) A zα= 1.15 would give result in a 75% two-sided confidence interval. 8-3 a.) A zα= 1.29 would give result in a 90% one-sided confidence interval. b.) A zα= 1.65 would give result in a 95% one-sided confidence interval. c.) A zα= 2.33 would give result in a 99% one-sided confidence interval. 8-4a.) 95% CI for 96.1,100020,10,====zxnσμ4.10126.987)10/20(96.11000)10/20(96.11000//≤≤+≤≤-+≤≤-μμσμσnzxnzxb.) .95% CI for 96.1,100020,25,====zxnσμ8.10072.992)25/20(96.11000)25/20(96.11000//≤≤+≤≤-+≤≤-μμσμσnzxnzxc.) 99% CI for 58.2,100020,10,====zxnσμ3.10167.983)10/20(58.21000)10/20(58.21000//≤≤+≤≤-+≤≤-μμσμσnzxnzxd.) 99% CI for 58.2,100020,25,====zxnσμ3.10107.989)25/20(58.21000)25/20(58.21000//≤≤+≤≤-+≤≤-μμσμσnzxnzx8-2 8-5 Find n for the length of the 95% CI to be 40. Za/2= 1.96 84.3202.39202.3920/)20)(96.1(length1/22=&¡¢£¤¥====nnnTherefore, n= 4. 8-6 Interval (1): 7.32159.3124≤≤μand Interval (2)::1.32305.3110≤≤μInterval (1): half-length =90.8/2=45.4 Interval (2): half-length =119.6/2=59.8 a.) 3.31704.459.31241=+=x3.31708.595.31102=+=xThe sample means are the same. b.) Interval (1): 7.32159.3124≤≤μwas calculated with 95% Confidence because it has a smaller half-length, and therefore a smaller confidence interval. The 99% confidence level will make the interval larger. 8-7 a.) The 99% CI on the mean calcium concentration would be longer. b). No, that is not the correct interpretation of a confidence interval. The probability that μis between 0.49 and 0.82 is either 0 or 1. c). Yes, this is the correct interpretation of a confidence interval. The upper and lower limits of the confidence limits are random variables. 8-8 95% Two-sided CI on the breaking strength of yarn: where x = 98 , σ= 2 , n=9 and z0.025= 1.96 3.997.969/)2(96.1989/)2(96.198//025.025.≤≤+≤≤-+≤≤-μμσμσnzxnzx8-9 95% Two-sided CI on the true mean yield: where x = 90.480 , σ= 3 , n=5 and z0.025= 1.96 11.9385.875/)3(96.1480.905/)3(96.1480.90//025.025....
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This note was uploaded on 04/09/2008 for the course MTHSC 301 taught by Professor Any during the Spring '08 term at Clemson.

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ch8 - 8-1 CHAPTER 8 Section 8-28-1a The confidence level...

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