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Unformatted text preview: 81 CHAPTER 8 Section 8281a.) The confidence level for nxnx/14.2/14.2+is determined by the by the value of z0 which is 2.14. From Table II, we find (2.14) = P(Z<2.14) = 0.9838 and the confidence level is 100(1.032354) = 96.76%. b.) The confidence level for nxnx/49.2/49.2+is determined by the by the value of z0 which is 2.14. From Table II, we find (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/85.1/85.1+is determined by the by the value of z0 which is 2.14. From Table II, we find (1.85) = P(Z<1.85) = 0.9678 and the confidence level is 93.56%. 82 a.) A z= 2.33 would give result in a 98% twosided confidence interval. b.) A z= 1.29 would give result in a 80% twosided confidence interval. c.) A z= 1.15 would give result in a 75% twosided confidence interval. 83 a.) A z= 1.29 would give result in a 90% onesided confidence interval. b.) A z= 1.65 would give result in a 95% onesided confidence interval. c.) A z= 2.33 would give result in a 99% onesided confidence interval. 84a.) 95% CI for 96.1,100020,10,====zxn4.10126.987)10/20(96.11000)10/20(96.11000//++nzxnzxb.) .95% CI for 96.1,100020,25,====zxn8.10072.992)25/20(96.11000)25/20(96.11000//++nzxnzxc.) 99% CI for 58.2,100020,10,====zxn3.10167.983)10/20(58.21000)10/20(58.21000//++nzxnzxd.) 99% CI for 58.2,100020,25,====zxn3.10107.989)25/20(58.21000)25/20(58.21000//++nzxnzx82 85 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. 86 Interval (1): 7.32159.3124and Interval (2)::1.32305.3110Interval (1): halflength =90.8/2=45.4 Interval (2): halflength =119.6/2=59.8 a.) 3.31704.459.31241=+=x3.31708.595.31102=+=xThe sample means are the same. b.) Interval (1): 7.32159.3124was calculated with 95% Confidence because it has a smaller halflength, and therefore a smaller confidence interval. The 99% confidence level will make the interval larger. 87 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 is 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. 88 95% Twosided CI on the breaking strength of yarn: where x = 98 , = 2 , n=9 and z0.025= 1.96 3.997.969/)2(96.1989/)2(96.198//025.025.++nzxnzx89 95% Twosided CI on the true mean yield: where x = 90.480 , = 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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 Spring '08
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 Statistics

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