11_01_1ans - STAT 400 1. Fall 2011 Examples for 11/01/2011...

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STAT 400 Examples for 11/01/2011 (1) Fall 2011 1. A machine makes ½-inch ball bearings. In a random sample of 41 bearings, the sample standard deviation of the diameters of the bearings was 0.02 inch. Assume that the diameters of the bearings are approximately normally distributed. Construct a 90% confidence interval for the standard deviation of the diameters of the bearings. s = 0.02. n = 41. The confidence interval : ( ) ( ) - - - 1 , 1 2 2 1 2 2 2 2 α α χ s χ s n n . 90% confidence level α = 0.10 α 2 = 0.05 . n – 1 = 40 degrees of freedom. 2 05 0 2 2 . χ χ = α = 55.76 . 2 95 0 2 2 1 . χ χ = α - = 26.51 . ( ) ( ) - - 51 . 26 02 . 0 1 41 , 76 . 55 02 . 0 1 41 2 2 ( 0.01694 , 0.02457 ) 2. A random sample of size n = 9 from a normal distribution is obtained: 4.4 3.7 5.1 4.3 4.7 3.7 3.5 4.6 4.7 Recall: x = 4.3, s 2 = 0.3025, s = 0.55. a)
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11_01_1ans - STAT 400 1. Fall 2011 Examples for 11/01/2011...

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