STAT 400 Lecture AL1 1 Spring 2015 Dalpiaz Answers for 7 1 Part 3 A machine makes 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 0 10 90 confidence level n 1 s 2 2 2 n 1 s 2 1 2 2 0 05 n 1 40 degrees of freedom 2 20 05 55 76 2 20 95 26 51 1 2 2 a 55 76 26 51 0 01694 0 02457 The following random sample was obtained from N 2 distribution 16 Recall 2 41 1 0 02 2 41 1 0 02 2 12 x 15 18 13 s 2 16 21 15 8 17 s 4 Construct a 95 confidence interval for the overall standard deviation Confidence Interval for 2 n 1 s 2 n 1 s 2 2 2 1 2 2 2 0 05 1 2 0 975 2 0 025 number of degrees of freedom n 1 8 1 7 2 16 01 2 2 1 690 1 2 8 1 16 8 1 16 1 690 16 01 6 9956 66 2722 Confidence Interval for b 66 2722 2 645 8 141 Construct a 95 confidence lower bound for the overall standard deviation n 1 s 2 2 7 degrees of freedom c 6 9956 8 1 16 14 07 02 05 14 07 2 82 Construct a 95 confidence upper bound for the overall standard deviation 95 conf upper bound for 0 n 1 s 2 21 0 8 1 16 0 7 19 2 167
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