STAT 400 Lecture AL1 Answers for 7.1 (Part 3) Spring 2015 Dalpiaz 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 , 1 221 2 22 2 ααχsχs nn. 90% confidence level = 0.10 2 = 0.05. n – 1 = 40 degrees of freedom. 2050 22 . = 55.76. 2950 221 . = 26.51. 51.2602.0 141 ,76.5502.0 141 22 ( 0.01694 , 0.02457 ) 2. The following random sample was obtained from N ( , 2 ) distribution: 16 12 18 13 21 15 8 17 Recall: x = 15, s 2 = 16, s = 4. a) Construct a 95% confidence interval for the overall standard deviation. Confidence Interval for 2 : nn 112222122ss,. = 0.05. 2 = 0.025. 12 = 0.975. number of degrees of freedom = n 1 = 8 1 = 7. 22 = 16.01. 122 = 1.690. 690.11618,01.161618 ( 6.9956 ; 66.2722 ) Confidence Interval for : 2722.66 , 9956.6 = ( 2.645 ; 8.141 ) b) Construct a 95% confidence lower bound for the overall standard deviation. ,αχ122 s n 7 degrees of freedom 205.0χ = 14.07. ,07.141618 ( 2.82 ; ) c) Construct a 95% confidence upper bound for the overall standard deviation. 95% conf. upper bound for : 212αχ1 , s 0n = 167.21618 , 0 = ( 0, 7.19
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