STAT 400 Lecture AL1 Examples for 7.1 (Part 3)Spring 2015 Dalpiaz EXCEL: = CHIINV ( , v ) gives v2 α χ for 2χ distribution with v degrees of freedom = CHIDIST ( y , v ) gives the upper tail probability for 2χ distribution with v degrees of freedom, P ( Y > y ). Recall: If X 1 , X 2 , … , X n are i.i.d. 2σμ , N . Then 2222σσXXS1 i n is 2 ( n – 1 ).A ( 1 ) 100 % confidence interval for the population variance 2 (where the population is assumed normal) 1 , 1 221 2 22 2 ααχsχs nn n – 1 degrees of freedom A ( 1 ) 100 % confidence interval for the population standard deviation (where the population is assumed normal) 1 , 1 221 2 22 2 ααχsχs nn OR 1 , 1 221 22 ααχsχsnn n – 1 degrees of freedom 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.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. b) Construct a 95% confidence lower bound for the overall standard deviation. c) Construct a 95% confidence upper bound for the overall standard
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