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Unformatted text preview: STAT 409 Examples for 09/23/2009 Fall 2009 EXCEL:
= CHIINV ( α , v ) 2
χ α (v ) for χ 2 distribution with v degrees gives of freedom
= CHIDIST ( y , v ) gives the upper tail probability for χ 2 distribution with v degrees of freedom, P ( Y > y ).
Recall:
If X 1 , X 2 , … , X n are i.i.d. N µ , σ 2 . Then ( n − 1 )⋅ S 2
σ 2 ∑(X i − X )
=
σ 2 2 is χ 2 ( n – 1 ). A ( 1 − α ) 100 % confidence interval
2
for the population variance σ
(where the population is assumed normal) 2 ( n − 1 )⋅ s , χ 2α 2 2 ( n − 1 )⋅ s
χ2 α
1− 2 n – 1 degrees of freedom A ( 1 − α ) 100 % confidence interval for the population standard
deviation σ (where the population is assumed normal) ( n − 1 )⋅ s
2 χα 2 2 , ( n − 1 )⋅ s
χ 2
1− α 2 2 OR s⋅ ( n −1 ) , s ⋅
χ 2α 2 ( n −1 ) χ2 α 1−
2 n – 1 degrees of freedom 1. A machine makes ½inch 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 service time in queues should not have a large variance; otherwise, the queue
tends to build up. A bank regularly checks service time by its tellers to determine
2 its variance. A random sample of 22 service times (in minutes) gives s = 8.
Assume the service times are normally distributed.
a) Find a 95% confidence interval for the overall variance of service time at the bank. b) Find the two onesided 95% confidence intervals for the overall variance of service
time at the bank. c) Find a 95% confidence interval for the overall standard deviation σ of service time
at the bank having minimum length. ( “Hint”: Use Table X ( p. 696 ). ) ...
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This note was uploaded on 10/12/2011 for the course STATISTICS stat 410 taught by Professor Stepanov during the Spring '11 term at University of Illinois, Urbana Champaign.
 Spring '11
 Stepanov
 Degrees Of Freedom, Probability

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