# 11_01_1 - STAT 400 Examples for(1 Fall 2011 EXCEL = CHIINV...

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STAT 400 Examples for 11/01/2011 (1) Fall 2011 EXCEL: = CHIINV ( α , v ) gives ( ) v 2 α χ for 2 χ distribution with v degrees of freedom = CHIDIST ( y , v ) gives the upper tail probability for 2 χ distribution with v degrees of freedom, P ( Y > y ) . Recall: If X 1 , X 2 , … , X n are i.i.d. 2 σ μ , N . Then ( ) ( ) 2 2 2 2 σ σ X X S 1 i n - = - is χ 2 ( n – 1 ).

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A ( 1 - α ) 100 % confidence interval for the population variance σ 2 (where the population is assumed normal) ( ) ( ) - - - 1 , 1 2 2 1 2 2 2 2 α α χ s χ s n n n – 1 degrees of freedom A ( 1 - α ) 100 % confidence interval for the population standard deviation σ (where the population is assumed normal) ( ) ( ) - - - 1 , 1 2 2 1 2 2 2 2 α α χ s χ s n n OR ( ) ( ) - - - 1 , 1 2 2 1 2 2 α α χ s χ s n n n – 1 degrees of freedom 1. A machine makes ½-inch ball bearings. In a random sample of 41 bearings, the

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11_01_1 - STAT 400 Examples for(1 Fall 2011 EXCEL = CHIINV...

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