10_27_2 - STAT 400 Fall 2011 Examples for 10/27/2011 (2) X...

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STAT 400 Examples for 10/27/2011 (2) Fall 2011 Let X 1 , X 2 , … , X n be i.i.d. 2 σ μ , N . Let n n n ... i X X X X X 2 1 + + + = = ( sample mean ) ( ) 1 X X S 2 2 - = - n i ( sample variance ) Then X and S 2 are independent; X has 2 σ μ , n N distribution; n σ μ X - has ( ) 1 0 , N distribution; ( ) 2 2 σ μ X i - has χ 2 ( n ) distribution; ( ) ( ) 2 2 2 2 σ σ X X S 1 i n - = - has χ 2 ( n – 1 ) distribution; n S X μ - has t ( n – 1 ) distribution. A (1 - α ) 100% confidence interval for the population mean μ n z x σ 2 α ± n s t x 2 α ± n 1 degrees of freedom
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William Gosset (1876-1937) The t Distribution EXCEL: = TINV ( α , v ) gives 2 α t for t distribution with v degrees of freedom = TDIST ( t , v , 1 ) gives the upper tail probability for t distribution with v degrees of freedom, P ( T > t ) . = TDIST ( t , v , 2 ) gives 2 × P ( T > t ) .
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1. A manufacturer of TV sets wants to find the average selling price of a particular model. A random sample of 25 different stores gives the mean
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10_27_2 - STAT 400 Fall 2011 Examples for 10/27/2011 (2) X...

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