# 10_27_2 - STAT 400 Fall 2011 Examples for(2 X 1 X 2 X n be...

This preview shows pages 1–5. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 ) .
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

10_27_2 - STAT 400 Fall 2011 Examples for(2 X 1 X 2 X n be...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online