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Unformatted text preview: Section Notes for Week 11 In this section, we are going to discuss Pivot Method for confidence intervals, which is one of the most important methods to find confidence intervals, and is convenient to implement. Definition : If X 1 , ,X n f ( x, ), and is unknown. A pivot is a function of the data X = ( X 1 , ,X n ) and of whose distribution does not depend on . Note: A pivot is not a statistics, but a statistics is a pivot. Exp1: If X 1 , ,X n N ( , 1) and are i.i.d, and is unknown: X N ( , 1 /n ), and X N (0 , 1 /n ). Thus, X is a pivot. There are two important types of pivots: tpivot and Fpivot: Definition :A tpivot has the following form: T ( x ) q ( ) S ( x ) , where S ( x ) > Recall how we introduced t distribution to get some idea of why this is called ttype. Definition :A Fpivot has the following form: T ( x ) q ( ) , where T ( x ) > ,q ( ) > ....
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 Summer '08
 WEBER

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