Or Classical Decision Theory4

# Or Classical Decision Theory4 - Approximate Tests for...

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Approximate Tests for Proportion The tests for proportion are derived using the normal distribution approximation to the binomial distribution. : If is the number of successes in independent Bernoulli trials of an experim p Theorem S n ent with a constant probability of success in each trial, then is approximately (0,1) if is large. : Approximation is good if 5 and 5. S np p npq N n Note np nq -

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{ } 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 In the following 3 situations: ( ) : : ( ) ( ) : : ( ) : : . Critical Region / is the number of successes in independent trials. a H p p H p p p p b H p p H p p c H p p H p p C s s s s n s np Z np α = = < = < < = = + 0 0 q
0 0 0 1 1 0 2 1 1 1 1 0 0 0 1 The power function is given by , ( ) ( ) Hence, in order to have ( ) 1 , ( ), should be large enough to satisfy the condition n p p Z np q P p npq P p p p n Z p q Z p q n p p α β - - - + 2245 Φ ≥ - < + - - - - - - - - - - ( )

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{ } 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 In the following 3 situations: ( ) : : ( ) ( ) : : ( ) : : . Critical Region / Power function is, ( ) ( ) 1 a H p p H p p p p b H p p H p p c H p p H p p C s s np Z np q n p p Z np q P p npq α - - = = = = + - + 2245 - Φ 1 1 0 To have ( ) 1 , ( ), should satisfy ( ) P p p p n β ≥ -
{ } ( 29 0 0 1 0 0 1 0 0 / 2 0 0 1 0 1 / 2 0 0 0 1 1 Consider the case : : : Critical Region / or Power function is ( ) 1 In order to have , n should H p p H p p C s s s s s s np Z np q s np Z np q s np s np P p npq npq p α β - = = = + = + - - 2245 Φ + - Φ 2 1 1 / 2 0 0 0 1 satisfy, Z p q Z p q n p p + -

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Problem 1 A production process is considered under control if the proportion
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## This note was uploaded on 02/23/2011 for the course MATH 122 taught by Professor Ritadubey during the Spring '11 term at Amity University.

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Or Classical Decision Theory4 - Approximate Tests for...

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