mont4e_sm_ch09_sec07 - Section 9-7 9-86 Expected Frequency...

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9-40 Section 9-7 9-86 Expected Frequency is found by using the Poisson distribution ! ) ( x e x X P x λ = = where 41 . 1 100 / )] 4 ( 4 ) 11 ( 3 ) 31 ( 2 ) 30 ( 1 ) 24 ( 0 [ = + + + + = Value 0 1 2 3 4 Observed Frequency 24 30 31 11 4 Expected Frequency 30.12 36.14 21.69 8.67 2.60 Since value 4 has an expected frequency less than 3, combine this category with the previous category: Value 0 1 2 3-4 Observed Frequency 24 30 31 15 Expected Frequency 30.12 36.14 21.69 11.67 The degrees of freedom are k p 1 = 4 0 1 = 3 a) 1) The variable of interest is the form of the distribution for X. 2) H 0 : The form of the distribution is Poisson 3) H 1 : The form of the distribution is not Poisson 4) α = 0.05 5) The test statistic is ( ) = = k i i i i E E O 1 2 2 0 χ 6) Reject H 0 if χχ o 2 0053 2 781 >= ., . 7) () ( ) ( ) ( ) 23 . 7 67 . 11 67 . 11 15 69 . 21 69 . 21 31 14 . 36 14 . 36 30 12 . 30 12 . 30 24 2 2 2 2 2 0 = + + + = 8) Since 7.23 < 7.81 do not reject H 0 . We are unable to reject the null hypothesis that the distribution of X is Poisson. b) The P-value is between 0.05 and 0.1 using Table IV. From Minitab the P-value = 0.0649.
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9-41 9-87 Expected Frequency is found by using the Poisson distribution ! ) ( x e x X P x λ = = where 907 . 4 75 / )] 9 ( 8 ) 10 ( 7 ) 11 ( 2 ) 1 ( 1 [ = + + + + = Estimated mean = 4.907 Value 1 2 3 4 5 6 7 8 Observed Frequency 1 11 8 13 11 12 10 9 Expected Frequency 2.7214 6.6770 10.9213 13.3977 13.1485 10.7533 7.5381 4.6237 Since the first category has an expected frequency less than 3, combine it with the next category: Value 1-2 3 4 5 6 7 8 Observed Frequency 12 8 13 11 12 10 9 Expected Frequency 9.3984 10.9213 13.3977 13.1485 10.7533 7.5381 4.6237 The degrees of freedom are k p 1 = 7 1 1 = 5 a) 1) The variable of interest is the form of the distribution for the number of flaws.
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This note was uploaded on 10/12/2009 for the course IND E 315 taught by Professor Kailashkapur during the Spring '09 term at University of Washington.

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mont4e_sm_ch09_sec07 - Section 9-7 9-86 Expected Frequency...

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