Please show all work and equations used. Thanks! Hypothesis Testing: 3. Distribu

Question

Please show all work and equations used. Thanks!

Hypothesis Testing:

3. Distribution Checking. Can parking spot pavement defects be predicted by the Poisson distribution? You evaluate almost 1800 parking spots and observe the following. spot pavement defects be Defects in parking spot, di 0 1 Parking spots with di defects, n 700 660 305 ! 20 24 Use the 8-step method with a significance level of 0.1. The Poisson distribution “r" is the average number of defects per parking spot. Estimate r as the total number of defects observed /total number of parking spots evaluated. Assume a value of 4 for the defects in the "24" category

Explanation / Answer

Ans:

Chi square test for Goodness of fit:

1)Hypothesis statements

H0:Number of defects follow poisson distribution

Ha:Number of defects does not follow poisson distribution.

2)Significance level=0.1

degree of freedom=n-1=5-1=4

(there are 5 number of categories)

3)Rejection region

critical chi square value=CHIINV(0.1,4)=7.779

4)Test statistic:

First estmate average number of defect for poisson parameter:

average number of defects,r=(700+660+305+85+20)/1800=1770/1800=0.983

Now,use this parameter to generate expected frquency of count from poisson distribution:

p=POISSON(di,0.983,FALSE)

Chi square test statistic=8.019

5)

As,calculate chi square=8.019>7.779,we reject null hypothesis.

There is insufficient evidence from sample data to conclude that parking spot pavement defects follow poisson distribution.

(i.e. defects does not follow poisson distribution)

di p Expected count(E) 0 0.3742 662.31 1 0.3678 651.05 2 0.1808 319.99 3 0.0592 104.85 4 0.0146 25.77

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