An article im Annals of Mathematical Statistics reports the following data on th

Question

An article im Annals of Mathematical Statistics reports the following data on the number of borers in each of 120 groups of borers. Does the Poisson pmf provide a plausable model for the distribution of the number of borers in a group? Use alpha 005 for the chi square test

a.) state the null and alternative hypothesis

b.) describe how to determine expected value

c.) calculate statistic chi squared value, critical chi squared value, and p-value

d.) what is the decision?

Number of Borers Observed 0 3 1 10 2 19 3 24 4 22 5 17 6 11 7 6 8 3 9 2 10 1 11 1 12 1

Explanation / Answer

Ans:

a)

H0:Number of borers follow poisson distribution.

Ha:Number of borers does not follow poisson distribution.

b)

estimate average rate as poisson parameter:

r=(number of borers*observed count)/120=476/120=3.97

p=POISSON(k,3.97,false)

Exected value=p*120

c)Test statistic:

Chi square=16.057

df=13-1=12

critical chi square=CHIINV(0.05,12)=21.026

p-value=CHIDIST(16.057,12)=0.189

d)As,p-value>0.05,we fail to reject null hypothesis.

There is sufficient evidence to conclude that the number of borers follow poisson distribution.

Number of Borers(k) Observed p Expected (O-E)^2/E 0 3 0.0189 2.26 0.239 1 10 0.0749 8.99 0.113 2 19 0.1487 17.85 0.074 3 24 0.1968 23.62 0.006 4 22 0.1953 23.44 0.089 5 17 0.1551 18.61 0.140 6 11 0.1026 12.32 0.140 7 6 0.0582 6.98 0.139 8 3 0.0289 3.47 0.063 9 2 0.0127 1.53 0.145 10 1 0.0051 0.61 0.254 11 1 0.0018 0.22 2.784 12 1 0.0006 0.07 11.871 Total 120 1.00 120 16.057

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