Random counts usually follow a model called the Poisson distribution, which is c
ID: 2955152 • Letter: R
Question
Random counts usually follow a model called the Poisson distribution, which is completely specified by the rate parameter, A. the average number of events in some fixed interval, say an hour, a mile, or a square meter. A biologist believes that a species of snail occurs randomly in a habitat with a density of 2 per square meter, giving the following probabilities for the counts he should see in one meter quadrats that he will sample: The biologist and his students examine n = 100 quadrats one Saturday, and get the following counts of snails: The biologist conducts a goodness of fit test to see if his counts match the Poisson probabilities. Show a table of expected values for the counts in each category. Find the degrees of freedom and critical value assuming alpha = 0.05. Calculate the chi-square distance statistic and determine whether the data k fits the proposed model.Explanation / Answer
x
P(X = x)
Obs
Exp
O - E
(O - E)2/E
0
0.135335
17
13.53353
3.466472
0.8879
1
0.270671
32
27.06706
4.932943
0.899024
2
0.270671
18
27.06706
-9.06706
3.037328
3
0.180447
21
18.0447
2.955296
0.484007
4
0.090224
9
9.022352
-0.02235
5.54E-05
5+
0.052653
3
5.265302
-2.2653
0.974605
100
100
0
6.28292
Step 1: State the null and alternative.
H0: The model fits a Poisson with parameter 2.
H1: The model does not fit a Poisson with parameter2.
x
P(X = x)
Obs
Exp
O - E
(O - E)2/E
0
0.135335
17
13.53353
3.466472
0.8879
1
0.270671
32
27.06706
4.932943
0.899024
2
0.270671
18
27.06706
-9.06706
3.037328
3
0.180447
21
18.0447
2.955296
0.484007
4
0.090224
9
9.022352
-0.02235
5.54E-05
5+
0.052653
3
5.265302
-2.2653
0.974605
100
100
0
6.28292
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