Records pertaining to the hourly brown trout catch have been obtained in order to include this parameter into a simulation model of hatcheries and fishing in a world-famous trout stream. You receive this table:
|
Number of Brown Trout Caught each Hour
|
Frequency of Occurrence
|
|
0
|
30
|
|
1
|
35
|
|
2
|
23
|
|
3
|
8
|
|
4
|
5
|
|
5
|
1
|
|
6
|
1
|
You think the data is Poisson distributed, i.e.: if X = number of brown trout caught each hour, then:
X ~ Poi(a) with p(x) =(e^-alpha * alpha^x) / x ! , x = 0, 1, 2, 3, 4, ...
a. What is the point estimate for the unknown parameter alpha?
b. Use the c2 goodness of fit test to test the hypothesis that the number of brown trout caught each hour is Poisson distributed, using the point estimate of alphaafrom part alpha. Use a significance level of 0.05 for the test. State your hypotheses, your test statistic, and complete the test with a conclusion.