) Ecology: Fish The Fish and Game Department stocked Lake Lulu with fish in the
ID: 3246688 • Letter: #
Question
) Ecology: Fish The Fish and Game Department stocked Lake Lulu with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later it sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the sample were distributed as follows: Catfish: 120 Bass: 85 Bluegill: 220 Pike: 75 In the 5-year interval, did the distribution of fish change at the 0.05 level? a) What is the level of significance? State the null and alternate hypotheses. b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? What sampling distribution will you use? What are the degrees of freedom? c) Find or estimate the P-value of the sample test statistic. d) Based on your answers in parts a) to c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of the categories? e) Interpret your conclusion in the context of the application.
Explanation / Answer
a) level of signficance =0.05
null hypothesis:Ho: population fits the specified distribution of the categories
alternate hypothesis:Ha:population does not fits the specified distribution of the categories
b)
applying chi square goodness of fit test:
from above chi square test stat =9.3333
c) for above 3 degree of freedom and chi square test stat ; p value =0.0252
d)as p value is less then 0.05 level we reject the null hypothesis.
e) there is sufficient evidence to conclude that population does not fits the specified distribution of the categories
observed Expected Chi square fish type Probability O E=total*p =(O-E)^2/E catfish 0.300 120.000 150.00 6.00 bass 0.150 85.000 75.00 1.33 bluegill 0.400 220.000 200.00 2.00 Pike 0.150 75.000 75.00 0.00 1 500 500 9.3333Related Questions
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