Question

The Wisconsin Fish and Game Department stocked a lake with 30% catfish, 15 % bass, 40% bluegill, and 15% Northern Pike. Five years later they took a random sample of 500 fish from the lake and found 120 catfish, 85 bass, 220 bluegill, and 75 Northern Pike. At the 5% level of significance, can we show that the distribution of fish changed over the 5-year interval? State and test appropriate hypotheses. State conclusions.

Answer 1

the necessary calculation table :-

types	observed	test proportion	expected
catfish	120	0.30	500*0.30 = 150	(120-150)^2/150 = 6
bass	85	0.15	500*0.15 = 75	1.33333
bluegill	220	0.40	500*0.40 = 200	2
pike	75	0.15	500*0.15 = 75	0
	sum= 500			sum= 9.33333

hypothesis:-

at least one of the proportions are different.

test statistic is :-

degrees of freedom = (4-1) = 3

p value is = 0.0252

[ in any blank cell of excel type =CHISQ.DIST.RT(9.3333,3)]

decision:-

p value = 0.0252 < 0.05 (alpha)

we reject the null hypothesis and conclude that there is enough evidence to claim  that the distribution of fish changed over the 5-year interval at 0.05 level of significance.

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