Question

A fisherman is interested in whether the distribution of fish caught in Green Valley Lake is the same as the distribution of fish caught in Echo Lake. Of the 192 randomly selected fish caught in Green Valley Lake, 107 were rainbow trout, 24 were other trout, 34 were bass, and 27 were catfish. Of the 292 randomly selected fish caught in Echo Lake, 117 were rainbow trout, 56 were other trout, 69 were bass, and 50 were catfish. Perform a test for homogeneity at a 5% level of significance.

• What is the test statistic? (Round your answer to two decimal places.)

• Part (f)

  What is the p-value? (Round your answer to four decimal places.)

Answer 1

Applying  test for homogeneity :

Expected	Ei=row total*column total/grand total	c	d	e	f	Total
	a	88.86	31.74	40.86	30.55	192
	b	135.14	48.26	62.14	46.45	292
	total	224	80	103	77	484
chi square    χ2	=(Oi-Ei)2/Ei	c	d	e	f	Total
	a	3.703	1.886	1.152	0.412	7.1520
	b	2.435	1.240	0.757	0.271	4.7027
	total	6.1384	3.1253	1.9088	0.6821	11.8547
test statistic X2 =		11.85
p value =		0.0079