Question

#11 Please show work: The data below represents the fields of specialization for a randomly selected sample of undergraduate students. We want to determine whether there is any dependency between the fields of specialization and the regions of the country.

	Northeast	Midwest	South	West	Total
Business	54	65	28	93	240
Engineering	15	24	8	33	80
Liberal Arts	65	84	33	98	280
Fine Arts	13	15	7	25	60
Health Sciences	3	12	4	21	40
	150	200	80	270	700

a. Determine the critical value of the chi-square χ2 for this test of independence.

b. Calculate the value of the test statistic.

c. What is the conclusion for this test? Let α= .05.

d.Let α= .05. Compute the test statistic for the goodness of fit test.

e. At the 5% level of significance using the p-value approach, test the hypotheses. What do you conclude about the distribution?

Answer 1

Observed
	Northeast	midwest	south	west	total
Business	54	65	28	93	240
Engg	15	24	8	33	80
Liberal arts	65	84	33	98	280
fine arts	13	15	7	25	60
health science	3	12	4	21	40
Total	150	200	80	270	700

Expected value = sum(coli)*sum(rowi)/total

Expected
	Northeast	midwest	south	west
Business	51.429	68.571	27.429	92.571
Engg	17.143	22.857	9.143	30.857
Liberal arts	60.000	80.000	32.000	108.000
fine arts	12.857	17.143	6.857	23.143
health science	8.571	11.429	4.571	15.429

test statistic, chi-square = sum((Oi - Ei)^2/Ei) = 8.67

a)
Critical value = 21.03

b)
test statistic, chi-square = 8.67

c)
Fail to reject null hypothesis.

d)
Test statistic, chi-square = 8.67

e)
p-value = 0.73

Fail to reject H0