Question

A? government's economic analysis branch recently released figures that they claimed showed a growth spurt in the western region of a certain country that is divided into 51

states. Using the accompanying? table, where the cell values are numbers of? states, determine if the percent change in real GDP by state was independent of region of the country. Use alpha?=0.05.

	GDP? %		Change
Region	Top? 40%		Bottom? 60%		Total
West	11		4		15
Midwest	4		8		12
Southeast	4		8		12
Northeast	2		10		12
Total	21		30		51

What is the test? statistic?

What is p value

Answer 1

H0 :  The percent change in real GDP by state was independent of region of the country

H1:  The percent change in real GDP by state was not independent of region of the country

Let the los be alpha = 5%

The expected frequencies are

	Gender
	Top 40%	Bottom 60%	Total
West	6.176	8.824	15
Midwest	4.9412	7.0588	12
Southeast	4.941	7.059	12
Northeast	4.941	7.059	12
Total	20.9992	30.0008	51

The chisquare contribution values are

		Contribution
Oi	Ei	(Oi-Ei)^2 /Ei
11	6.176	3.768
4	8.824	2.6372
4	4.9412	0.1793
8	7.0588	0.1255
4	4.941	0.1792
8	7.059	0.1254
2	4.941	1.7506
10	7.059	1.2253
	Total:	9.9905

Test Statistic, X^2: 9.99
Critical X^2: 7.814736
P-Value: 0.0187

Here chsiquare value > chsiquare critical value and P-value < alpha 0.05 so we reject H0

Thus we conclude that the percent change in real GDP by state was not independent of region of the country