Question

1. From a poll of 800 television viewers, the following data have been accumulated as to their levels of education and their preference of television stations.

                                                           

	Level of Education
	High School	Bachelor	Graduate	Total
Public Broadcasting	110	190	100	400
Commercial Stations	80	220	100	400
Total	190	410	200	800

           

1. Determine the degrees of freedom

2. Determine the expected frequencies (fill in the table below)

	Level of Education
	High School	Bachelor	Graduate	Total
Public Broadcasting				400
Commercial Stations				400
Total	190	410	200	800

3. Compute the test statistic

4. Test at a = .05 to determine if the selection of a TV station is dependent upon the level of education.

Answer 1

a)

degree of freedom(df) =(rows-1)*(columns-1)=(2-1)*(3-1) =

2

b)

Expected	Ei=row total*column total/grand total	High School	Bachelor	Graduate	Total
	Public Broadcasting	95.000	205.000	100.000	400
	Commerical Stations	95.000	205.000	100.000	400
	total	190	410	200	800

c)

Applying chi square test of independence:

chi square    χ2	=(Oi-Ei)2/Ei	High School	Bachelor	Graduate	Total
	Public Broadcasting	2.368	1.098	0.000	3.4660
	Commerical Stations	2.368	1.098	0.000	3.4660
	total	4.7368	2.1951	0.0000	6.9320
test statistic X2 =		6.9320

d)

for 2 df and 0.05 level , critical value       χ2=

5.991

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that selection of a TV station is dependent upon the level of education.