Test of homogeneity , Mathematics

Test of homogeneity

This is concerned along with the proposition that several populations are homogenous along with respect to some characteristic of interest for example; one may be interested in knowing if raw material available from various retailers is homogenous. A random sample is drawn from each of the population and the number in each of sample falling into every category is determined. The sample data is shown in a contingency table

The analytical procedure is the similar as that discussed for the test of independence

Illustration

A random sample of 400 persons was selected from each of three age groups and every person was asked to specify which types of TV programs are preferred. The results are displayed in the given table

Kind of program

Age group

A

B

C

Total

Under 30

120

30

50

200

30 - 44

10

75

15

100

45 and above

10

30

60

100

Total

140

135

125

400

 

Test the hypothesis that populations are homogenous along with respect to the types of television program they prefer, at 5 percent level of significance.

Solution

Assume that take hypothesis that the populations are homogenous with respect to different forms of television programs they prefer

Applying χ2 test

O

E

(O - E) 2

(O - E) 2 /E

120

70.00

2500.00

35.7143

10

35.00

625.00

17.8571

10

35.00

625.00

17.8571

30

67.50

1406.25

20.8333

75

33.75

1701.56

50.4166

30

33.75

14.06

0.4166

50

62.50

156.25

2.500

15

31.25

264.06

8.4499

60

31.25

826.56

26.449

 

 

 

Σ(O - E) 2 /E = 180.4948

χ2 = Σ(O - E)2/E

The table value of χ2 for 4d.f. at 5 percent level of significance is 9.488

The calculated value of χ2 is greater than the table value. We reject/refuse the hypothesis and conclude to the populations are not homogenous with respect to the type of TV programs preferred, conversely the different age groups vary in choice of TV programs.

Posted Date: 2/19/2013 2:40:19 AM | Location : United States







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