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







Related Discussions:- Test of homogeneity , Assignment Help, Ask Question on Test of homogeneity , Get Answer, Expert's Help, Test of homogeneity Discussions

Write discussion on Test of homogeneity
Your posts are moderated
Related Questions
Find the sum-of-products expression for subsequent function,  F (x,y,z) = y + Z‾ Ans: The sum of the product expression for the following function f is DNF (disjunc

Some interpretations of the derivative Example    Is f ( x ) = 2 x 3 + 300 +4 increasing, decreasing or not changing at x = -2 ? Solution:  We already know that the rate

How do I find percentages with doing COS Sheets


How we find locus of the middle points of chord of an ellipse which are drawn through the positive end of the minor axes

a car comes to a stop from a speed of 30m/s in a distance of 804m. The driver brakes so as to produce a decelration of 1/2m per sec sqaured to begin withand then brakes harder to p


report on shares and dovidend using newspaper

Determine the minimum capacity C of a Capacitor given that: C =(ax/(x-a))+(xy/(y-b))+(yb/(b-y)) given that "a" and "b" are fixed values and "x" and "y" vary independently such th

The dimensions of a rectangular prism can be expressed as x + 1, x - 2, and x + 4. In terms of x, what is the volume of the prism? Since the formula for the volume of a rectang