Question

b. Two research workers classified some people in income groups on the basis
of sampling studies. Their results are as follow:
Investigators Income groups Total
Poor Middle Rich
A 160 30 10 200
B 140 120 40 300
Total 300 150 50 500
Show that the sampling technique of atleast one research worker is defective.

Answer 1

Task b. Two research workers classified some people in income groups on the basis of sampling studies. Their results are as follow:

Investigators Income groups Total

Poor Middle Rich

A 160 30 10 200

B 140 120 40 300

Total 300 150 50 500

Show that the sampling technique of at least one research worker is defective.

Answer

Let us make the hypothesis that the techniques adopted by both the groups are similar and the data is similar also.

Expected frequencies are

$$\lambda^2 = \sum \frac{(O - E)^2}{E} = \frac{(160 - 120)^2}{120} + \frac{(30 - 60)^2}{60} + \frac{(10 - 20)^2}{20} + \frac{(140 - 180)^2}{180} + \frac{(120 - 90)^2}{90} + \frac{(40 - 30)^2}{30} = 55.54$$

Degree of freedom = (3-1)(2-1)=2

Table value of $2\lambda^2$ for 2 degree of freedom at $5\%$ level of significance is 5.991. Since the calculated value is bigger than the table value, we conclude the rejection of null hypothesis at $5\%$ level of significance. Technique adopted by one of two groups in data collection is defective.