Question

Question 5 (17 marks) The sample result concerning the lifetime, in weeks of service, before a failure of the color television picture tube in a random sample of 10 television sets manufactured by Company A and 8 television set (a) s manufactured by Company B are given as follows: ХА-| 76.61 XB = 165.625 s2 145.8222 | s = 159.4107 Perform an appropriate hypothesis test to verify whether the average lifetime before a failure of the picture tube manufactured by Company A and B are different or not at 5% level of significance. State the necessary assumption(s). (12 marks) What is cluster sampling? Cite an example to briefly explain the procedure of doing it. When is it suitable to adopt cluster sampling in drawing sample? (b) (5 marks) END OF SECTION B]

Answer 1

(b)

Cluster Sampling:

The total population is divided, into some recognisable sub-divisions which are termed as clusters and a simple random sample of these clusters is drawn. Each and every unit in the selected clusters is then observed, measured and interviewed.

For Example,

If we are ineterested in obataining the income or opinion data in a city, the whole city may be divided into N different blockd or localities (which determine the clusters) and a simple random sample of n blocks is drawn. The individuals in the selected blocks determine the cluster sample.

Cluster sampling is suitable when:

(i) No reliable listing of elements is available and it is expensive to prepare it.

(ii) Even if the list of elements is available, the location or identification of the units may be difficult.

(iii) Every unit of the population under study corresponds to one and only one unit of the cluster so that the total number of sampling units in the frame covers all the units of the population under study without any omission or duplication. When this condition is not satisfied, bias is introduced.