Question

The members of a population have been numbered 1-50. A sample of size 20 is to be taken from the​ population, using cluster sampling. The clusters are of equal size​ 10, where cluster​ #1 consists of the members of the population numbered 1dash​10, cluster​ #2 consists of the members of the population numbered 11-20, and so forth.
a. What are the clusters taken from the​ population?
b. Suppose that clusters​ #1 and​ #3 are selected from the clusters determined in part​ (a). What is the​ sample?
a. Which of the following represent the​ clusters?
A.
1dash​10, 11-20, 21-​40, 41-50
B.
1-10, 11-​20, 21-​30, 31-40, 41-50
C.
1-10, 11-20, 21-​30, 31-50
D.
1-5, 6-​10, 11-​15, 16-​20, 21-25, 26-30, 31-35, 36-40, 41-​45, 46-50
E.
1-20, 21-40, 41-50

Answer 1

Answer:

Given that (some important point need to be focus)

• population have been numbered 1-50.
• We need Sample of size 20
• all clusters are of equal size​ 10
• cluster​ #1 consists of the members 1-10, cluster​ #2 consists of the members 11-20, and so on upto 41-50.

(a)-

WE have need only the sampl of size 20 , each cluster having 10 members since we can taken any two cluster from the population.

(b)- If clusters​ #1 and​ #3 are selected from the clusters then each cluster consist sample of 10 members since total sample size 20.

(C)- The represented ​ clusters are

1-10, 11-20, 21-30,31-40, 41-50

since option (B) is true.