Chapter 4: Q. 23 (page 239)

High-speed Internet Laying fiber-optic cable is expensive. Cable companies want to make sure that if they extend their lines to less dense suburban or rural areas, there will be sufficient demand so the work will be cost-effective. They decide to conduct a survey to determine the proportion of households in a rural subdivision that would buy the service. They select a simple random sample of $5$ blocks in the subdivision and survey each family that lives on one of those blocks.
a. What is the name for this kind of sampling method?
b. Give a possible reason why the cable company chose this method.

Short Answer

Expert verified

(a) The name of the sampling method is a cluster sample

(b) This method is chosen because of its cost efficiency and more time.

Step by step solution

Part (a) Step 1: Given information

We need to find out the name of method of sampling

Part (a) Step 2: Explanation

Every family in the specified sample is surveyed, which is a random sample of $5$ blocks.

As a result, the blocks are the subgroups, and the entire selected subgroup is in the sample (since every household in the block is surveyed), implying that the sample must be a cluster sample.

Part (b) Step 1: Given information

We need to find the reason for choosing this method of sampling

Part (b) Step 2: Explanation

Cluster sampling was most likely employed for convenience, as it is more time and cost-effective than an SRS or a random sample with blocking, which both require identifying and visiting a large number of different households in various areas.