Question

High-speed Internet Laying fiber-optic cable is expensive. Cable companies want to make sure that, if they extend their lines out to less dense suburban

or rural areas, there will be sufficient demand and 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 sample of 5 blocks in the subdivision and survey each family that lives on those blocks.

(a) What is the name for this kind of sampling method?

(b) Suppose there are 65 blocks in the subdivision. Use technology or Table D to select 5 blocks to be sampled. Explain your method clearly.

Short answer

Part (a) Cluster sample.

Part (b) It involve finding and going to many different houses scattered out at different locations.

Step-by-step solution

 Part (a) Step 1: Given information

A poll was undertaken to establish the percentage of rural subdivision families who would purchase the service. They took a basic random sample of five blocks in the development and polled every family that lived on one of them.

Concept

Divide the population into groups, or clusters, to select a cluster sample. Pick a few of these clusters at random. The sample includes all of the people in the chosen clusters.

Part (a) Step 3: Explanation

A sample of size n is used in simple random sampling, and each sample of size $\text{'}n$ has an equal probability of being chosen. Simple random samples are obtained from independent subgroups using stratified random sampling (stratum). Cluster sampling separates the population into non-overlapping subgroups (clusters), which are subsequently included in the sample. Every $k^{th}$ participant in the sample is included in systematic random sampling ($k$ integer). A voluntary response sample is one in which the individuals can choose whether or not to participate. Convenience sampling selects a subset of the population that is easily accessible. Every family in the specified sample is surveyed, which is a random sample of $5$ blocks. As a result, the subgroups are the blocks, and the whole selected subgroup is in the sample (because every family in the block is surveyed), necessitating a cluster sample.

Part (b) Step 1: Explanation

Assume the subdivision consists of $65$ blocks. Choose $5$ blocks to sample using technology or Table D. Cluster sampling was most likely employed for convenience, as it is faster and less expensive than an SRS or a random sample with blocking, which both require identifying and visiting a large number of residences in various regions.