Question

A TV station wishes to obtain information on the TV viewing habits in its market area.

The market area contains one city of population $170,000$, another city of$70,000,$ and

four towns of about $5000$residents each. The station suspects that the viewing habits

may be different in larger and smaller cities and in the rural areas. Which of the

following sampling designs would yield the type of information the station requires?

a. A stratified sample from the cities and towns in the market area

b. A cluster sample using the cities and towns as clusters

c. A convenience sample from the market area

d. A simple random sample from the market area

e. An online poll that invites all people from the cities and towns in the market area to

participate.

Short answer

The correct option is:

a. A stratified sample from the cities and towns in the market area

Step-by-step solution

Given information

We have been given four options from which we have to select the correct one.

a. A stratified sample from the cities and towns in the market area

b. A cluster sample using the cities and towns as clusters

c. A convenience sample from the market area

d. A simple random sample from the market area

e. An online poll that invites all people from the cities and towns in the market area to

participate.

Explanation

Simple random sampling involves selecting a sample from which each person has an equal probability of being chosen.

Simple random samples are obtained from independent subgroups using stratified random sampling.

Cluster sampling separates the population into non-overlapping subgroups, which are subsequently included in the sample.

Convenience sampling, for example, uses a voluntary response or a demographic segment (that is conveniently chosen).