Question

The City Council wants to gather input from residents about the recreational opportunities in the city. Categorize each technique as simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample.

a) Get an alphabetical list of all residents and question every 250th resident on the list.

b) Have 10 volunteers go downtown on Saturday afternoon and question people that they see. The volunteers may quit when they have questioned 25 people.

c) Get an alphabetical list of all residents and use a random number to get a sample of 3000 residents to question.

d) Divide the town into 25 distinct geographical neighborhoods then randomly choose 50 residents in each neighborhood to question.

e) Divide the town into 25 distinct geographical neighborhoods then randomly choose 10 of the neighborhoods. Question all the residents in the chosen neighborhoods

Answer 1

Let first understand each of the sampling

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.

Stratified sampling refers to a type of sampling method . With stratified sampling, the researcher divides the population into separate groups, called strata. Then, a probability sample (often a simple random sample) is drawn from each group.

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval.

Cluster sampling refers to a type of sampling method . With cluster sampling, the researcher divides the population into separate groups, called clusters. Then, a simple random sample of clusters is selected from the population.

Convenience sampling is a non-probability sampling technique where subjects are selected because of their convenient accessibility and proximity to the researcher.

Based on the above definitions, answers are as below:

a. Here we see that sample are selected with starting point 250th resident, hence is it Systematic sample.

b. Here we see that it is done as per the convenience of the volunteers, hence it is Convenience sample.

c. It is an example of random sampling, hence answer is Simple Random Sample.

d. Here we see that data is divided into strata and then simple random sampling is done in each strata, hence answer is Stratified Sample.

e. Here population is divided into the separate group and then groups are selected randomly to form the sample, hence answer is Cluster Sample.