Question

A manager at a bus company wants to survey employees about the new uniforms. Which of the following best describes a stratified sample of employees?

a) The manager forms groups of 8 employees based on the departments the employees are in. Then, she selects all of the employees in 9 randomly chosen groups.
b) The manager forms 6 groups of employees based on the departments the employees are in. Then, she selects 12 employees at random from each group.
c) The manager uses a computer program to draw 72 employees at random and selects these employees.
d) Every set of 72 employees is equally likely to be drawn by the computer program.

Answer 1

Option (b) accurately describes a stratified sample of employees, where a manager forms groups based on departments and selects employees randomly from each group. This approach ensures that all departments have representation within the sample. A stratified sample involves drawing participants from each subgroup, or stratum, to create a sample that reflects the overall population.

Step-by-step explanation:

The question from the student relates to sampling methods, specifically stratified sampling, which is a topic within the field of statistics, in the discipline of Mathematics. In stratified sampling, a population is divided into subgroups, known as strata, that share similar characteristics. A sample is then drawn from each stratum. The purpose of using a stratified sample is to ensure that the sample more closely resembles the entire population on characteristics of interest.

To answer the student's question, option (b) best describes a stratified sample of employees. A manager forms 6 groups of employees based on the departments they are in and then selects 12 employees at random from each group. This structure ensures that the sample includes representation from all departments, reflecting the broader employee body.

For example 15. the survey design conducted by the manager interviewing all employees of randomly selected departments is a cluster sampling design. Cluster sampling and stratified sampling are similar in that they both use groups, but in cluster sampling, entire groups are chosen randomly, whereas in stratified sampling, members within each group are chosen randomly.

Example 77. (a) represents a convenience sampling, whereby questionnaires are distributed to an accessible subset of the population, not necessarily at random. In contrast, (b) represents a form of systematic sampling, where a rule, like selecting particular rows, determines the sample.