Question

a consultant wants to ask workers at a factory about the workers job satisfaction. which of the following best describes a systematic sample of workers?
(a) the consultant assigns each worker a different number. using a random number table, he draws 90 of those numbers at random. then, the consultant selects the workers assigned to the drawn numbers. every set of 90 workers is equally likely to be drawn using the random number table.
(b) the consultant forms 5 groups of workers based on the workers shifts. then, he selects 18 workers at random from each group.
(c) a manager at a bus company wants to survey employees about the new uniforms. which of the following best describes a convenience sample of employees?
the manager asks for volunteers and selects every volunteer until 80 employees are selected. she selects the volunteers because these employees are easily accessible.
(d) the manager takes a list of the employees and selects every 4th employee until 80 employees are selected.
the manager uses a computer program to draw 80 employees at random and selects these employees. every set of 80 employees is equally likely to be drawn by the computer program.
a city manager wants to poll residents about a park renovation. which of the following best describes a stratified sample of residents?
the first 54 residents who walk into city hall one day are easily accessible. so, the city manager selects these residents.
the city manager forms groups of 9 residents based on the streets the residents live on. then, she selects all of the residents in 6 randomly chosen groups.
the city manager forms 6 groups of residents based on the residents incomes. then, she selects 9 residents at random from each group.

Explanation:

Step1: Recall sampling - method definitions

Systematic sampling involves selecting every \(k^{th}\) element from a list. In part (a), the consultant selects every \(5^{th}\) worker until 90 workers are selected, which is a systematic - sampling method.

Step2: Analyze convenience sampling

Convenience sampling is choosing the most accessible individuals. In part (b), the manager asks for volunteers and selects from them, which is convenience sampling as the sample is based on ease of access.

Step3: Recall stratified - sampling definition

Stratified sampling divides the population into subgroups (strata) and then samples from each subgroup. In part (c), the city manager divides residents into groups based on streets and then samples from each group, which is stratified sampling.

Answer:

(a) Systematic sample
(b) Convenience sample
(c) Stratified sample