Final answer:
Spatial sampling using a systematic sample relies on a predetermined system such as selecting every nth item. The manager's department store survey is an example of cluster sampling while the instructor's approach at Lake Tahoe Community College is stratified sampling. Both cluster and stratified sampling involve grouping the population before sampling, unlike systematic sampling which uses a fixed interval.
Step-by-step explanation:
When performing spatial sampling on data, a systematic sample can be implemented according to a predetermined system, such as selecting every nth item from a list. In the scenario provided, the manager of a department store decides to measure employee satisfaction by selecting four departments at random and interviewing all the employees in those departments. This constitutes a cluster sample, as entire groups (departments) are randomly selected and every individual within these groups is surveyed.
Another example is the instructor at Lake Tahoe Community College who performs stratified sampling by selecting five randomly chosen students from each math class, ensuring that each subsection of the population (math class) is represented in the sample.
Contrastingly, systematic sampling is exemplified by a health club asking every tenth customer on a specified day to complete a survey. This method involves a start point and a fixed interval (every tenth customer) and differs from cluster and stratified sampling which group the population before selection.