Final answer:
The most unbiased method for measuring air quality in an apartment complex would be stratified sampling based on proximity to a pollution source to ensure all relevant subgroups are sampled.
Step-by-step explanation:
The most unbiased and effective sampling method for determining the average air quality rating in an apartment complex would be stratified sampling based on the proximity to the factory (option C). This method ensures that all areas of the complex, regardless of their distance from the factory which might significantly affect air quality, are represented in the sample. In contrast, random sampling without considering strata (A) might overlook important subgroups, systematic sampling within each building (B) might introduce bias if buildings vary in their proximity to the factory, and convenience sampling of apartments closest to the factory (D) would likely result in a highly biased assessment due to the deliberate selection of potentially the most affected areas.
As an example of other types of sampling methods, the manager of a department store who selects four departments at random and conducts interviews with all employees there is using a cluster sampling method. Clustering involves selecting entire groups or 'clusters' and includes all members from the selected clusters in the sample. It's often used when a population is naturally divided into groups and is practical when it's too costly or difficult to sample from the entire population.