Final answer:
the correct option for the best sample to determine the average age of students at BYU-Idaho would be C) Many randomly selected students from each apartment building in Rexburg.
Step-by-step explanation:
When determining the average age of students at BYU-Idaho, the goal is to get a representative sample that reflects the broader student population's characteristics. Among the given options, C) Many randomly selected students from each apartment building in Rexburg, would be the best sample. This method aligns with the principle of proportionate random sampling, where if a particular class or living situation comprises a certain percentage of the student population, an equal percentage should be represented in the sample.
Option A might be limited due to capturing a sample during a specific time that might not be representative. Option B includes only dorm residents and may miss the variability in ages presented by students living off-campus. Option D is problematic because it includes only male students and omits the entire female student population. For a sample to truly represent the university's average student age, it should include both male and female students from various living situations and not be time or location-bound as in options A and B.
Examples of effective sampling methods include using class rosters to select students proportionally (as seen in reference 13), utilizing a random number generator (reference b), and ensuring a sample from diverse backgrounds as seen in the algebra students population example.
Therefore, the correct option for the best sample to determine the average age of students at BYU-Idaho would be C) Many randomly selected students from each apartment building in Rexburg.