To determine which of Mr. Sanchez's samples is biased, let's analyze the methods used for each sample collection and see if they potentially introduce any bias.
Sample 1:
- Mr. Sanchez surveyed every third person on each first-period class roster.
- This sampling method could be considered random if the list of names on the class roster is not systematically arranged according to any criterion that might influence the survey's outcome, such as alphabetical order or seating arrangement.
- However, if the list has any underlying non-random structure, it may introduce bias. Given that it's difficult to guarantee the randomness of such lists in school settings, there's a possibility that this sample could introduce bias, but it is not certain.
Sample 2:
- Mr. Sanchez surveyed his five honors math classes.
- This sampling method is definitely biased. Honors math students represent a specific subset of the student population, typically those who are more academically inclined or have a particular interest in math.
- The preferences of honors students may not reflect the preferences of the entire student body. For example, honors students might prefer activities that involve group thinking and problem-solving, or they might have different social dynamics compared to the general population.
Given this analysis, it is clear that Sample 2 does not represent the entire student population accurately since it only includes a specific subgroup (honors math students). Thus, Sample 2 is biased.
Upon reviewing the answer choices:
- Sample 1 is biased.
- Sample 2 is biased.
- Both samples are biased.
- Neither sample is biased.
The correct statement is:
Sample 2 is biased.
