A school principal randomly choose 75 students for a survey on the cafeteria food. Determine whether the sample may be biased. Explain.
If it is truly random, it is not likely to be biased. What is the definition of random?
To determine if the sample may be biased, you need to consider if it is representative of the entire student population. A biased sample is one where certain groups or characteristics are over- or underrepresented compared to the population they are supposed to represent.
In this case, since the school principal randomly chose 75 students for the survey, the sample does have the potential to be biased. To understand why, we need to consider a few factors:
1. Sample Size: The sample size of 75 students is relatively small compared to the total population of students in the school. If the population is large, a smaller sample may not accurately represent the diverse opinions and experiences of all students.
2. Selection Process: The method of random selection is a good way to minimize bias, as it gives every student an equal chance of being included. However, it's important to ensure that the random selection process is truly random and that no specific groups or characteristics are intentionally or unintentionally excluded.
3. Representation: To determine if the sample is biased, we need to consider if it represents the diversity of the student population. Are students from different grade levels, genders, ethnic backgrounds, and socioeconomic statuses adequately represented in the sample? If certain groups are underrepresented, the sample may be biased.
4. Purpose of the Survey: The specific purpose of the survey is also important to consider. If the principal wants to understand the opinions of all students regarding the cafeteria food, the sample should reflect the entire student population. If the sample is biased, the survey results may not accurately represent the opinions of all students.
To conclusively determine if the sample is biased or not, it is crucial to evaluate these factors and assess if the sample adequately represents the entire student population.