We are given information about a survey conducted by a teacher in our school. Let's consider the sampling method used by the teacher.
A student is chosen at random from each table in the cafeteria and asked for their opinion of school food.
Since a population of students is divided into tables in the cafeteria, this sample is a stratified sample. We want to determine whether this is a good sample. In general, a good sample cannot introduce any bias to the results. Let's consider the following factors that could cause bias.
Factor
Potential Bias
Sample Size
Because the teacher surveys one student from each table, the sample size could be too small to give valid results. It may depend on the size of the cafeteria and the number of students sitting at each table.
Location of the Survey
Some schools allow students to have their lunch at home or at a restaurant. In such cases, we cannot be sure that the sample is representative of the population of students.
Time of the Survey
There may be a grade wide field trip or an away game for a large sports team on the day of the survey. Then, a particular group of students would be absent from school, which could lead to bias in the sample.
Students may eat lunch during different lunch hours. For the sample to be unbiased, the teacher should ask students during all of the lunch hours.
A stratified sample is usually unbiased. However, based on the mentioned factors, the given sample is biased.
