The California Department of Education wants to gauge the difficulty of a new ex
ID: 3042173 • Letter: T
Question
The California Department of Education wants to gauge the difficulty of a new exam by having a sample of students at a particular school take the exam. The quality of the students at the chosen school varies widely and the school administrators are allowed to choose who gets to take the exam. The administrators have a strong incentive for the school to do well on the exam. Do you think the results will represent the true ability of the students at school? What kind of bias, if any, do you think will be present? Explain.
Explanation / Answer
- Whenever a sample of a population is taken, it is absolutely necessary that the sample represents the whole population to the best level. The sample is a bad one if it comprises of people that don't really represent the whole population as such. Ex: If the sample only has the top 10% students or if the sample has the lowest 20% students or only in the 45%-55% band. A good example would be to take a student or two from each 10% band - like 1 from 0-10%, 1 from 10-20%,...., 1 from 90-100%.
- A possibility is that because of the strong incentive for the school to do well on the exam, they might pick the good students and hence that wont represent the whole school student population. Students might do well on the exam and they mostly will because they normally do well on tests, but that doesn't mean the other students would and it doesn't really solve the problem of gauging a test by taking a sample. As explained in the first point, the sample needs to really represent the difficulty level and the solving level of the whole student population.
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