Estimate one-child household probability
Quick Overview
This question evaluates understanding of probability and survey sampling, specifically conditional probabilities and sampling bias when inferring household-level distributions from respondent-level data, and is categorized under Statistics & Math with a focus on practical application of conceptual sampling theory.
You survey 100 children at a school and ask how many children are in their family. The responses are:
- 50 children say their family has 1 child
- 20 children say their family has 2 children
- 30 children say their family has 3 children
Now you go to a random house in the same town and ask how many children live there. Assuming the school sample is representative and that family sizes larger than 3 do not occur, what is your best estimate of the probability that the randomly chosen house has exactly 1 child? Explain your reasoning carefully, including any sampling bias.