Sampling and inference
Sampling and Inference
Sampling and Inference is a topic in Statistics & Probability in the California Common Core State Standards. It is aligned to Standard S-IC.1, which requires students to understand statistics as a process for making inferences about population parameters based on a random sample.
A sample is a subset of a population studied to make inferences; random sampling avoids bias and a statistic estimates a parameter.
Theory
- Population: the entire group of interest.
- Sample: the subset actually studied.
- A statistic (from the sample) estimates a parameter (of the population).
The idea:
How to sample well
- Define the population.
- Select a random sample.
- Compute the sample statistic.
- Infer the population parameter, noting uncertainty.
The whole group is the population; those asked are the sample.
| \(\text{population}\) | \(=\) | \(200{,}000\ \text{voters}\) |
| \(\text{sample}\) | \(=\) | \(500\ \text{polled}\) |
Random selection avoids bias, so the sample represents the population fairly.
A sample statistic estimates the population parameter.
| \(52\%\) | \(\text{estimates}\) | \(\text{the true } \%\) |
A larger random sample generally gives a more reliable estimate (less variability).
Common pitfalls
Frequently asked questions
What is the difference between a population and a sample?
The population is the whole group; the sample is the subset studied.
Why use random sampling?
To avoid bias and represent the population fairly.
What is a parameter?
A numerical fact about the population, estimated by a sample statistic.
Does a bigger sample remove bias?
No — it reduces variability, but only random selection removes bias.