Random Sampling and Inference
A free Pre-Algebra lesson from the “Statistics and Probability” unit, with a worked example and practice problems including step-by-step solutions.
Random sampling uses chance to select members of a population. In a simple random sample of a fixed size, every possible sample of that size has the same chance of selection, so every member has an equal chance. Random selection reduces selection bias but does not guarantee a representative result; samples still vary. To estimate a population total from a simple random sample, use sample-count / sample-size = estimated total / population, and remember that the result is an estimate.
What you'll learn
- Recognize random vs biased samples
- Use a sample proportion to estimate a population total
- Understand that larger random samples are usually more reliable
Worked example
Problem. A random sample of 100 voters shows 60 support a measure. Estimate support among 1000 voters.
- Sample proportion: 60 / 100 = 0.6 (60%).
- Apply to the population: 0.6 * 1000 = 600.
- Connect the calculation back to Random Sampling and Inference so the method, not just the arithmetic, is clear.
- Check the result against the original question before writing the final answer.
Answer: 600
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. In a simple random sample, every member of the population has:
Choices: Equal chance of being chosen · No chance · A higher chance if they speak up
Show solution
- A simple random sample gives every possible sample of the required size the same chance.
- Consequently, every individual has the same chance of being chosen.
Answer: Equal chance of being chosen
2. Surveying only students in the gym about favorite school activities is:
Choices: Random · Biased
Show solution
- Gym-goers may favor sports more than the general population.
Answer: Biased
3. A sample of 100 randomly chosen voters predicts 60% support a measure. Estimate support in 1000 voters.
Show solution
- 60% of 1000 = 600.
Answer: 600
4. Under the same simple-random-sampling method, larger samples generally have:
Choices: Less sample-to-sample variation · More sample-to-sample variation
Show solution
- Larger samples tend to reduce chance variation in an estimate.
- This does not guarantee that one particular larger sample will be closer to the true value.
Answer: Less sample-to-sample variation
5. A capture-recapture sample of 50 fish has 5 tagged. The lake has 1000 fish total. Estimate the tagged population.
Show solution
- 5/50 = x/1000 means x = 100.
Answer: 100
Practice this interactively with instant feedback and an AI tutor.
Practice Random Sampling and Inference Take the free placement check