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.
A random sample gives every member of the population an equal chance of being chosen — only random samples reliably represent the whole population. A biased sample over- or under-represents groups. To estimate a population total from a sample, set up a proportion: sample-count / sample-size = unknown / population.
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.
Answer: 600
Practice problems
1. A random sample means every member of the population has:
Choices: Equal chance of being chosen · No chance · A higher chance if they speak up
Show solution
- Warm-up: First identify exactly what the question is asking: A random sample means every member of the population has:
- For data questions, identify what each statistic measures before calculating so the result matches the question.
- That is the definition of random sampling.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Equal chance of being chosen
2. Surveying only students in the gym about favorite school activities is:
Choices: Random · Biased
Show solution
- Warm-up: First identify exactly what the question is asking: Surveying only students in the gym about favorite school activities is:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Gym-goers may favor sports more than the general population.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Biased
3. A sample of 100 randomly chosen voters predicts 60% support a measure. Estimate support in 1000 voters.
Show solution
- Warm-up: First identify exactly what the question is asking: A sample of 100 randomly chosen voters predicts 60% support a measure. Estimate support in 1000 voters.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 60% of 1000 = 600.
- Check the result by substituting or estimating: the response should match 600 and make sense in the original problem.
Answer: 600
4. Larger random samples generally give:
Choices: More accurate estimates · Less accurate estimates
Show solution
- Core Practice: First identify exactly what the question is asking: Larger random samples generally give:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- More data narrows the margin of error.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: More accurate estimates
5. A capture-recapture sample of 50 fish has 5 tagged. The lake has 1000 fish total. Estimate the tagged population.
Show solution
- Core Practice: First identify exactly what the question is asking: A capture-recapture sample of 50 fish has 5 tagged. The lake has 1000 fish total. Estimate the tagged population.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 5/50 = x/1000 means x = 100.
- Check the result by substituting or estimating: the response should match 100 and make sense in the original problem.
Answer: 100
Practice this interactively with instant feedback and an AI tutor.
Practice Random Sampling and Inference Take the free placement check