Practice Random Sampling in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Selecting individuals from a population where every member has an equal chance of being chosen.

Drawing names from a hat where all names are equally likely to be picked. No favoritism, no convenience, just pure chance. This is how we ensure the sample represents the whole population, not just the easy-to-reach people.

Example 1

easy
A school has 500 students numbered 001–500. Describe how to select a simple random sample of 20 students using a random number generator.

Example 2

medium
Explain the difference between simple random sampling, stratified sampling, and systematic sampling. Give an example scenario where stratified sampling would be preferred.

Example 3

medium
A factory produces 10,000 widgets per day. A quality inspector wants to check 100 widgets. She takes every 100th widget off the production line, starting with widget number 37 (chosen randomly). What type of sampling is this? What potential problem could arise?

Example 4

hard
A university has 12,000 students: 7,200 undergraduates and 4,800 postgraduates. A researcher wants a stratified sample of 200 students. (a) How many undergraduates and postgraduates should be in the sample? (b) How does this compare to what might happen with a simple random sample?
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