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A class has 16 boys and 16 girls. Ms Okafor wants a fair sample of 8 for a survey…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A class has 16 boys and 16 girls. Ms Okafor wants a fair sample of 8 for a survey. She draws 4 boys' names from one hat and 4 girls' names from another. Every student then has the chance of being chosen. Is her sample a simple random sample of the class? Explain, and name the method she really used.
Need a reminder? The key ideaShow
In a simple random sample of from , every group of is equally likely, so each member has the chance . Use random.sample (no repeats), never random.choices, and check that the list you choose from covers everyone.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Each student. The chance for each student is , which is the same as in a simple random sample.
Step 2. Each group. Her method always gives exactly 4 boys and 4 girls. A group of 8 girls, or of 5 boys and 3 girls, can never be chosen. So not every group of 8 is equally likely.
Answer: it is not a simple random sample. It is a stratified sample with the strata boys and girls, shared in proportion.
What if? For a survey where boys and girls may answer differently, her plan is a good one. Fair does not have to mean simple.
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