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A made-up survey of 200 students records family income, whether the student has a laptop at home…
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A made-up survey of 200 students records family income, whether the student has a laptop at home, and a test mark. In the higher-income group, 80 students have a laptop and 20 do not. In the lower-income group, 30 have a laptop and 70 do not. Inside each income group, owners and non-owners have the same mean mark: 70 marks for higher income and 55 marks for lower income. Find the mean mark of all laptop owners and of all non-owners, to one decimal place. Find the gap. Explain where the gap comes from.
Need a reminder? The key ideaShow
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. Owners. marks.
Step 2. Non-owners. marks.
Step 3. The gap. marks.
Step 4. Where it comes from. Inside each income group, a laptop makes no difference. But most owners come from higher-income families, who score more anyway. Income is a confounding variable.
Answer: about and marks, a gap of about marks, all due to income.
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