Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A made-up survey of teenagers asks whether they play a sport and whether they usually sleep eight hours or more. Of the who play a sport, sleep eight hours or more. Of the who do not, do. Find the probability of eight hours given sport, and given no sport. Find the count of sport players with eight hours that you would expect if the two answers were independent. How many more were observed than expected? Give four decimal places where needed.
Two answers are independent when the share of one is the same in every group of the other, so . Then each expected count is the row total times the column total, divided by the grand total.
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. The two shares. Sport: . No sport: .
Step 2. The expected count. Eight hours or more in all: . Expected: teenagers.
Step 3. The difference. teenagers more than expected.
Answer: , about , and teenagers. The two answers seem to be associated.
Watch out. This table does not show that sport makes teenagers sleep more. Perhaps teenagers who sleep well have more energy for sport, or a third thing affects both. A table shows a link, not its cause.
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