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A park has 2400 trees. A forest officer checks a random sample of 80 trees and finds that 14 of…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A park has 2400 trees. A forest officer checks a random sample of 80 trees and finds that 14 of them have a leaf disease. Find the sample proportion as a percentage. Then estimate the number of diseased trees in the whole park.
Need a reminder? The key ideaShow
A parameter describes the whole population and is usually unknown. A statistic is worked out from a sample and is used as its estimate. If a fair sample of has with a property, , and the estimate for a population of is .
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. The statistic. , which is .
Step 2. The estimate. trees.
Answer: , and about 420 diseased trees.
Check. One tree in about six has the disease (), and . A second sample of 80 would give a slightly different estimate, so say "about 420".
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