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A battery maker runs 25 batteries from a batch of 6000 until they are flat, to measure how long…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A battery maker runs 25 batteries from a batch of 6000 until they are flat, to measure how long they last. The 25 batteries last a mean of hours. Why does the maker not test every battery in the batch? What percentage of the batch is used up by the test? Give your answer to two decimal places.
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. Why a sample. The test runs each battery flat, so a tested battery cannot be sold. Testing all 6000 would leave nothing to sell.
Step 2. The share used up. .
Answer: the test destroys the batteries, and it uses up only about of the batch.
What if? The mean of hours is a statistic. The maker uses it to estimate the parameter, the mean life of all 6000 batteries.
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