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A juice company fills 5000 bottles a day…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A juice company fills 5000 bottles a day. Every evening a worker opens 40 bottles chosen at random from the day's bottles and measures the juice in each. The mean of the 40 bottles today is . Name the population, the sample, the parameter that the company wants to know and the statistic that it has. Then say why the worker does not measure every bottle.
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
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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. Population and sample. The population is the 5000 bottles filled today. The sample is the 40 bottles that were opened.
Step 2. Parameter. The company wants , the mean volume of juice in all 5000 bottles. It does not know it.
Step 3. Statistic. It has , the mean of the 40 bottles. This is its estimate of .
Step 4. Why a sample. An opened bottle cannot be sold, and measuring 5000 bottles a day would take a long time. A random sample of 40 tells the company enough.
Answer: population 5000 bottles, sample 40 bottles, parameter (the mean of all bottles), statistic .
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