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# Populations and samples used in research

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1. Why would you use a small sample to draw inference about a large population?
2. What is the difference between a sample parameter (X-bar and s) and a proportion parameter (&#961;)?
3. When would you use a two population test with a small sample size at your place of employment, in your education, or in politics?
4. When testing two populations with small sample sizes, do both sample sizes have to be identical? Why or why not?
5. What are the differences among a proportion, a percentage, and a ratio?
6. What do you do when testing two populations, if one sample's size is small and the other sample's size is large?

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Populations and samples used in research are discussed in great detail in this solution.

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1. Why would you use a small sample to draw inference about a large population?
We use a small sample to draw inference about a large population because the population is too large, too expensive and too time consuming to collect information from every member of the population, so a sample is used to draw inference.

2. What is the difference between a sample parameter (X-bar and s) and a proportion parameter (&#961;)?
The proportion parameter p represents the proportion in the population. This is similar to the probability that an observation selected at random from the population has the attribute being studied.
The statistic that is calculated from a sample data is called s. It is ...

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