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1. What characterizes a regular definition (dictionary) and an operational definition?

2. What is the purpose of sampling?

3. In distributions of populations, please consider Chebyshev's rule and the Empirical Rule. This takes some thinking.

a) When (what kind of a situation) would you use each in business? Why are they important? How are they calculated?

4. However we need to look closer at "causal research". Now concerning causal research let us look deeper: What must we actually show (necessary and sufficient conditions) if we are to prove cause and effect?

5. An important practical consideration when sampling is the sample size. So, what determines sample size? What influences our decisions?

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1. What characterizes a regular definition (dictionary) and an operational definition?

A regular definition is descriptive in nature and is based on fads that have occurred within the world over the past year. However, an operational definition deals with much extensive research and is based off much research. The goal is to have the hypothesis to fit with it. In other words, an operational definition is research-based more so than that of a regular definition.

2. What is the purpose of sampling?

The purpose of sampling is to get as many individuals to participate as possible. This allows for less bias and for the results to have as little skewness as possible. When one keeps these two areas in mind, the results from the research are accurate at least 99% of the time. One has to note that this is not an easy task because of how human everyone is and because of the possibility that it is easy to make mistakes along the way. For example, an individual could act ...

Solution Summary

This solution defined operational and sampling of a population as well as answered business research.

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Sufficiency and Order Statistics

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ]
having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x).

Argue that the mle of theta; equals theta;hat= max(-Y1, Yn).
Demonstrate that the mle theta;hat is a sufficient statistic for theta;.
Define at least two ancillary statistics for this distribution

See attachment for better symbol representation.

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