Suppose that a publisher is considering how to pay an author for writing a book. The publisher would like the author to put forth his maximum effort, but the publisher is unable to observe the author's effort. 
Definitions:
Confidence Interval
A range of values, derived from sample statistics, that is used to estimate the true value of a population parameter with a certain level of confidence.
Population Mean
The average value of all the individuals or elements within a complete population.
Lower Tail
The lower tail of a distribution refers to the section of the distribution that contains the smaller values, often used in the context of probabilities and statistical significance.
Confidence Interval
An array of values, extracted from sample statistics, considered likely to have within it the value of an unknown population parameter.
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