# ch3-1 - Chapter 3 Review of Statistics (Part 1) Review of...

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Chapter 3 Review of Statistics (Part 1)

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Review of Statistics Suppose we want to know the mean of the distribution of earnings of recent college graduates. I One way is to perform an exhaustive survey of the population of workers. I However, such a comprehensive survey would be extremely expensive (U.S. Census cost \$10 billion). I Instead, we can select 1,000 members of the population at random (random sampling). Using statistical methods, we can learn about characteristics of the population.
Estimators Suppose you want to know the mean value of Y in a population, μ Y . I A natural way to estimate this mean is to compute Y from randomly sampled Y 1 , ..., Y n . I Another way is simply use the Y 1 . I Both Y and Y 1 is a function of the data, both are estimators of μ Y (there are many estimators). An estimator is a function of a sample of data to be drawn randomly from a population. I An estimator is a random variable. It has sampling distribution. An estimate is the numerical value of the estimator when it is actually computed using data from a speciﬁc sample. I An estimate is a nonrandom number.

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Desirable Characteristics of an Estimator There are many possible estimators, but what are desirable characteristics? Let b μ Y denote some estimator of μ Y . I b μ Y is an unbiased estimator of μ Y , if E ( b μ Y ) = μ Y , otherwise is b μ Y is biased . I b μ Y is a consistent estimator of μ Y , if b μ Y p μ Y . Let ˜ μ Y be another estimator of μ Y , and suppose that both b μ Y and ˜ μ Y are unbiased. I Then b μ Y is said to be more efﬁcient than ˜ μ Y if var ( b μ Y ) < var ( ˜ μ Y ) .
Properties of the Sample Average ¯ Y As shown in Ch.2: I E ( Y ) = μ Y , Y is an unbiased estimator of μ Y . I

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## This note was uploaded on 11/20/2011 for the course ECONOMICS 220:322 taught by Professor Otusbo during the Fall '10 term at Rutgers.

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ch3-1 - Chapter 3 Review of Statistics (Part 1) Review of...

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