14 - Lecture 4

14 - Lecture 4 - Introduction to Econometrics Econ 322...

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Introduction to Econometrics Econ 322 Summer, 2011 Lecture 4: Review of Statistical Concepts June 13, 2011 Lecture 4: Review of Statistical Concepts () June 13, 2011 1 / 1
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Topics Covered 1 Hypothesis tests 2 p-values of tests 3 critical values and rejection regions Lecture 4: Review of Statistical Concepts () June 13, 2011 2 / 1
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Hypothesis Tests We are interested in making inferences about unknown parameters. We have discussed how we would like to construct estimators that have desirable properties. Once we are happy with an estimator (i.e. it is unbiased, consistent and e¢ cient), we then use this estimator to make an estimate of our parameter that we are studying. Lecture 4: Review of Statistical Concepts () June 13, 2011 3 / 1
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Hypothesis Tests We are interested in making inferences about unknown parameters. We have discussed how we would like to construct estimators that have desirable properties. Once we are happy with an estimator (i.e. it is unbiased, consistent and e¢ cient), we then use this estimator to make an estimate of our parameter that we are studying. We know that this estimate is one realization from a random variable and so we know that the estimate will not be equal to the true value of the parameter. The nice properties that we construct for our estimator, however, allows us to get an estimate that is &close±to the true value. Lecture 4: Review of Statistical Concepts () June 13, 2011 3 / 1
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Hypothesis Tests While we can never know for certainty what the true value of a random variable is, we are able to make some probability statements about the true value. These probability statements come in various forms such as a statistical hypothesis test or the closely related concept of a con&dence region. Lecture 4: Review of Statistical Concepts () June 13, 2011 4 / 1
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Hypothesis Tests A statistical hypothesis test consists of 3 components: a statement of the NULL hypothesis takes the form of e.g. H 0 : μ = c or H 0 : μ & c or H 0 : μ ± c &rst example is an example of a ±point² hypothesis while second and third are examples of ±composite² hypotheses a statement of the ALTERNATIVE hypothesis a statement on the size of the test (more about this later) Lecture 4: Review of Statistical Concepts () June 13, 2011 5 / 1
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An example of a point hypothesis Consider the following example: Suppose we wish to know the mean attendance at a swimming pool on a Sunday. We are interested in this number because we need to know how many lifeguards to have on duty for this coming Sunday. Lecture 4: Review of Statistical Concepts () June 13, 2011 6 / 1
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An example of a point hypothesis Consider the following example: Suppose we wish to know the mean attendance at a swimming pool on a Sunday. We are interested in this number because we need to know how many lifeguards to have on duty for this coming Sunday.
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14 - Lecture 4 - Introduction to Econometrics Econ 322...

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