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lect5_2010 - 1 / 28 Introduction to Econometrics Econ 322...

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Unformatted text preview: 1 / 28 Introduction to Econometrics Econ 322 Fall, 2010 Lecture 5: Review of Statistical Concepts II September 20, 2010 Topics Covered triangleright Topics Covered Hypothesis Tests p-values of tests Critical Values and Rejection Regions 2 / 28 1. Hypothesis tests 2. p-values of tests 3. critical values and rejection regions Hypothesis Tests Topics Covered triangleright Hypothesis Tests Hypothesis Tests An example of a point hypothesis An example of a composite hypothesis The Testing Problem Testing a Two-sided Hypothesis p-values of tests Critical Values and Rejection Regions 3 / 28 Hypothesis Tests Topics Covered Hypothesis Tests triangleright Hypothesis Tests An example of a point hypothesis An example of a composite hypothesis The Testing Problem Testing a Two-sided Hypothesis p-values of tests Critical Values and Rejection Regions 4 / 28 square 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 efficient), we then use this estimator to make an estimate of our parameter that we are studying. square 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. Hypothesis Tests Topics Covered Hypothesis Tests triangleright Hypothesis Tests An example of a point hypothesis An example of a composite hypothesis The Testing Problem Testing a Two-sided Hypothesis p-values of tests Critical Values and Rejection Regions 5 / 28 square 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 confidence region. Hypothesis Tests Topics Covered Hypothesis Tests triangleright Hypothesis Tests An example of a point hypothesis An example of a composite hypothesis The Testing Problem Testing a Two-sided Hypothesis p-values of tests Critical Values and Rejection Regions 6 / 28 square A statistical hypothesis test consists of 3 components: 1. a statement of the NULL hypothesis takes the form of e.g. H : = c or H : c or H : c first example is an example of a point hypothesis while second and third are examples of composite hypotheses 2. 3. An example of a point hypothesis Topics Covered Hypothesis Tests Hypothesis Tests triangleright An example of a point hypothesis An example of a composite hypothesis The Testing Problem Testing a Two-sided Hypothesis p-values of tests Critical Values and Rejection Regions 7 / 28 square Consider the following example: Suppose we wish to know the mean attendance at a swimming pool on a Sunday. We are interested inattendance at a swimming pool on a Sunday....
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lect5_2010 - 1 / 28 Introduction to Econometrics Econ 322...

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