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Unformatted text preview: 1 / 16 Introduction to Econometrics Econ 322, Fall, 2010 Lecture 6: Review of Statistical Concepts III September 22, 2010 Topics Covered triangleright Topics Covered OneSided Hypothesis Tests Calculating the Test Statistic Calculating the pvalue The Rejection region Confidence Intervals The confidence interval when σ 2 is unknown Testing for Differences in Means Estimators for Covariance and Correlation 2 / 16 1. onesided tests 2. confidence intervals 3. Testing for differences in means 4. Correlation and Covariance OneSided Hypothesis Tests Topics Covered triangleright OneSided Hypothesis Tests Calculating the Test Statistic Calculating the pvalue The Rejection region Confidence Intervals The confidence interval when σ 2 is unknown Testing for Differences in Means Estimators for Covariance and Correlation 3 / 16 square So far we have looked at two different ways of testing a statistical hypothesis when the alternative is a twosided alternative. That is the test is H : μ = c vrs. H A : μ negationslash = c. square To test this hypothesis we 1. calculated the pvalue of the test 2. set a fixed significance level, calculated the critical value and compared this to the test statistic. OneSided Hypothesis Tests (cont) Topics Covered triangleright OneSided Hypothesis Tests Calculating the Test Statistic Calculating the pvalue The Rejection region Confidence Intervals The confidence interval when σ 2 is unknown Testing for Differences in Means Estimators for Covariance and Correlation 4 / 16 square Now consider the 1sided test H : μ ≤ c vrs. H A : μ > c. or H : μ ≥ c vrs. H A : μ < c. square In order to work out the pvalue of a test we need to think about the following: – how do we calculate the test statistic – when do we reject the test – how do we calculate the pvalue square Consider the first type of 1sided test. We believe that the value of μ is less than or equal to c . The alternative is that it is greater than c . Calculating the Test Statistic Topics Covered OneSided Hypothesis Tests triangleright Calculating the Test Statistic Calculating the pvalue The Rejection region Confidence Intervals The confidence interval when σ 2 is unknown Testing for Differences in Means Estimators for Covariance and Correlation 5 / 16 square The test statistic is generally: t = ˆ μ μ H SE (ˆ μ ) where μ H is the value of μ if the Null hypothesis is true. square The problem here is that the null hypothesis doesn’t give me one value of μ under the null....
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This document was uploaded on 10/26/2011 for the course ECON 327 at Rutgers.
 Fall '11
 LANDONLANE
 Econometrics

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