ECON206_1011_01_Handout_08

ECON206_1011_01_Handout_08 - ECON 206 METU Department of...

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Unformatted text preview: ECON 206 December 13, 2010 METU- Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] 1 LECTURE 08 HYPOTHESIS TESTING - II Outline of today’s lecture: I. Comments about Hypothesis Testing ................................................................................. 1 II. Small Sample Hypothesis Testing..................................................................................... 2 A. Small Sample Tests for Mean ....................................................................................... 3 B. Small Sample Tests for Comparing Two Population Means ........................................ 7 III. Testing Hypotheses Concerning Variances ..................................................................... 9 A. Tests for a Population Variance .................................................................................... 9 B. Tests for Comparing Two Population Variances ........................................................ 13 I. Comments about Hypothesis Testing Attention 1 Since there is always a room for Type II error, β when we carry out hypothesis testing: o You should say “Fail to Reject” the null hypothesis, H Æ You should not say “accept” null hypothesis, H Attention 2 Use the equality sign in null hypothesis when you do a one tailed-test. o In fact it is a controversial issue in statistical science. Some statisticians prefer to use ≤ or ≥ signs in null hypothesis. However, when we use the null hypothesis such as : . 8 H μ = , calculating the level of α is simple: we just found (value of test statistic is in RR when : 0.8 is true) P H μ = . If we used : . 8 H μ ≥ as the null hypothesis, our previous definition ECON 206 December 13, 2010 METU- Department of Economics Instructor: H. Ozan ERUYGUR e-mail: [email protected] 2 of α [ (value of test statistic is in RR when : 0.8 is true) P H μ = ] would be inadequate because the value of (value of test statistic is in RR) P will change for different possible values of μ since in this case any value for μ is possible within the interval 0.8 μ ≥ . In cases like this, α is defined to be the maximum (over all values of 0.8 μ ≥ ) value of (value of test statistic is in RR) P . This maximum value happens when 0.8 μ = , the “boundary value” of μ in : . 8 H μ ≥ . Thus, using : . 8 H μ = instead of : . 8 H μ ≥ leads to the correct testing procedure and the correct calculation of α without needlessly raising additional considerations. II. Small Sample Hypothesis Testing In order to apply large-sample hypothesis-testing procedures, the sample size must be large enough that ( ) ˆ ˆ / Z θ θ θ σ = − has approximately a standard normal distribution....
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ECON206_1011_01_Handout_08 - ECON 206 METU Department of...

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