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Unformatted text preview: 1 Wk 14 Tests of Significance • EX) Suppose a new tax code is to be introduced. The authorities argue that the new tax code is revenueneutral (i.e. tax revenue will remain the same). • change = tax under new rule – tax under old rule • The treasury department has records of 100,000 representative tax returns. • We sample 100 forms … • Sample Average = 2190 Baht • SD + of sample = 7200 Baht • Was it due to chance, or something else? 2 • The box model has 100,000 tickets, from which we draw 100 tickets. • Let’s assume that the average of the box is “0” (i.e. average of change before and after new tax code is zero). • SE of sample average is: 7200 100 • If the average of the box was really “0”, then we should expect the sample average to be “0”. But we got 2190. • This is 3 SE’s below the expected value: 2190 3 720 =  • The area left of 3 under the normal curve is about 0.1 of 1% (or 1/1000). 3 The NULL and the ALTERNATIVE • Null Hypothesis (H ): Average of box = 0 • Alternative Hypothesis (H A ): Average of box < 0 • The null hypothesis expresses the idea that an observed difference is due to chance . • To make a test of significance, the null hypothesis has to be set up as a box model for the data. • The alternative hypothesis is often what someone sets out to prove. The null hypothesis is then an “alternative” explanation for the findings, in terms of chance variation. 4 Test Statistics and Significance Levels • A test statistic is used to measure the difference between the data and what is expected in the null hypothesis. 2190 3 720 =  observed expected 3 720 z = =  • z says how many SEs away an observed value is from its expected value, where the expected value is calculated using the null hypothesis. 5 • (From the table, the area is 0.135 of 1%; rounding off, we get 0.1 of 1%; this is 0.1 of 0.01 = 0.001 = 1/1,000) • The chance of getting this sample is 1/1000, i.e. This is called the observed significance level or P value ....
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This note was uploaded on 03/14/2010 for the course ECON Statistics taught by Professor Yy during the Spring '10 term at Seoul National.
 Spring '10
 YY

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