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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. Lets 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 SEs 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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 Spring '10
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