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ch14 - Wk 14 TestsofSignificance EX).The (i.e. change= ,000

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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 revenue-neutral  (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?
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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 0 3 720 - - = - The area left of -3 under the normal curve is about 0.1  of 1% (or 1/1000).
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3 The NULL and the ALTERNATIVE • Null Hypothesis (H 0 ):  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.
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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 0 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.
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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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