Acceptance Or Rejection Of The Null Hypothesis Economics Essay

Acceptance Or Rejection Of The Null Hypothesis Economics Essay The appropriate value of t is 2.100. Since we are concerned whether b (the slope of original regression line) is significantly different fro B (the hypothesized slope of population regression), this is a two tailed test, and the critical values are  ±2.100. The standardized regression coefficient is 0.063, which is inside the acceptance region for our hypothesis test. Therefore, we accept null hypothesis that B is equal to 0.01. Step 6: Interpretation of the Result There is not enough difference between b and 0.01 for us to conclude that that B has changed from its historical value. Because of this, we feel that a one hundred percent increase in inflation would increase the poverty headcount by around 0.01%, as it has in the past. 2. Inflation and Ginni Coefficient The slope for the regression line that shows a relationship between inflation and gini coefficient is 0.5956. This means that a 100% increase in inflation would result in 0.5956% increase in gini coefficient. Now we wou ld perform the same hypothesis testing procedure to determine the authenticity of slope and whether the slope justifies the relationship between inflation and gini coefficient. Step 1: State the Null and the Alternative Hypothesis Let B denotes the hypothesized slope of actual regression line, the value of the actual slope of regression line is b = 0.5956. The first step is to find some value for B to compare with b= 0.5956. Suppose that over an extended past period of time, the slope of the relationship between inflation and gini coefficient was 0.5. To test whether this is still the case, we could define the hypothesis as: H0: B= 0.50 (Null hypothesis) H1: B à ¢Ã¢â‚¬ °Ã‚   0.50 (Alternative hypothesis) Step 2: Decide on Significance Level and Degree of Freedom Significance level ÃŽÂ ± = 0.05 and Degree of freedom (df) = n-2 = 19 – 2 = 17 Step 3: Find out Standard Error of b Where Sb = standard error of the regression coefficient Se = standard error of estimate Xi = valu es of the independent variable X-Bar = mean of the values of the independent variable n = number of the data points Year X Y X – X-Bar (X-X-Bar)2 Y2 XY 1963-64 4.19 38.6 -2.607368 6.79837008 1489.96 161.734 1966-67 8.58 35.5 1.7826316 3.17777535 1260.25 304.59 1968-69 1.58 33.6 -5.217368 27.2209332 1128.96 53.088 1969-70 4.12 33.6 -2.677368 7.16830166 1128.96 138.432 1970-71 5.71 33 -1.087368 1.18237008 1089 188.43 1971-72 4.69 34.5 -2.107368 4.44100166 1190.25 161.805 1979-80 8.33 37.3 1.5326316 2.34895956 1391.29 310.709 1984-85 5.67 36.9 -1.127368 1.27095956 1361.61 209.223 1985-86 4.35 35.5 -2.447368 5.98961219 1260.25 154.425 1986-87 3.6 34.6 -3.197368 10.2231648 1197.16 124.56 1987-88 6.29 34.8 -0.507368 0.25742271 1211.04 218.892 1990-91 12.66 40.7 5.8626316 34.370449 1656.49 515.262 1992-93 9.83 41 3.0326316 9.19685429 1681 403.03 1993-94 11.27 40 4.4726316 20.0044332 1600 450.8 1996-97 11.8 40 5.0026316 25.0263227 1600 472 1998-99 5.74 41 -1.057368 1.11802798 1681 23 5.34 2001-02 3.54 27.52 -3.257368 10.610449 757.3504 97.4208 2004-05 9.28 29.76 2.4826316 6.16345956 885.6576 276.1728 2005-06 7.92 30.18 1.1226316 1.26030166 910.8324 239.0256 Summation 129.15 678.06 0 177.829168 24481.06 4714.9392 X-Bar = 6.79 Y-Bar = 35.68 Se = 3.59 By putting Se and Summation (X-X-Bar) 2 in Sb, we have Sb = 0.269 Step 4: Find the Standardized Value of b t = b – BH0/Sb Where b = slope of fitted regression BH0 = actual hypothesized slope Sb = standard error of the regression coefficient By putting the values of the above in t, we have t = 0.355 Step 5: Conclusion on Acceptance or Rejection of the Null Hypothesis The appropriate value of t is 2.10. Since we are concerned whether b (the slope of original regression line) is significantly different from B (the hypothesized slope of population regression), this is a two tailed test, and the critical values are  ±2.10. The standardized regression coefficient is 0.355, which is inside the acceptance region for our hypothesis test. Therefore, we accept null hypothesis that B is equal to 0.5 Step 6: Interpretation of the Result There is not enough difference between b and 0.50 for us to conclude that that B has changed from its historical value. Because of this, we feel that a one hundred percent increase in inflation would result in an increase of 0.50% in gini coefficient, as it has in the past.