An analyst specifies an economic model Y = Bo+ B X + B2 X2+ BsW +e. You may find the following numbers helpful for this problem. The random variable Z ~ N(0,1) is standard normal. P(Z>128)=.1 P(Z > 1.65) = .05 P(Z >1.96) =.025 P(Z >2.33)=.01 P(Z > 2.58) = .005. An equivalent way of representing this, using the notation in class, is gi1 = 1.28 g1.05 = 1.65 g1.025 = 1.96 q1_.o01 = 2.33 q1.005 = 2.58 i. The analyst considers the hypothesis that X does not affect Y, all else equal. Write this hypothesis as a restriction on a parameter or parameters of the economic model. ii. The analyst considers the hypothesis that W makes Y increase, all else equal. Write this hypothesis as a restriction on a parameter or parameters of the economic model. iii. The analyst specifies a statistical model Yi = Bo + BIXi + B2X, + B3Wit ui, where MLR.1-MLR.4 hold. The analyst has a large sample. The analyst estimates this model and obtains the following result Y =-1+2X - 3X2 +4W. The analyst constructs standard errors s.e.(Bo) = 2 s.e. (31) = 1 s.e. (B2) = 3 s.e. (B3) = 2. Test the following hypothesis at the a = .10 level. Please show enough work to demonstrate which numbers you used Ho : 32 = 2 H1 : B2 # 2. iv. The number 2 is in front of X in the regression results above. Is 2 a population parameter? v. Maintaining the previous setup, test the following hypothesis at the a = .05 level. Please show enough work to demonstrate which numbers you used. Ho : B1 5 0 H1 : B1 > 0