1Q1/ (a): Let x -b (5, 0), with size a =Find the best critical region321to test a null hypothesis H, :0= against the alternative hypothesisH:0 =4%3D

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Answered: Q1/ (a): Let x -b (5, 0), with size a =…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Patients diagnosed with retinopathy (disease of the retina) were admitted into a study where they were randomly assigned to one of the two treatments and monitored for 6 years. The study found that 143 of the 352 patients assigned to the conventional treatment (group 1) showed an improvement of their disease. Whereas 177 of the 363 patients assigned to the intensive treatment (group 2) had improvement of the disease. Suppose you are hypothesizing that the intensive treatment (Group 2) is more effective than the conventional treatment (Group 1) but hypotheses are written in the form of Group 1-Group 2. Conducting a test of significance (at a 5%) with the hypotheses you chose from Question 9, you calculated a p-value equal to which made you decide to O A) 0.9861; fail to reject Ho B) 2.20; fail to reject Ho OC) 0.0139; reject Ho D) 0.0139; fail to reject Ho E) -2.20; reject Ho
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Suppose X1, .., X, iid Beta(a,ß) 1. Find the LRT “Likelihood ratio test for Ho: a = ß = 1 versus H :not Ho 2. Find the LRT “Likelihood ratio test for H,:a = ß versus H1: a + ß
b) Suppose you are given the following information for an OLS regression: Σχι X; Y = 830102,T = 22,x=416.5, y = 86.65, x = 3919654, RSS = 130.6 i) Calculate the ordinary least square regression line. Calculate SE (a) and SE (B) Perform the hypothesis test such that Ho: a = -60 versus H₁: α = -60 Perform the hypothesis test such that Ho: P = 0.4 versus H₁: B = 0.4 In both cases use a significance of 5%. ii) iii) iv)
"You run a regression with 9 variables on Y with 40 observations. A t-stat of one of the variables come up as 2.115 for a null hypothesis. At the 95% confidence level, you would" A reject the null hypothesis in favor of the alternative since t is greater than the critical value. B reject the null hypothesis in favor of the alternative since t is less than the critical value. fail to reject the null hypothesis since t is less than the critical value. D fail to reject the null hypothesis since t is greater than the critical value.
Consider a simple linear regression model, Y₁ = Bo + B₁X₁ + ₁ for i=1,2,...,n with the usual random error term (&) assumptions. Suppose that hypotheses Ho: P₁ = 0 against H₁:₁ <0 were tested and Ho: B₁ = 0 was rejected. Assume ₁e₁² = 0. ei i) Briefly explain what the conclusion of the test means for the values of Y given the values of X. -1 ii) Draw an example of a scatter plot with the fitted regression line for the problem mentioned above. iii) Calculate and interpret the correlation coefficient for the problem at hand.
Consider the linear model y=B,+B,x,+B,x,,+B,x+B,+u, You estimate the model y =B,+B,x,+B,x, observations and obtain the OLS residuals . You then estimate the auxiliary regression +u based on 123 31 3" 3i 41 The LM statistic +1 4/ you obtain to test the null hypothesis that H:B,=B,=0 is 20.91. What is the R2 of the auxiliary regression? It is not possible to say O 0.17 O 0.175714 0.177203
You are performing a two-tailed z-test If a = 0.2, find the positive critical value, to two decimal places.
9) Find L3.2 (5) using the nodes xo = 3,x1 = 4, x2 = 6 ,x3 = 8 %3D
1) Adsorption rates against equilibrium concentrations (Ce) were measured in an experimental| study and are given in the table: C. 5.4 12.6 25.7 55.3 qe 7.3 13.7 17.15 22.35 K,C, -) model, find km, KL using least square estimation method. 1+ k„C, In Langmuir (q.
8 Let’s suppose that you have the following specification: yt=B0+B1xt+ut where ut might be autocorrelated: ut=ρut-1+vt . Having obtained the estimates, b0 and b1 for B0 and B1 , you calculate the predicted values and residuals. You find that t=2n(et-et-1)2=20 and t=1n(et)2=200 . What is the Durbin Watson test statistic? What is ρ ?
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Q1/ (a): Let x -b (5, 0), with size a = 32 Find the best critical region to test a null hypothesis H,:0 against the alternative hypothesis H, :0 =? 4.