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Let X1, X2,, X, be iid N(0, o?). Consider the hypothesis test: Ho : o = 1 H : o² = 4 Let C1 = {(s')² > K1}, C2 = {s² > K2} where (s')² = E, X as defined in %3D problem 1 (here u = 0). a. Find K1, K2 so that both C1, Ca have size a. b. Let a = 0.05 and n = 5. Use the following Chi-square calculation website to find the approximate values of K1, K2. (Hint: you may want to enter the degree of freedom in first and observe the density graph to get a decent guess on the value of x with desired probability). You can also use a tool of your choice (Python, R etc.) as long as the calculation is correct.

Let X1, X2,, X, be iid N(0, o?). Consider the hypothesis test: Ho : o = 1 H : o² = 4 Let C1 = {(s')² > K1}, C2 = {s² > K2} where (s')² = E, X as defined in %3D problem 1 (here u = 0). a. Find K1, K2 so that both C1, Ca have size a. b. Let a = 0.05 and n = 5. Use the following Chi-square calculation website to find the approximate values of K1, K2. (Hint: you may want to enter the degree of freedom in first and observe the density graph to get a decent guess on the value of x with desired probability). You can also use a tool of your choice (Python, R etc.) as long as the calculation is correct.

MATLAB: An Introduction with Applications
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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Let X1, X2,, X, be iid N(0, o?). Consider the hypothesis test : ... Ho : a? = 1 %3! H : o² = 4 Let C = {(s')² > K1}, C2 = {s² 2 K2} where (s')² = E, (X-p as defined in problem 1 (here u = 0). a. Find K1, K2 so that both C1, C2 have size a. b. Let a = 0.05 and n = 5. Use the following Chi-square calculation website to 72 %3D find the approximate values of K1, K2. (Hint: you may want to enter the degree of freedom in first and observe the density graph to get a decent guess on the value of x with desired probability). You can also use a tool of your choice (Python, R etc.) as long as the calculation is correct. b. Show directly by calculating the B of the two regions using the tool as part b that Ci is more powerful than C2. (Quoting Neyman-Pearson directly is not allowed here).
Transcribed Image Text:Let X1, X2,, X, be iid N(0, o?). Consider the hypothesis test : ... Ho : a? = 1 %3! H : o² = 4 Let C = {(s')² > K1}, C2 = {s² 2 K2} where (s')² = E, (X-p as defined in problem 1 (here u = 0). a. Find K1, K2 so that both C1, C2 have size a. b. Let a = 0.05 and n = 5. Use the following Chi-square calculation website to 72 %3D find the approximate values of K1, K2. (Hint: you may want to enter the degree of freedom in first and observe the density graph to get a decent guess on the value of x with desired probability). You can also use a tool of your choice (Python, R etc.) as long as the calculation is correct. b. Show directly by calculating the B of the two regions using the tool as part b that Ci is more powerful than C2. (Quoting Neyman-Pearson directly is not allowed here).
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