Exercise 5. Assume that we have observed the following values from a normal distribution withknown variance o2 = and unknown mean .1.23 -0.67 1.16 1.67 0.24 2.99 0.02 ..17 0.27 ..21.5%.Test the hypothesis Ho: = 0 against the alternative H₁: 0 at significance level a =Exercise 6. Let 0> 0 and XU[0,0], i.e. X is uniformly distributed on the interval [0,0].a) As a function of 0, determine P(X ≤ 1).b) Assume that is unknown, but we can observe X. For given 00, we want to test thehypothesis H: 020 against the alternative H₁: 0 < 0o. Consider the test which rejectsHo, if and only if X < c. How should we choose c, as a function of 00 and a, to get a testwith significance level a? Carefully justify your answer.

Answered: Image /qna-images/answer/3f4c6264-5d10-4586-8c17-3843d69745d4.jpg

Answered: Exercise 5. Assume that we have…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Exercise 5. Assume that we have observed the following values from a normal distribution with known variance o2 = and unknown mean . 1.23 -0.67 1.16 1.67 0.24 2.99 0.02 ..17 0.27 ..21. Test the hypothesis Fo: = 0 against the alternative H₁: 0 at significance level a = 5%.