stochastic calculus

stochastic calculus - W-1-6 JOMO KENYATTA UNIVERSITY OF...

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W1-2-60-1-6 JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY UNIVERSITY EXAMINATIONS 2014/2015 THIRD YEAR SECOND SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE: BAS/BST/BBS/BFE STA 2301: TESTS OF HYPOTHESES DATE: APRIL 2015 TIME: 2 HOURS INSTRUCTIONS: ANSWER QUESTION ONE AND ANY OTHER TWO QUESTIONS QUESTION ONE (30 MARKS) a) Define the following terms: i) Type I error [1 mark] ii) Type II error [1 mark] iii) Most powerful test [2 marks] b) Suppose we want to carry out the following hypothesis test for the mean, , of a normal distribution, with known variance, 2 = 125; H 0 : = 100 and H 1 : > 100. Suppose we decide to take a sample of size 36 and the level of significance, , is 0.05. i) What is the critical region? [3 marks] ii) What is the power of the test at = 110? [3 marks] c) A random sample of 41 observations from a normal population possessed a standard deviation of S = 6.9. Test H 0 : 2 = 30 against H 1 : 2 >30. Use = 0.05. [5 marks] d) Let x 1 , x 2 , ……. 2 n be a random sample from the binomial distribution given by: f(x, ɵ ) =

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