Tutorial 10

Tutorial 10 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1302 PROBABILITY AND STATISTICS II (2009-10) EXAMPLE CLASS 10 1. Take a random sample X 1 ,...,X n from the distribution f ( x | θ ) = θ 2 xe - θx ,x > 0. Quoting the large- sample theory of the mle, construct the critical region of a size 5% (Wald’s) test of H 0 : θ = θ 0 against H 1 : θ 6 = θ 0 . 2. (a) The following ﬁgures give the % extension under a given load for two random samples of lengths of yarn, the ﬁrst sample being taken before washing and the second after six washings. Before washing: 12.3 13.7 10.4 11.4 14.9 12.6 After 6 washings: 15.7 10.3 12.6 14.5 12.6 13.8 11.9 Do they provide any justiﬁcation for concluding that extensibility is aﬀected by washing? Support your conclusion by means of a size 0.05 test. (You may assume that % extension has a normal distribution with a standard deviation which is unaltered by the washings.) (b) In another experiment with the same type of yarn, six lengths of yarn were

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This note was uploaded on 05/04/2011 for the course STAT 1302 taught by Professor Smslee during the Spring '10 term at HKU.

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Tutorial 10 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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