Tutorial 9

Tutorial 9 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1302 PROBABILITY AND STATISTICS II (2009-10) EXAMPLE CLASS 9 1. The numbers of members of a learned society born in the different months are as- sumed to be Poisson random variables with probably different means. The numbers are observed as follows: J F M A M J J A S O N D 39 28 51 49 48 48 41 39 33 60 48 44 It is claimed that members are born at a constant rate throughout the whole year. Test H : a constant rate against H 1 : the rate may vary from month to month. (a) Determine the likelihood ratio for the specified hypotheses. (b) Calculate the (approximate) p-value of the generalized likelihood ratio test with the help of Wilk’s Theorem. 2. From each of six batches of seed a random sample of 100 seeds was selected for sowing. The numbers of seeds that failed to germinate in the six samples of 100 seeds were 12, 20, 9, 17, 24, 16. Calculate the p-value for the Pearson chi-squared test of the hypothesis that the proportion of non-germinating seeds was the same for all batches....
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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 9 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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