MathematicsHL 06 paper3

MathematicsHL 06 paper3 - IB DIPLOMA PROGRAMME PROGRAMME DU...

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IB DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI M06/5/MATHL/HP3/ENG/TZ0/XX MATHEMATICS HIGHER LEVEL PAPER 3 Monday 15 May 2006 (afternoon) INSTRUCTIONS TO CANDIDATES ± Do not open this examination paper until instructed to do so. ± Answer all the questions in one section only. ± Unless otherwise stated in the question, all numerical answers must be given exactly or correct to three signiFcant Fgures. 2206-7206 11 pages 1 hour 22067206 http://www.xtremepapers.net
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M06/5/MATHL/HP3/ENG/TZ0/XX 2206-7206 – 2 – Please start each question on a new page. Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. In particular, solutions found from a graphic display calculator should be supported by suitable working, e.g. if graphs are used to ±nd a solution, you should sketch these as part of your answer. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. You are therefore advised to show all working. SECTION A Statistics and probability 1. [Maximum mark: 8] A drug company claims that a new drug cures 75 % of patients suffering from a certain disease. However, a medical committee believes that less than 75 % are cured. To test the drug company’s claim, a trial is carried out in which 100 patients suffering from the disease are given the new drug. It is found that 68 of these patients are cured. (a) State suitable hypotheses. [2 marks] (b) Find the p -value of your test. [4 marks] (c) State your conclusion using a signi±cance level of (i) 10 % ; (ii) 1 % . [2 marks] 2. [Maximum mark: 12] A scienti±c expedition discovers a large colony of birds. The weights x kg of a random sample of 200 of these birds are measured and the following results obtained: x x x = = 224 4 5 823 2 ., () . (a) Calculate unbiased estimates of the mean µ and the variance σ 2 of the weights of these birds. [4 marks] (b) Find a 95 % con±dence interval for . [6 marks] (c) State, with a reason, whether or not your answer requires the assumption that the weights are normally distributed. [2 marks]
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M06/5/MATHL/HP3/ENG/TZ0/XX 2206-7206 – 3 – Turn over 3. [Maximum mark: 9]
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This note was uploaded on 08/15/2011 for the course MATH 141 taught by Professor Diestel during the Fall '08 term at South Carolina.

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MathematicsHL 06 paper3 - IB DIPLOMA PROGRAMME PROGRAMME DU...

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