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# ec9 - The University of Hong Kong Department of Statistics...

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1 The University of Hong Kong Department of Statistics and Actuarial Science STAT0302 Business Statistics Semester 2 2009/2010 Example Class 9 Question 1. 40 similar machines, each using 16 components which perform the same function but wear independently of each other, were examined after 30 days of continuous running. The following numbers of worn components were recorded: 8 7 5 8 8 6 8 1 4 3 2 8 5 5 6 7 0 5 3 8 7 5 7 4 5 6 9 1 4 4 6 3 4 8 2 8 4 5 10 5 (a) Obtain an unbiased estimate of p , the probability that a component is worn after a period of 30 days. (b) Construct a 90% confidence interval for p . (c) How many more machines are required for a further similar experiment if the maximum estimation error, based on the combined information of the two experiments, is desired to be 2 percentage points, with 0.95 probability? 2. 200 Turnip seeds (120 of variety A and 80 of variety B ) were sown and kept under identical laboratory conditions for three weeks. At the end of this period it was found that 90 seeds of A and 54 seeds of B had germinated.

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