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final07

# final07 - ISMT111 Business Statistics Final Examination For...

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1 ISMT111 Business Statistics Final Examination For sections L5, L6, only 12 December 2007 Directions 1) Answer ALL SIX questions. Marks are shown in square brackets. 2) There are 4 pages in this examination paper including the cover page. Check to make sure you have a complete set and notify the invigilator immediately if part of it is missing. 3) Key formulas and Statistical tables are provided separately. 4) Calculator may be used in this examination. 5) You are given THREE HOURS to complete this examination. Do not begin until you are told to do so.

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2 Question 1: [18 Marks] A broker, John, on the Hong Kong Stock Exchange is curious about the amount of time between the placement and execution of a market order. He sampled 45 orders and found that the mean time was 24.3 minutes with a standard deviation of 3.2 minutes. (a) Please calculate a 95% confidence interval for the expected time between placement and execution of market orders. (b) If John wants to have a 95% confidence interval no more than one minute long, what is the minimum sample size? (c) John noted that 3 out of 45 orders took more than 30 minutes to execute. Please find a 95% confidence interval for the proportion of orders taking more than 30 minutes to execute. Hint: If it is necessary to make adjustment on the interval, please do so. (d) John thought it is very unlikely that the population proportion will exceed the upper confidence limit found in (c). He used this information to determine the minimum sample size for estimating the proportion within 5% at confidence level 95%. What is the sample size he should adopt? (e) If the sample size is 25 instead of 45 in part (a), please recalculate the 95% confidence interval.
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final07 - ISMT111 Business Statistics Final Examination For...

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