final06 - ISMT111 Business Statistics Final Examination For...

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1 ISMT111 Business Statistics Final Examination For sections L3, L4, only 15 th December 2006 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] Data on the monthly service fee in dollars when a customer’s account falls below the minimum required $5000 balance for a sample of 26 banks yields a sample mean of 71.5 and a sample standard deviation of 30.55. (a) Please find a 95% confidence interval for the population mean monthly service fee. (b) Can we say that with probability 0.95 the interval obtained in (a) will include the population mean? If not, then what is the correct interpretation? Explain briefly . (c) Data on 10 more banks were added so that the sample size increased to 36 and we obtained a 95% confidence interval [59.55, 80.45]. What is the mean of the sample of 36? (d) Continue from (c). What is the standard error for the sample mean? (e) Assume that the estimated population standard deviation in (d) equals the true population s.d. What is the minimum sample size required so that the length of the 95% interval is less than 16? (f) Continue from (c). If there are four banks in the sample of 36 do not charge monthly service fee when the balance fall below $5000. Please find a 95% confidence interval for the proportion of banks that do not charge monthly service fee. Q
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final06 - ISMT111 Business Statistics Final Examination For...

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