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The following information refers to the next four questions: An insurance company wishes to examine the relationship between income (in $,000) and the amount of life insurance (in $,000) held by families. The company drew a simple random sample of families and obtained the following results: Family Income Amount of life insurance A 50 120 B 80 200 C 100 220 D 80 160 E 80 180 F 120 270 G 70 150 H 100 240 I 60 160 J 90 210 QUESTION 01 What is the least squares estimate of the slope? Answer should be to four decimal places e.g. 1.2345. Please do NOT include any units in your answer. QUESTION 02 What is the least squares estimate of the Y intercept? Answer should be to four decimal places e.g. 1.2345. Please do NOT include any units in your answer. QUESTION 03 What is the prediction for the amount of life insurance for a family whose income is $85,000? Answer should be to four decimal places and be consistent with your original data set, e.g. if your answer was $75,410.90, you would enter 75.4109 as your answer. Please do NOT include any units in your answer. QUESTION 04 What would be the residual (error) term for a family income of $90,000? Answer should be to four decimal places and be consistent with your original data set e.g. if your answer was $940.90, you would enter 0.9409. If your answer was $9,400.90, you would enter 9.4009 etc.. Please do NOT include any units in your answer. The next six questions refer to the following information: International Pictures is trying to decide how to distribute its new movie ?Claws?. ?Claws? is the story of an animal husbandry experiment at the University of Southern Queensland that goes astray, with tragic results. An effort to breed meatier chickens somehow produces an intelligent, 200 kilogram chicken that escapes from the lab and terrorises the campus. In a surprise ending the chicken is befriended by coach Tim Galvano, who teaches it how to play Rugby and help his team win State, National and World Championships. Because of the movie?s controversial nature, it has the potential to be either a smash hit, a modest success, or a total bomb. International is trying to decide whether to release the picture for general distribution initially or to start out with a ?limited first-run release? at a few selected theatres, followed by general distribution after 3 months. The company has estimated the following probabilities and conditional profits for ?Claws?: PROFITS (Millions of $) Level of success Probability Limited release General distribution Smash .3 22 12 Modest .4 9 8 Bomb .3 ?10 ?2 International can run sneak previews of ?Claws? to get a better idea of the movies? ultimate level of success. Preview audiences rate movies as either good or excellent. On the basis of past experiences, it was found that 90% of all smash successes were rated excellent (and 10% rated good), 75% of all modest successes were rated excellent (25% rated good) and 40% of all bombs were rated excellent (60% rated good). The cost of running sneak previews is not cheap. Currently, this stands at $1m. QUESTION 05 What is the opportunity loss for a Limited release for a Bomb level of success? Answer should be to whole numbers only. You do not need to put any units in your answer. QUESTION 06 What would the optimal action be for International before running the sneak preview? Run a limited release with an expected payoff of $7.20m Run a limited release with an expected payoff of $6.20m Run a general distribution with an expected payoff of $7.20m Run a general distribution with an expected payoff of $6.20m QUESTION 07 What is the maximum amount of money that International would be prepared to pay for an absolutely reliable forecast of the movies? level of success? $9.6m $7.2m $6.2m $2.4m QUESTION 08 What would be the joint probability for a ?bomb success? and good preview given that in the past, it was found that 60% of all bomb successes were rated good? Answer should be to two decimal places e.g. 0.12, 0.23, etc. Please do NOT include any units in your answer. QUESTION 09 What is the posterior probability of a smash success given the sneak preview indicates good? Answer should be to four decimal places e.g. 0.1234, 0.2345 etc. Please do NOT include any units in your answer. QUESTION 10 What is the maximum amount that should be paid for the sneak preview (i.e. what would be the expected value of sample information (EVSI))? Select the closest correct answer. Use four decimal places in your calculations but you can round off the final answer to 2 decimal places.) $1.04 million $2.58 million $7.2 million $8.24 million The next six questions refer to the following information: (All calculations should be to at least three decimal places) The tourist industry is subject to enormous seasonal variation. A hotel in North Queensland has recorded its occupancy rate for each quarter during the past 5 years. These data are shown in the accompanying table. Table 1: Occupancy rate Year 2004 2005 2006 2007 2008 Quarter 1 0.261 0.295 0.312 0.362 0.396 Quarter 2 0.302 0.324 0.345 0.388 0.418 Quarter 3 0.502 0.568 0.598 0.696 0.782 Quarter 4 0.568 0.615 0.698 0.738 0.802 QUESTION 11 What is the centred moving average that would correspond to Quarter 1 in 2006? Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc. Please do NOT include any units in your answer. QUESTION 12 What is the adjusted seasonal index for Quarter 1 __________%? Answer should be listed to three decimal places in the form 0.123 i.e. 0.123 represents 12.3%, 1.234 represents 123.4% etc. Please do NOT include the units (%) in your answer. QUESTION 13 The trend line for this decomposition model can be read off the partial regression printout (at 5 decimal places) to be Y = 0.36806 + 0.01195 T where T represents time. Analysing the partial regression printout, what is the coefficient of determination (R2) for this trend line? (Select the closest correct answer). 0.2973 (i.e. 29.73%) 0.5452 (i.e. 54.52%) 0.7165 (i.e. 71.65%) 0.9886 (i.e. 98.86%) QUESTION 14 What would be the forecast in Quarter 1, 2009 using the trend line given previously (recall that to three decimal places it was Y = 0.368 + 0.012 T) and the relevant adjusted seasonal index? Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc. Please do NOT include any units in your answer. QUESTION 15 If we exponentially smooth the data in Table 1 with a smoothing constant of 0.2, the smoothed value for Quarter 4 in 2004 would be? Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc. Please do NOT include any units in your answer. QUESTION 16 If we exponentially smooth the data in Table 1 with a smoothing constant of 0.2, the forecast for Quarter 1 2009 would be? Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc. Please do NOT include any units in your answer. The following information refers to the next question: A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is fifty (50) minutes with a standard deviation of forty (40) minutes (the very large standard deviation is due to a variety of factors including a large variation in skills amongst the ?Do it yourself? home handyman which is traditionally one of the companies customer base). Suppose a random sample of 64 purchasers of this table saw is taken. QUESTION 17 What is the probability that the sample mean will be less than 46 minutes __________? Answer should be to four decimal places which is consistent with the number of decimal places listed in your appendix tables e.g. 0.1234 etc. Please do NOT include any units in your answer. The following information refers to the next question: A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired length of the insulation is 12 metres. It is known that the standard deviation in the cutting length is 0.15 metres. A sample of 144 cut sheets yield a mean length of 12.14 metres. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. QUESTION 18 What are the two limits of the confidence interval __________ and __________? Answer should be to four decimal places e.g. 1.2345 and 2.3456. Please do NOT include any units in your answer. min = max = The following information refers to the next two questions: Refer to the following table which contains the sales (in $,000) for a department store for the first ten months of the year. Month Sales January 440 February 480 March 590 April 400 May 500 June 550 July 470 August 500 September 600 October 520 QUESTION 19 Using a three period moving average (i.e. MA(3)) as a forecasting method, what is the MSE for this forecasting model? Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc. Please do NOT include any units in your answer. QUESTION 20 Using simple exponential smoothing (with a smoothing constant of 0.2) as a forecasting method, what is the MAD for this forecast model? Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc. Please do NOT include any units in your answer. The following information refers to the next question: The ordered array below resulted from taking a sample of 25 batches of 500 computer chips and determining how many in each batch were defective. Defects 1 2 4 4 5 5 6 7 9 10 12 12 14 17 20 21 23 23 24 26 27 27 28 29 29 QUESTION 21 If a frequency distribution for the defects data is constructed, using ?0 but less than 5? as the first class, what would be the cumulative relative frequency of the ?10 but less than 15? class __________%? Answer should be a percentage value to whole numbers e.g. 12, 23, 34 etc. Please do NOT include units (%) in your answer.,Appreciate the feedback. Regards, Steve,I can't see any solution to questions 5 to 10. Are you able to offer any feedback on these? Regards, Steve

 

Paper#8316 | Written in 18-Jul-2015

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