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Unformatted text preview: THE UNIVERSITY OF HONG KONG 07/08 DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT0301 Elementary Statistical Methods Assignment 5 (Do ALL. Hand in solutions to the FOUR starred questions on or before 30.11.07.) 1. The Autical Corporation, a producer of botical gears, had the following sales volumes ($m) reported quarterly: Quarter Sales, ( Y ) Quarter Sales, ( Y ) 2003 Q.1 9.8 2005 Q.1 14.5 Q.2 15.3 Q.2 22.3 Q.3 13.5 Q.3 18.5 Q.4 10.4 Q.4 13.4 2004 Q.1 12.7 2006 Q.1 15.5 Q.2 19.6 Q.2 24.9 Q.3 15.4 Q.3 19.6 Q.4 13.2 Q.4 14.1 (a) Find the four seasonal factors. (b) Fit a straight line trend to the (deseasonalized) data. (c) Predict the sales volumes for the four quarters of 2007. *2. The table below shows the numbers of issues sold (in 1000) of a bimonthly magazine over a threeyear period: Year Jan Mar May Jul Sep Nov 2004 5.5 6.8 8.0 7.4 5.9 6.0 2005 6.2 7.5 8.2 8.5 6.8 8.0 2006 8.0 9.2 10.3 9.4 7.6 8.7 (a) Find the bimonthly seasonal indexes. (b) Determine a trend line T = a + bx , taking January, 2004 as x = 1. (c) Forecast the sales of the coming six issues in 2007. 3. A company reports its profits (in $m) three times a year, each profit covering a term of four months. Past figures are as follows: 2003 2004 2005 2006 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 9.6 14.4 12.0 11.4 16.8 13.8 12.6 18.6 15.9 14.1 20.7 17.4 1 (a) Find the seasonal factors for the three terms. (b) Fit a trend line T = a + bx to the data, taking the first term of 2003 as x = 1. (c) Estimate the profits of the three terms of 2007, based on a multiplicative model without the (longterm) cyclic component. 4. A manufacturer has produced a large batch of fanbelts. From past experience he knows that his machine capability is σ = 0.7 cm which represents the standard devi ation of fanbelt lengths in any large batch produced. To estimate the mean length ( μ cm) of the batch, the manufacturer randomly selected 20 items and obtained these measurements (in cm): 52.5, 53.0, 52.3, 52.4, 52.7, 51.7, 52.1, 52.8, 53.1, 54.0, 52.9, 52.3, 51.6, 52.7, 52.6, 53.0, 52.3, 52.1, 51.7, 53.0....
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 Spring '07
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