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QUESTION 1 (25 MARKS The annual earnings of a company's salesmen at its Johannesburg and Capr Town offices are as follows: Number of salesmen in Earnings(R1000s) Johannesburg Cape Town 6.<8 3 2 8-<10 7 3 10-<12 13 6 12.<14 14--16 16-<20 20-<25 6 17 8 4 3 4 2 N 2 1.2.1. Approximate the sample mean of the annual earnings of a company's salesmen at its Johannesburg offices 1.2.2. Approximate the sample mean of the annual earnings of a company's salesmen at its Cape Town offices. 1.2.3. Approximate the sample variance of the annual earnings in Johannesburg offices. 1.2.4. Approximate the sample variance of the annual earnings in Cape town offices. 1.2.5. Compare the variability of the annual earnings in Johannesburg offices to the one of the annual earnings in Cape Town offices. 1.2.6. Approximate the semi-interquartile annual earnings in Johannesburg offices. 1.2.7. Approximate and interpret the sample median of the annual earnings in Johannesburg offices.
QUESTION 2 During bad economic times, industrial workers are dismissed and are often replaced by machines. The history of 100 workers whose loss of employment is attributable to technological advances is reviewed. For each of these individuals, it is determined if he or she was given an alternative job within the same company, found a job with another company in the same field, found a job in a new field, or has been unemployed for 1 year, In addition, the union status of each worker is recorded. The following table summarizes the results. Union Nonunion 40 15 Same company New company (same field) New field Unemployed 13 10 11 4 2 un 5 If the selected worker found a job with the same company or a new company in the same field, what is the probability that the worker is a union member? QUESTION 3 A printing company that specialises in the business stationary (i.e. letterheads, business cards, reports, invitations) has recorded its usage and cost of printer cartridges for its four different printers. The printer cartridges are classified as HQ21, HQ25, HQ26, and HQ32. 2008 2010 Cartridge Unit price Quantity used Unity price Quantity used 149 36 145 24 HQ21 HQ25 HQ26 172 37 160 44 236 12 262 14 HQ32 314 10 299 11
3.1 Use 2008 as the base period to compute and interpret the price relative for 2010 for HQ26. 3.2 Compute and interpret the quantity relative for HQ32 (use august 2008 as the base). 3.3 Construct a price index to reflect the overall change in cost of printer cartridges for the period 2000 -2010. Use the Laspeyres approach. Interpret your price index. 3.4 Construct a quantity index to reflect the overall change in quantities of printer cartridges used for the period 2008 - 2010. Use the Paasche approach. Interpret your index. 3.5 Calculate the unweighted aggregate price index for 2010 on 2008 as base year. Interpret your index QUESTION 4 Assume the following are quarterly sales recorded for the period 2008-2011 of Food Lovers shop (in millions of NS). Year Quarter Sales 2008 1 170 2 187 196 3 4 204 2009 153 1 2 3 195 162 144 4 2010 1 2 3 188 196 150 194 154 4 2011 1 2 190 3 159
4.1 Compute the 4-period centered moving average for the quarterly sales. 4.2 Compute the adjusted seasonal indexes for these quarterly occupancy rates. 4.3 De-seasonalise the first two quarterly sales and interpret the first de-seasonalised quarterly sale. 4.4 Use the method of least squares from regression analysis to determine the trend line of best fit. Use the zero-sum method for coding. Quarter 3 of vear 4.5 Using the trend line produced in 2.4, estimate the trend value of the time series for 2012 4,6 Find the seasonally adjusted trend estimate quarterly sale for Quarter 3 of year 2012