Statistics: Practice Problems Solutions

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1. (24 points)

If needed, additional workspace is provided on the next sheet.

Doug Moodie is the president of Garden Products Limited. Over the last 5 years, his vice president of marketing has been providing the sales forecast using his special “focus” forecasting technique. The actual sales for the past ten years and the forecasts from the vice president of marketing are given below.

|Year |Sales |VP/Marketing Forecast | |1 |170,300 |-- | |2 |168,250 |-- | |3 |165,700 |-- | |4 |169,000 |-- | |5 |168,000 |-- | |6 |167,300 |170,000 | |7 |175,250 |170,000 | |8 |172,500 |180,000 | |9 |156,700 |180,000 | |10 |176,300 |160,000 |

Doug wonders if perhaps a weighted moving average or an exponential smoothing approach to forecasting might be better than having the vice president of marketing prepare the forecast. Doug wants to evaluate a two-period weighted moving average with weights of 0.7 and 0.3 for the most recent and next most recent periods. He also wants to evaluate the exponential smoothing with an α = 0.3 and a starting forecast for period 6 of 168,000 units.

a) Which of the three methods (weighted moving average, exponential smoothing and VP/Marketing) provides the best forecasting method if you were to evaluate these methods for their forecasting accuracy for Years 8 through 10. Use one of the evaluation methods we have discussed.

See next page

b) In part a) we identified which is the best method of those three methods. However, would you recommend using this method for forecasting sales for Year 11? Why or Why not?

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c) What would be the forecast for Year 11 using both the weighted moving average and the exponential smoothing methods?

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2. (23 points)

Lake Charles Seafood makes 500 wooden packing boxes for fresh seafood per day, working in two 10-hour shifts. The marketing department has advised that demand has increased so that 650 wooden boxes for fresh seafood are required daily. Due to higher demand, plant managers are considering operating three 8-hour shifts instead. Productivity is measured in terms of boxes produced per hour worked.

a) Calculate the productivity of the operation for the two-shift operation producing 500 boxes.

500/20 = 25 boxes per hour

b) Calculate the productivity of the operation for the three-shift operation producing 650 boxes.

650/24 = 27.08

c) Using the two-shift operation as the base, calculate the percentage difference between the two-shift operation and the three-shift operation as described in parts a) and b).

(27.08-25)25 = 1.083 or an increase...
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