CASE: BROWN AND BECKER’S BUDGET

Brown and Becker is a consumer products manufacturer. The president has requested budgetary

input for the next fiscal year. The head of new product development must generate data for the

required funding. This will be done on a product-by-product basis, as if those items are already in

existence, already part of the company’s regular product mix.

One of the largest cost components for new products is direct manufacturing labor, used almost

exclusively in assembling products supplied by Asian vendors. Forecast levels of direct labor will

be based partly on the estimated productivity of existing products. For the electronics group, the

following specialized data have been obtained for sample production runs.

Units Direct labor Cost

5,240 $65,720

8,330 $79,249

1,125 $13,450

24,360 $261,420

8,550 $ 91,050

12,500 $105,200

5,550 $49,720

3,355 $42,060

15,610 $163,400

1,500 $17,400

The above data will be helpful in establishing the forecast cost of a new cellular modem.

The ultimate budgetary impact of the cellular modem will depend on the unit sales volume. The

demand for the product will remain uncertain until it is on the market, the price has been

established, and the marketing plan is in place. Several statistical samples will provide

management with information regarding these factors.

Questions for Discussion.

1. Discuss the advantages of using a point estimate to forecast the labor cost segment of the

budget for new product manufacturing. Why might management also require an interval

estimate?

2. Convert the sample direct labor cost data to direct labor cost per unit. Calculate the

sample mean and standard deviation of the cost per unit.

3. Construct a 95% confidence interval estimate of the mean direct labor cost per unit of all

the electronics group items.

4. Suppose that the unit direct labor cost of assembling cellular modems is estimated to be

double that of the sample products. What is the point estimate of this cost component?

5. The product demand will depend, to a great extent, on the proportion of the market

targeted to buy the product. Suppose that the modem will cost $100. A sample of

potential users is asked if they would buy one, and the data obtained will be used to

estimate the true proportion of would-be buyers.

(a) Using a guess of 0.10 for the population proportion, how large must the sample size

be for the sample proportion to fall within 0.02 of the population parameter with

probability 0.95?

(b) If you are unable to guess where the population proportion will fall, select a sample

size that guarantees achieving or exceeding the above specifications.

6. For a sample similar to the one above, the quantity of interest is the most a potential

customer would be willing to pay for a cellular modem. Management feels that almost

nobody would pay $500, but that nearly everybody would be willing to pay $20. The

sample size must be chosen to obtain sample responses. Assume the standard deviation is

$120.

(a) What sample size is necessary if the population mean maximum price is to be

estimated within plus of minus $10, with reliability 0.95?

(b) Suppose that the management can only afford a sample of n = 100, and that the

standard deviation is unchanged. What is the resulting reliability if the tolerable error

level remains at $10? What is the resulting tolerable error level if the reliability

probability 0.95 remains unchanged?

7. A sample of n = 100 is selected to estimate the proportion in Question 5. Four of the

sample persons said that they would buy a $100 cellular modem. Construct a 95%

confidence interval estimate of the true proportion of the market targeted to buy that

priced modem.

8. A sample of n = 15 persons is selected for estimating the mean maximum price of the

modem. The following results have been obtained.

$100 $50 $200 $700 $10 $300 $150 $250 $75 $150

$50 $350 $400 $250 $90

(a) Calculate the sample mean and standard deviation.

(b) Construct a 95% confidence interval estimate of the population mean maximum

price.

9. Discuss any further sample information that management might find useful in

establishing the budget for cellular modems.

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