# Thread: mixed static problems help

1. ## mixed static problems help

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.