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Math Help - mixed static problems help

  1. #1
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    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.

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  2. #2
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    Please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. It is better for forum organization and better for you to get your questions answered in a more timely manner if you start new threads as necessary for remaining questions. eg. If you have five questions, post two of them in two threads and start a new thread for the remaining one etc.

    And if the question has more than two parts to it, it is best to post only that question and its parts in the thread and start a new thread for other questions.

    Furthermore, this looks like an assignment that might count towards a final grade. MHF policy is to not knowingly help with such questions.
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