Problem 1 LIFO TO FIFO:

Most inventories owned by Deere & Company and its United States equipment subsidiaries are valued at cost, on the “last-in, first-out” (LIFO) basis. Remaining inventories are generally valued at the lower of cost, on the “first-in, first-out” (FIFO) basis, or market. The value of gross inventories on the LIFO basis represented 58 percent and 60 percent of worldwide gross inventories at FIFO value on October 31, 2007 and 2006, respectively. If all inventories had been valued on a FIFO basis, estimated inventories by major classification at October 31 in millions of dollars would have been as follows:

2007   2006

Raw materials and supplies ...........................................                $ 882 $ 712

Work-in-process ...........................................................                      425    372

Finished machines and parts .........................................               2,263 2,013

Total FIFO value ........................................................                       3,570 3,097

Less adjustment to LIFO value .......................................               1,233    1,140

Inventories .................................................................                      $2,337 $1,957

Other Key information from Deere & Company

                                                     2007               2006      

Sales                                       $ 21,489.1       $ 19,884.0

COGS                                        16,252.8          15,362.0

Current Assets                          25,503.0          23,387.0

Current Liabilities                     15,738.1          12,787.5      

What adjustments to the financial statements (balance sheet and income statement) are necessary to convert from LIFO to FIFO for 2007: Assume 31% tax rate.

Epsilon Airlines services predominantly the eastern and southeastern united States. The vast majority of Epsilon’s customers make reservations through Epsilon’s website, but a small percentage of customers make reservations via phones. Epsilon employs call center personnel to handle these reservations and to deal with website reservation system problems and for the rebooking of flights for customers whose plans have changed or whose travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon’s management team. Having too many employees on hand is a waste of money, but having too few results in very poor customer service and the potential loss of customers.

Epsilon analysts have estimated the minimum number of call center employees needed by day of the week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are as follows:

The call center employees work for five consecutive days and then have two consecutive days off. An employee may start work on any day of the week. Each call center employee receives the same salary. Assume that the schedule cycles and ignore start up and stopping of the schedule.

Develop a model that will minimize the total number of call center employees needed to meet the minimum requirements.

The call center employees work for five consecutive days and then have two consecutive days off. An employee may start work on any day of the week. Each call center employee receives the same salary. Assume that the schedule cycles and ignore start up and stopping of the schedule.

Develop a model that will minimize the total number of call center employees needed to meet the minimum requirements.

Find the optimal solution.

Total Number of Employees =

Give the number of call center employees that exceed the minimum required.

Excess employees:

6. A company has 48 sales representatives, one for each state in the contiguous United States.

Each state is divided into four regions. Each state sales representative only reports the average sales from the state he or she covers each week. The average reported is calculated from one individual data point per region. Before the New National Sales Manager was hired, the average sales reported per state each week was $95,000 with a standard deviation of $12,000.

The National Sales Manager claims that under her leadership, sales have increased despite the weakening economy. A sample was taken when the manager’s annual review was being written and average sales were $105,100.

a) Based on an a=.02, can the National Sales Manager make her claim?

Use and show the 5-Step Process.

Use Z or t Values as demonstrated in class, not p-values

b) What is the cutoff point of sales that allows or would allow the National Sales Manager to make the claim?

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μμ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.810.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 500500 .

In answering the questions, use zz‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 495495 and 505505 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 3636 students. What is the standard deviation of the sampling distribution of their average score ¯xx¯ ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 495495 and 505505 ? (Enter your answer rounded to four decimal places.)

probability:

Your company, a manufacturer (primarily major kitchen appliances) based in the United States, has decided to pursue international expansion opportunities in sub-Saharan Africa. In order to achieve some economies of scale, your strategy is to minimize local adaptation. Focusing on a comparison of two sub-Saharan African countries of your choice, prepare an executive summary that features aspects of the product where stabilization will simply not be possible and adaptation to local conditions will be essential.

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score ? of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 510 . In answering the questions, use ? ‑scores rounded to two decimal places.

a) If you choose one student at random, what is the probability that the student's score is between 505 and 515 ?

b) You sample 36 students. What is the standard deviation of the sampling distribution of their average score ?¯ ?

Davis Stores sells clothing in 15 stores located around the southwestern United States. The managers at Davis are considering expanding by opening new stores and are interested in estimating costs in potential new locations. They believe that costs are driven in large part by store volume measured by revenue. The following data were collected from last year’s operations (revenues and costs in thousands of dollars):

Skill-biased Immigration.

(a) Let us consider the immigration dynamics between the United States and Mexico. The minimum wage of the U.S. is $7.25, while that of Mexico is $5.1 in U.S. dollars. Let the return to skills in Mexico be two times of that of the U.S., partly because the U.S. (Mexico) is relatively abundant (scarce) in the availability of skilled workers. In other words, if we plot skills x on the horizontal axis and hourly wage y on the vertical axis, the equations that characterize the return to skills of the two countries are:

yM X = 5.1 + 2x

yUS = 7.25 + x

In this exercise, plot the above equations on a Cartesian plane, clearing labelling your axis, equations, and intersection point. Is there positive or negative selection of immigrants from Mexico to the U.S.? Explain

(b) The northern region of Mexico that borders the U.S. has a higher minimal wage of $8.8 U.S. dollars. Assuming that the northern border area has more supply of skilled workers that lowers its return to skills to one-half of that of the U.S., such that:

y ′ M X = 8.8 + 0.5x

On a new graph, plot the return to skills for the northern border area of Mexico and the U.S. What can you say about the flow of immigrant workers?

(C) Assuming that the U.S. raises the minimum wage to $9, while the minimum wages for Mexico in general and its northern border area remain unchanged. Redo the above exercises and interpret your results

1. Unwanted calls (including illegal and spoofed robocalls) are the FCC's top consumer complaint. The United States is the 8^th most spammed country in the world, and the annoying calls are on the rise according to a new report. Suppose that a spammer is testing a scheme to get people to buy something over the phone and getting the “customer” to provide credit card information. He wants to test his scheme in the following way. He has hacked another company’s customer list containing all 200,000 of its customers’ phone numbers. He randomly calls 1,000 of these customers, and he is able to get 123 of the called customers to reveal their credit card information. (Use R)

1. Create a 90% confidence interval for the true proportion p for all 200,000 customers on his list who might reveal credit card information if in fact he decides to call all 200,000 of them. Be sure to check all necessary assumptions and conditions.
2. Explain what your interval means by explaining what “90% confidence” means in this context.
3. The scammer only wants to call all 200,000 people on the customer list if he thinks he will be able to convince at least 5% of them to reveal their credit card information. What does you confidence interval imply about this?
4. In the interval you constructed in a), the probability that the true population proportion p is actually in your specified interval is .90. True or False (and if false, why)?
5. Generally speaking, for two confidence intervals with the same level of confidence and with random samples from the same population, the interval with the larger sample size has a better chance of containing the population parameter being estimated. True of False (and if false, why)?

A study identified top accounting firms across the United States. The Southeast and Gulf Coast regions reported the highest combined growths. A characteristic description of the accounting firms in the Southeast and Gulf Coast regions included the number of partners in the firm. Below represents the number of partners within various firms of the two regions [Southeast and Gulf Coast].

Southeast     174          Gulf Coast     79
Southeast     45            Gulf Coast     106
Southeast     29            Gulf Coast     22
Southeast     51            Gulf Coast     22
Southeast     40            Gulf Coast     38
Southeast     10            Gulf Coast     17
Southeast     29            Gulf Coast     27
Southeast     37            Gulf Coast     21
Southeast     32            Gulf Coast     17
Southeast     22            Gulf Coast     12
Southeast     9              Gulf Coast     9
Southeast     30            Gulf Coast     6
Southeast     21            Gulf Coast     9
                                       Gulf Coast     12
                                       Gulf Coast     18

(a)At the 0.05 level of significance, is there evidence of a difference in the variability in numbers of partners for Southeast region accounting firms and Gulf Coast accounting firms? (Include: null and alternate hypotheses, value of test statistic, decision rule, conclusion in a complete sentence that includes why in terms of the decision rule.)

(b) Interpret the p-value.

(c) What assumption do you have to make about the two populations in order to justify the use of the F test?

(d) Based on (a) and (b), which t test [Pooled Variance t-test or Separate Variance t-Test] should you use to test whether there is a significant difference in the mean number of partners for Southeast region accounting firms and Gulf Coast accounting firms?