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Determine best degree program in terms of projected income
Course:- Applied Statistics
Reference No.:- EM13752619

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Problem 1

The director of career advising at Orange Community College wants to use decision analysis to provide information to help students decide which 2-year degree program they should pursue. The director has set up the following payoff table for six of the most popular and successful degree programs at OCC that shows the estimated 5-year gross income (\$) from each degree for four future economic conditions:

 Degree Program Economic Conditions Recession Average Good Robust Graphic Design 145,000 175,000 220,000 260,000 Nursing 150,000 180,000 205,000 215,000 Real Estate 115,000 165,000 220,000 320,000 Medical Tech 130,000 180,000 210,000 280,000 Culinary Tech 115,000 145,000 235,000 305,000 Computer IT 125,000 150,000 190,000 250,000 Probability 0.2 0.4 0.3 0.1

Determine the best degree program in terms of projected income, using the following decision criteria:

a. Maximax

b. Maximin

c. Equal likelihood

d. Hurwicz (alpha = .6)

e. Minimax regret

f.  EOL (expected opportunity loss)

g. The director of career advising at Orange Community College has paid a small fee to a local investment firm to indicate a probability for each future economic condition over the next 5 years, which is shown in the last row of the above table. Using expected value determine the best degree program in terms of projected income.

h. Determine the EVPI of this problem.

Problem 2

The Americo Oil Company is considering making a bid for a shale oil development contract to be awarded by the federal government. The company has decided to bid \$112 million. The company estimates that it has a 60% chance of winning the contract with this bid. If the firm wins the contract, it can choose one of three methods for getting the oil from the shale. It can develop a new method for oil extraction, use an existing (inefficient) process, or subcontract the processing to a number of smaller companies once the shale has been excavated. The results from these alternatives are as follows:

Develop new process:                                                               Use present process:

 Outcomes Probability Profit (\$1,000,000s) Great success .30 \$ 600 Moderate success .60 300 Failure .10 -100
 Outcomes Probability Profit (\$1,000,000s) Great success .50 \$ 300 Moderate success .30 200 Failure .20 -40

Subcontract:

 Outcome Probability Profit (\$1,000,000s) Moderate success 1.00 250

The cost of preparing the contract proposal is \$2 million. If the company does not make a bid, it will invest in an alternative venture with a guaranteed profit of \$30 million. Construct a sequential decision tree for this decision situation and determine whether the company should make a bid.

Problem 3

Consider the following data from a small bookstore.
Number of sales people working------Sales (in \$1000)
2---------------------10
3---------------------11
7---------------------13
9---------------------14
10---------------------18
10---------------------20
12---------------------20
15---------------------22
16---------------------22
20---------------------26
x = 10.4------------------y = 17.6
SD(x) = 5.64----------------SD(y) = 5.34

1. Calculate the mean and standard deviation of # of sales people (x) and sales (y). Find sample size n.

2. Calculate the correlation coefficient with all three methods (covariance method, z-score method, and correlation tool in Excel).

3. Find b0 and b1 for the linear regression model with all three methods (two different formulas and Solver). Interpret the meaning of b1 of this linear regression model.

4. Calculate Se and SST.

5. Calculate R square with both methods (correlation coefficient method and the formula r square = 1 - SSE/SST). Interpret the meaning of R square of this linear regression model.

6. Use Regression tool in Excel to find b0, b1, SSE, SST, r, R square, and Se.

7. Estimate the sales if the number of sales people working is 8, 13, and 19, respectively.

Problem 4

The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 12 months:

Month  Gasoline Demanded (gal.)

October               800

November          725

December           630

January                                500

February              645

March                   690

April                       730

May                       810

June                      1,200

July                        980

August                  1,000

September         850

1. Compute a 2-month moving average demand forecast for the months of December to September. Calculate MAD, MAPD and MSE.
2. Compute the optimal 2-month weighted moving average demand forecast for the months of December to September. Calculate MAD, MAPD and MSE.
3. Assume the demand forecast for October is equal to the actual demand of October, 800. Compute the optimal exponentially smoothed demand forecast for the months of November to September. Calculate MAD, MAPD and MSE.
4. Assume the demand forecast for October is 800 and trend for October is 0. Compute the optimal double exponentially smoothed demand forecast for the months of November to September. Calculate MAD, MAPD and MSE.
5. Compute linear trend line demand forecast for the months of October to September. Calculate MAD, MAPD and MSE.
6. Compare the five forecasting methods by using MAD, MAPD and MSE and indicate which method is the best fit for the data based on MAD, MAPD (or MAPE), and MSE, respectively.

Problem 5

Consider a project which consists of the following set of activities:

 Activity Days Required Immediate Predecessor Activities A 3 -- B 4 A C 4 A D 3 A E 3 D F 4 B G 6 B H 5 F, C, E I 6 G, H J 4 F, C, E K 2 D L 6 I, J, K
1. Draw the CPM network for this problem in Excel.
2. Calculate the earliest and latest start and finish times, and the slack for each activity.
3. Identify (Highlight) the critical path.
4. Create a Gantt chart for this project in Excel.

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