Statistics Assignment

August 31, 2017

Question
The attached assignment has the answers to the questions but I need to submit the excel file showing the work. Can you help me with that?

Name:

Directions:

· In this project you will be using the States Datafile that is found in Doc Sharing under the Instructor-Graded Projects:

· Steps for accessing the States Data file:

1. Open your Excel with PhStat2

2. Click File—Open

3. Select the States Data file

· Not all questions require the use of technology or the States Date file.

· You may insert your answers, including any charts, graphs, or output, on this document.

· Be sure to put your name on this document and save it to your computer.

1. Allen Machines specializes in developing weed-harvesting equipment that is used to clear small lakes of weeds. Allen Machines is contemplating the construction of a machine that would harvest weeds on narrow rivers and waterways. The activities and time in weeks necessary to build one of these experimental machines are shown in the table below.

Activity

Immediate Predecessors

Time in Weeks

A

none

6

B

none

5

C

A

3

D

A

2

E

B

4

F

B

6

G

C,E

10

H

D,F

7

1. What is the minimum possible time required for completing the project?

The minimum possible time to complete the project is 19 wks.

2. What is the latest possible time that Activity D may be started without delaying the completion of the project?

The latest possible time that Activity D may be started without delaying the completion of the project is 10 wks.

3. What is the latest finish time for Activity F?

The latest finish time for Activity F is 12 wks.

4. What is/are the critical path(s)?

The critical paths are A, B, C, E, G

2. The following is the activity and associated costs for the renovation of the local high school football stadium. The times are in weeks.

Activity

Immediate Predecessor

Time

Cost (\$)

A

4

25,000

B

5

30,000

C

A

3

15,000

D

B

8

50,000

E

B

2

12,000

F

C, D

3

15,000

G

C, D

7

46,000

H

E, F

2

20,000

1. What is the critical path for this project?

The critical path for this project is B, D, G

2. How much of the total budget would be spent in Week 8 (Period 8) with the earliest start budget?

\$100,750 would be spent in Week 8.

Week

Period

Cost

A

0-4

\$ 25,000

B

0-5

\$ 30,000

C

4-7

\$ 15,000

D

5-13

\$ 18,750

E

5-7

\$ 12,000

\$ 100,750

3. Precision Manufacturing has a government contract to produce stainless steel rods for use in military aircraft. Each rod is required to be 20 millimeters in diameter. Each hour, random samples of size n = 4 rods are measured to check process control. Five hours of observations yielded the following:

Diameter

Time

Rod 1

Rod 2

Rod 3

Rod 4

9 A.M.

19.8

20.4

19.9

20.3

10 A.M.

20.1

20.2

19.9

19.8

11 A.M.

19.9

20.5

20.3

20.1

Noon

19.7

19.8

20.3

20.2

1 P.M.

19.7

20.1

19.9

19.9

1. Construct the xbar-chart and the R-chart.

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2. Is the process in control?

X bar chart: UCL=20.512 and LCL=19.555

Since all the sample/means are between the control limits (19.555 and 20.512), the process is in control.

4. Modern Electronics specializes in manufacturing modern electronic components. It also builds the equipment that produces the components. Modern Electronics is considering building a new facility but the estimated profits would be impacted by the type of market that develops. The probability for a strong market is 0.3; for a fair market is 0.5; and for a poor market is 0.2. You are responsible for advising the president of Modern Electronics on the type facility that should be built or to not build a facility at all. The table shows the estimated profits under each market and for each size facility.

Estimated Profits

Strong Market

Fair Market

Poor Market

Build a large facility

550,000

110,000

-310,000

Build a medium-size facility

300,000

129,000

-100,000

Build a small facility

200,000

100,000

-32,000

Do not build a facility

0

0

0

1. Provide a recommendation to the president that maximizes profits

Large facility = (0.3)(550,000) + (0.5)(110,000) + (0.2)(-310,000) = 158,000

Medium facility = (0.3)(300,000) + (0.5)(129,000) + (0.2)(-100,000) = 134,500

Small facility = (0.3)(200,000) + (0.5)(100,000) + (0.2)(-32,000) = 103,600

No facility = 0

The largest expected profit corresponds with building a large facility.

2. Provide a second recommendation to the president that minimizes regret.

A second recommendation that minimizes the regret is the medium size facility because the estimated profit is the second highest and minimizes the regret.

5. Consulting income at Kaplan Associates for the period February – July is shown in the table below. Assume that the initial forecast for February is \$65,000. Use Exponential smoothing to forecast August’s income.

Month

Income (\$1,000)

February

70.0

March

68.5

April

64.8

May

71.7

June

71.3

July

72.8

1. Use a smoothing constant of ? = 0.2.

The exponential forecast for the month of August using alpha 0.2 is 70.33

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2. Use a smoothing constant of ? = 0.5.

The exponential forecast for the month of August using alpha 0.5 is 71.57

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3. Which forecasting constant is best in this situation?

Based on the MAD value alpha=0.2 is better than the alpha: 0.5 since MAD value for alpha= 0.2 is 2.89 which is less than the MAD value for alpha: 0.5 is 3.006.

6. Johnson Construction Company is in the process of installing power lines to a large housing development. The company wants to minimize the total length of wire used, which would minimize the company’s cost. The housing development is shown below. Each house has been numbered, and the distances between houses are given in hundreds of feet.

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1. What do you recommend to Johnson Construction Company?

Path 1-3-6-7-9-8 = 1+3+3+6+3 = 16

Path 1-4-5 =2+4 = 6

Path 1-2 = 4

Path 9-10-11-13 = 4+3+3 = 10

Path 9-12-14 = 5+4 = 9

Minimum length of wire required is the sum of all paths listed above:

16+6+4+10+9 = 45.

Length of wire required: 45*100 = 4500 Feet

7. The storm drains in the Cedar Rapids, Iowa, have been upgraded following the devastating floods of 2008. The network of storm drains and the capacities are shown below. Determine the maximum flow (in hundreds of gallons of water per minute) from node 1 to node 5. Remember that the arc has both capacity and reverse capacity.

From Node

To Node

Fluid Flow

1

2

250

2

1

100

1

3

100

3

1

150

1

4

400

4

1

400

1

5

150

5

1

200

2

4

300

4

2

200

3

4

250

4

3

300

3

5

300

5

3

250

4

5

300

5

4

0

Node 1 to node 3: (100,150), minimum value: 100

Node 1 to node 4: (400,400), minimum value: 400

Node 1 to node 5: (150,200), minimum value: 150

Node 2 to node 4: (300,200), minimum value: 200

Node 3 to node 4: (250,300), minimum value: 250

Node 3 to node 5: (300,250), minimum value: 250

Node 4 to node 5: (300, 0), minimum value: 0

The sum of all minimum for maximum value:

100+100+400+150+200+250+250+0 = 1250 gallons of water per minute.

8. From the States Data Set the following output for the Income in 2000 and for the Income in 2010 was created.

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1. Which variable has the greatest relative variation?

The coefficient of variation for income in 2000 is 914.6546 / 41773.5 = 0.0219

The coefficient of variation for income in 2010 is 1063.1547 / 50007.02 = 0.0213

The income in 2000 has the greatest relative variation.

9.You are a consultant working for Kaplan Consulting. The U.S. Department of Labor has requested assistance in evaluating the impact of economic stimulus on the unemployment rate. From the States Data Setthe following t test was conducted to answer the question:
“Has there been a significant reduction in the national unemployment rate between January and June?”

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1. What is the Null and the Alternative Hypotheses?

Null Hypotheses Ho: There has been significant reduction in the national unemployment rate between January and June.

Alternate Hypotheses Ha: No significant reduction in the national unemployment rate between January and June

2. What is your level of alpha (?)?

Alpha = 1%

t-stat > t Critical & p value

1. What would be the predicted median household income if the percentage of the population in the state were 50% or 50?

Predicted income Y = 1267.425919*Bachelors + 16034.93568

Predicted income = 1267.425919*50 + 16034.93568 = \$79,406.

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