files.transtutors.com … · Web viewDirections: The following software may be used: Excel->Data Analysis. Excel QM. PhStat. Please make sure to insert your answers, including any

Directions: The following software may be used:

o Excel->Data Analysiso Excel QMo PhStat

Please make sure to insert your answers, including any charts, graphs, or output, on this document. You may be required to also upload original files from Excel.

The calculations are not your final answer. A summary/explanation in your own word for each question posed should be included.

Questions 1,3,6,7 and 11 require the use of the Salary Data File. The Salary Data file is located in Doc Sharing->Instructor Graded Projects.

For each the following variables from the Salary Data Set provide the measures of location and measures of dispersion for the following variables:

1. Current Salary

Answer:.

Explanation (include any calculations or software output):

2. Beginning SalaryAnswer:.


3. Which variable has the greatest relative variability?

Answer:


1

You are the manager of a high-end ladies fashion store. For the past few months you have been gathering data and found that 35% of persons entering the store actually make a purchase. Assume these data follow a Binomial Distribution and use Excel to calculate the following binomial probabilities:

1. If 15 people enter the store, what is the probability that exactly 7 of them will make a purchase?

Answer:


2. What is the probability that more than 7 of the 15 people will make a purchase?

Answer:.


2

. Using the Salary Data Set what is the probability of randomly selecting one individual (male or female) with a current annual salary of over $50,000?

Answer:


. The time required to complete a project is normally distributed with a mean of 79 weeks and a standard deviation of 2 weeks. The construction company must pay a penalty if the project is not finished by the due date of the contract. If a construction company bidding on this contract wishes to be 95 percent sure of finishing by the due date, use the NORMINV Excel Function to determine what due date (project week #) should be negotiated?

Answer:


3

. In a state lottery participants select 6 numbers between 1 and 99. At the end of the week, the state lottery commission randomly draws 6 numbers between 1 and 99. How many different possible winning number combinations could be drawn by the lottery commission?

Answer:


. From the Salary Data Set and assuming that the salary data is a random sample from the population of salaries from the multi-national company use the 95% confidence level in PHStat to estimate the mean current salary for company executives.

1. The 95% confidence level interval is:

Answer:


2. If you were to change the confidence level to 99%, what would happen to the confidence interval? What is the 99% confidence interval?

Answer:.


4

Using the Salary Data Set,

1. Create a scatter plot to show this relationship between education and current salary

2. Determine the correlation coefficient between the variables. What does this tell us about the relationship?

Answer:.


5

8. Explain why rejecting the null hypothesis does not make the alternative hypothesis true.

Answer in your words:

9. What is the purpose of statistical inference?


10. What is the difference between sampling error and the standard error of the mean?


6

. You are a consultant working for a Consulting Company. The Director of Human Resources for a multi-national company has requested help in investigating a pay discrimination complaint brought by a female executive. The company provided the data in the Salary Data Set. Use PHStat and the appropriate t test, to investigate the claim of pay discrimination in the Beginning Salary.

“Is there a significant difference between the average female and average male salaries?”

1. What is the Null and the Alternative Hypotheses?Ho:

Ha:

2. What is your level of alpha (α)?Answer:

Why did you choose this level? Please explain in terms of Type I or Type II errors.

3. What is the output from your analysis?Software output or calculations:

4. What is your decision about the hypothesis based on the software output?Answer in your words:

5. Is there a significant difference between the average female and average male salaries? Please write a written statement to the director of Human Resources as to whether they should be concerned about the complaint.


Even though independent gasoline stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gas station. Susan’s problem is to

7

decide how large her station should be. The annual returns will depend on both the size of the station and a number of marketing factors related to oil industry and demand for gasoline. After careful analysis, Susan developed the following table:

Size of Gasoline Station Good Market ($) Fair Market ($) Poor Market ($)Small $1500 $750 -$500Medium $3500 $1500 -$1000Large $7500 $4500 -$20,000

You may use Excel QM or QM for Windows:

1. What is the Maximax decision?Answer:

Explanation (include software output or calculation):

2. What is the Maximin decision?Answer:


3. What is the criterion of realism decision? Use α = 0.4.Answer: Explanation (include software output or calculation):

4. Develop an Opportunity Loss Table.Table:

5. What is the Minimax Regret Decision?

Answer:


8

Data collected on the yearly demand for 50-pound bags of fertilizer at Sunshine Garden Supply are shown in the following table.

Year Demand for Fertilizer (1,000s of Bags)

1 152 133 124 105 96 97 128 149 10

10 1511 12

You may use Excel QM to:

1. Develop a three-year moving average to forecast sales in year 12. Answer:


2. Develop a three-year weighted average to predict demand in year 12, in which sales in the most recent year is given a weight of 4, the second most recent year is weighted 2 and sales in the third most recent year has a weight of 1.

Answer:


3. Develop a regression/trend line to estimate the demand for fertilizer in year 12. Answer:


4. Analysis of the forecasting errors indicates which forecasting method (moving average, weighted moving average or regression) is best in this situation?

Answer:

Explanation:

9

The College has decided to "wire" its campus. The first stage in this effort is to install the "backbone," i.e., to connect all the buildings. The table below gives the distances between the various buildings on campus in hundreds of feet.

You may use QM for Windows or complete it by hand:

Distances in Hundreds of FeetFrom To

Building 1 Building 2 Building 3 Building 4 Building 5 Building 6Building 1 25 22 10 12 15Building 2 18 12 9 16Building 3 12 23 24Building 4 20 27Building 5 19Building 6

1. How should the buildings be connected to minimize the total length of cable?

Answer:

Explanation (including any calculations or software output):

2. What length of cable is required?

10

4. The following represents the distances in miles from a warehouse (node 1) to various cities in Montana. The major outlet store is located at node 7.

From Node To Node Distance1 2 5001 4 2502 3 2002 4 1203 4 503 5 753 6 3504 5 5004 7 2005 6 2455 7 3756 7 400


1. Find the shortest route and distance from Node 1 to Node 7.

Answer:


11

The network of a city sewer system and their capacities are shown below. Remember that the arc has both capacity and reverse capacity. For example, row 1 is the flow from node 1 to node 2 and row 2 is the reverse flow from node 2 to node 1. There are seven branches in this network.

From Node

To Node Fluid Flow

1 2 502 1 201 3 753 1 1001 4 1254 1 751 5 255 1 152 4 504 2 753 4 1004 3 453 5 355 3 25


1. Determine the maximum flow (in hundreds of gallons of water per minute) from node 1 to node 5.

Answer:


12

The governor of Michigan believes that the state can improve the state’s poverty rate if the state can reduce the college debt carried by its citizens and if they can reduce the percent of the population not covered by health insurance. (This requires you to use the States Dataset file that is included in Doc Sharing->Instructor Graded Projects.)

1. Using the States Data Set and Excel DataAnalysis (Regression), create the multiple regression prediction equation of the form Ŷ = 0 + 1(X1) + 2(X2)

Answer:


2. Predict the poverty rate for Michigan if the college debt was $30,000 and the percent not covered by insurance was 10% or 10?

Answer:


13

A concessionaire for the local ballpark has developed a table of conditional values for the various alternatives (stocking decisions) and states of nature (size of crowd).

Stocking Decision Large Crowd ($) Average Crowd ($) Small Crowd ($)Large Inventory $15,000 $12,000 -$1,000Average Inventory $12,500 $25,000 $7,500Small Inventory $4,000 $3,000 $2,500

You may use Excel QM or QM for Windows:

If the probabilities associated with the states of nature are 0.20 for a large crowd, 0.25 for an average crowd, and 0.55 for a small crowd, determine:

1. The alternative that provides the greatest expected monetary value (EMV).

Answer:


2. The expected value of perfect information (EVPI).

Answer:


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 WeeksA none 4B A 3C B 2D A 4E A 2F E 2G B, C 2H D,F 1

14

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

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

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

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

Explanation: (Please include Gantt Chart and/or Network Graph):

15

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

Explanation: You can enter the above information into QM for Windows->Project Management->Cost Budgeting.

Activity Immediate Predecessor Time Cost ($)A - 8 20,000B - 4 12,000C A 6 15,000D B 2 15,000E B 3 10,000F C, D 7 50,000G C, D 5 35,000H E, F 1 1,000

1. What is the critical path and total time required for this project? Answer:

Explanation: (include Gantt Chart and/or Network Graph):

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

Answer:

Explanation (include cost budgeting table):

16

Precision Manufacturing has a government contract to produce stainless steel rods for use in military aircrafts. Each rod is required to be 35 millimeters in diameter. Each hour, random samples of size n = 5 rods are measured to check process control. Four hours of observations yielded the following:

Explanation: You are looking at the control limits for the variable, average diameter. You can use Excel QM or QM for Windows->Quality Control->x-bar and r-charts.

DiameterTime Rod 1 Rod 2 Rod 3 Rod 4 Rod 5

9 A.M. 34.5 34.9 37.9 36 35.910 A.M. 35.1 34.7 33 35.4 34.911 A.M. 38.9 35 37.9 38.3 36.5Noon 25 35.2 32.1 38.1 35

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

Please include charts below:

2. Is the process in control?

xbar chart UCL = R-chart UCL =

xbar chart LCL = R-chart LCL =

Explanation:

17

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 0.3; and for a poor market is 0.4. 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.

Explanation: You can use QM for Windows->Decision Analysis->Decision Table with the above information.

Estimated ProfitsStrong Market Fair Market Poor Market

Build a large facility 30,000 25,000 -20,000

Build a medium-size facility 27,500 25,000 -10,000

Build a small facility 15,000 12,500 -1000

Do not build a facility 0 0 0

1. What is your recommendation to the president based on expected value that maximizes profits (EMV).

Answer:

Explanation (include expected monetary value):

Software Output:

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


Software Output:

18

Consulting income at Consulting Associates for the period February – July is shown in the table below. Assume that the initial forecast for February is $90,000. Use Exponential smoothing to forecast August’s income.

Explanation: You can use Excel QM—Forecasting—Exponential with the above information.

Month Income ($1,000)February 90.0March 88.5April 74.8May 91.7June 91.3July 92.8

1. Use a smoothing constant of α = 0.1.

Answer:

Explanation (include software output):


Answer:


3. Analysis of the forecasting errors indicates which forecasting constant is best in this situation?

Answer:

Explanation:

19

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.

Explanation: We want to create the minimum spanning tree (MST) for this network since all houses need to be connected. You can use QM for Windows to do this.

1. What do you recommend to Johnson Construction Company?

Answer:

Explanation (including software output):

20

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.

Explanation: You can use QM for Windows—Networks—Maximal Flow with the above information.

From Node

To Node Fluid Flow

1 2 1252 1 1001 3 2503 1 1001 4 2504 1 4501 5 2005 1 752 4 1004 2 3003 4 1504 3 2503 5 1905 3 4004 5 505 4 100

Answer:


21

From the States Data Set the following output for College and for the Bachelors was created.

Mean 62.264 Mean 26.804Standard Error 1.033743978 Standard Error 0.672727983

Median 62.8 Median 25.5Mode 65.4 Mode 25.5

Standard Deviation 7.309673769 Standard Deviation 4.756905185Sample Variance 53.43133061 Sample Variance 22.62814694

Kurtosis -0.098148498 Kurtosis -0.151637421Skewness -0.396540362 Skewness 0.333725213

Range 31.7 Range 21.4Minimum 45.7 Minimum 15.3Maximum 77.4 Maximum 36.7

Sum 3113.2 Sum 1340.2Count 50 Count 50

College Bachelors

1. Which variable has the greatest relative variation?

Answer:

Explanation (including calculations):

22

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

Output from PhStat2: Output from Excel-DataAnalysis:

Paired t Test

Hypothesized Mean Diff. 0Level of significance 0.05

Sample Size 50DBar 0.1140degrees of freedom 49S D 0.2507Standard Error 0.0355t Test Statistic 3.2151

Lower Critical Value -2.0096Upper Critical Value 2.0096p -Value 0.0023

Data

Intermediate Calculations

Two-Tail Test

t-Test: Paired Two Sample for Means

Jan Unemp Mar UnempMean 7.05 6.936Variance 2.709081633 2.641942857Observations 50 50Pearson Correlation 0.988330285Hypothesized Mean Difference 0df 49t Stat 3.215129241P(T<=t) one-tail 0.001154822t Critical one-tail 1.676550893P(T<=t) two-tail 0.002309644t Critical two-tail 2.009575237

6. What is the Null and the Alternative Hypotheses?Ho: Ha:

7. What is your level of alpha (α)?

8. What is your decision about the hypothesis based on the software output?

9. Has there been a significant reduction in the national unemployment rate between January and February?

23

The Governor of a southern state has asked the Consulting Company to determine if the state were able to increase the percentage of its population with a Bachelor’s Degree to 45%, what might be the expected median household income based on 2000 data? Here is the output from the Regression procedure from Excel.

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.718033536R Square 0.515572158Adjusted R Square 0.505479912Standard Error 4548.142979Observations 50

Coefficients Standard Error t Stat P-valueIntercept 15606.01508 3717.168291 4.198361188 0.000115689Bachelors 976.2529817 136.5876943 7.147444626 4.37107E-09

1. What would be the predicted median household income if the percentage of the population in the state were 45% or 45?

Answer:

Explanation (include all calculations):

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 WeeksA none 4B A 3C B 2D A 4E A 2F E 2G B, C 2H D,F 1

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

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

24

7. What is the latest finish time for Activity H?

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

Explanation: (Please include Gantt Chart and/or Network Graph):

25

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

Explanation: You can enter the above information into QM for Windows->Project Management->Cost Budgeting.

Activity Immediate Predecessor Time Cost ($)A - 8 20,000B - 4 12,000C A 6 15,000D B 2 15,000E B 3 10,000F C, D 7 50,000G C, D 5 35,000H E, F 1 1,000

3. What is the critical path and total time required for this project? Answer:

Explanation: (include Gantt Chart and/or Network Graph):

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

Answer:

Explanation (include cost budgeting table):

26

Precision Manufacturing has a government contract to produce stainless steel rods for use in military aircrafts. Each rod is required to be 35 millimeters in diameter. Each hour, random samples of size n = 5 rods are measured to check process control. Four hours of observations yielded the following:

Explanation: You are looking at the control limits for the variable, average diameter. You can use Excel QM or QM for Windows->Quality Control->x-bar and r-charts.

DiameterTime Rod 1 Rod 2 Rod 3 Rod 4 Rod 5

9 A.M. 34.5 34.9 37.9 36 35.910 A.M. 35.1 34.7 33 35.4 34.911 A.M. 38.9 35 37.9 38.3 36.5Noon 25 35.2 32.1 38.1 35

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

Please include charts below:

4. Is the process in control?

xbar chart UCL = R-chart UCL =

xbar chart LCL = R-chart LCL =

Explanation:

27

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 0.3; and for a poor market is 0.4. 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.

Explanation: You can use QM for Windows->Decision Analysis->Decision Table with the above information.

Estimated ProfitsStrong Market Fair Market Poor Market

Build a large facility 30,000 25,000 -20,000

Build a medium-size facility 27,500 25,000 -10,000

Build a small facility 15,000 12,500 -1000

Do not build a facility 0 0 0

3. What is your recommendation to the president based on expected value that maximizes profits (EMV).

Answer:


Software Output:

4. Provide a second recommendation to the president that minimizes regret. Answer:


Software Output:

28

Consulting income at the Consulting Organization for the period February – July is shown in the table below. Assume that the initial forecast for February is $90,000. Use Exponential smoothing to forecast August’s income.

Explanation: You can use Excel QM—Forecasting—Exponential with the above information.

Month Income ($1,000)February 90.0March 88.5April 74.8May 91.7June 91.3July 92.8


Answer:



Answer:


6. Analysis of the forecasting errors indicates which forecasting constant is best in this situation?

Answer:

Explanation:

29

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.

Explanation: We want to create the minimum spanning tree (MST) for this network since all houses need to be connected. You can use QM for Windows to do this.

2. What do you recommend to Johnson Construction Company?

Answer:

Explanation (including software output):

. 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.

Explanation: You can use QM for Windows—Networks—Maximal Flow with the above information.

From Node

To Node Fluid Flow

1 2 1252 1 1001 3 250

30

3 1 1001 4 2504 1 4501 5 2005 1 752 4 1004 2 3003 4 1504 3 2503 5 1905 3 4004 5 505 4 100

Answer:


From the States Data Set the following output for College and for the Bachelors was created.

Mean 62.264 Mean 26.804Standard Error 1.033743978 Standard Error 0.672727983

Median 62.8 Median 25.5Mode 65.4 Mode 25.5

Standard Deviation 7.309673769 Standard Deviation 4.756905185Sample Variance 53.43133061 Sample Variance 22.62814694

Kurtosis -0.098148498 Kurtosis -0.151637421Skewness -0.396540362 Skewness 0.333725213

Range 31.7 Range 21.4Minimum 45.7 Minimum 15.3Maximum 77.4 Maximum 36.7

Sum 3113.2 Sum 1340.2Count 50 Count 50

College Bachelors

2. Which variable has the greatest relative variation?

Answer:

31

Explanation (including calculations):

32

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

Output from PhStat2: Output from Excel-DataAnalysis:

Paired t Test

Hypothesized Mean Diff. 0Level of significance 0.05

Sample Size 50DBar 0.1140degrees of freedom 49S D 0.2507Standard Error 0.0355t Test Statistic 3.2151

Lower Critical Value -2.0096Upper Critical Value 2.0096p -Value 0.0023

Data

Intermediate Calculations

Two-Tail Test

t-Test: Paired Two Sample for Means

Jan Unemp Mar UnempMean 7.05 6.936Variance 2.709081633 2.641942857Observations 50 50Pearson Correlation 0.988330285Hypothesized Mean Difference 0df 49t Stat 3.215129241P(T<=t) one-tail 0.001154822t Critical one-tail 1.676550893P(T<=t) two-tail 0.002309644t Critical two-tail 2.009575237

10. What is the Null and the Alternative Hypotheses?Ho: Ha:

11. What is your level of alpha (α)?

12. What is your decision about the hypothesis based on the software output?

13. Has there been a significant reduction in the national unemployment rate between January and February?

33

The Governor of a southern state has asked Consulting to determine if the state were able to increase the percentage of its population with a Bachelor’s Degree to 45%, what might be the expected median household income based on 2000 data? Here is the output from the Regression procedure from Excel.

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.718033536R Square 0.515572158Adjusted R Square 0.505479912Standard Error 4548.142979Observations 50

Coefficients Standard Error t Stat P-valueIntercept 15606.01508 3717.168291 4.198361188 0.000115689Bachelors 976.2529817 136.5876943 7.147444626 4.37107E-09

2. What would be the predicted median household income if the percentage of the population in the state were 45% or 45?

Answer:

Explanation (include all calculations):

34

Documents

files.transtutors.com … · Web viewDirections: The following software may be used: Excel->Data Analysis. Excel QM. PhStat. Please make sure to insert your answers, including any