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Sunday, July 14, 2013
Statistics, Statistics Project
Charlie’s Ski Sports, a chain of ski equipment shops in Vancouver, purchases skis from a manufacturer each fall
for the upcoming winter season. The most popular intermediate model costs $160 and sells for $240. Any skis
left over at the end of the winter are sold at a blow-out sale for $100. Sales over the years are quite stable.
Gathering data from all its stores, Charlie’s Ski Sports developed the following probability distribution for
demand:
Demand 150 175 200 225 250
Probability 0.05 0.2 0.35 0.3 0.1
Charlie also knows from experience that if their stores are stocked out of this ski (i.e., no more inventory) and
the customer wants it, Charlie will lose business on ski and other related snow equipment as customers will
shop at his competitors and tend not to return. He quantifies lost sales to be valued at $40.00 whenever
customer demand for this intermediate model ski exceeds his supply.
left over at the end of the winter are sold at a blow-out sale for $100. Sales over the years are quite stable.
Gathering data from all its stores, Charlie’s Ski Sports developed the following probability distribution for
demand:
Demand 150 175 200 225 250
Probability 0.05 0.2 0.35 0.3 0.1
Charlie also knows from experience that if their stores are stocked out of this ski (i.e., no more inventory) and
the customer wants it, Charlie will lose business on ski and other related snow equipment as customers will
shop at his competitors and tend not to return. He quantifies lost sales to be valued at $40.00 whenever
customer demand for this intermediate model ski exceeds his supply.
Help Charlie determine how many skis to order for the upcoming winter season by answering the questions
below. The manufacturer will take orders only for multiples of 20. Assume the demand/costing information
provided is accurate for the upcoming season.
a. Construct a payoff matrix.
b. What decision should be made according to the maximax decision rule?
c. What decision should be made according to the maximin decision rule?
d. What decision should be made according to the EMV decision rule?
e. What decision should be made according to the minimax regret decision rule?
f. What decision should be made according to the EOL decision rule?
g. How much should Charlie be willing to pay to obtain a forecast of customer demand that is 100%
accurate?
h. Which decision rule would you recommend Charlie use? Provide a clear explanation why you are
recommending a particular decision rule.CLICK HERE TO ORDER THIS ESSAY!!!!
below. The manufacturer will take orders only for multiples of 20. Assume the demand/costing information
provided is accurate for the upcoming season.
a. Construct a payoff matrix.
b. What decision should be made according to the maximax decision rule?
c. What decision should be made according to the maximin decision rule?
d. What decision should be made according to the EMV decision rule?
e. What decision should be made according to the minimax regret decision rule?
f. What decision should be made according to the EOL decision rule?
g. How much should Charlie be willing to pay to obtain a forecast of customer demand that is 100%
accurate?
h. Which decision rule would you recommend Charlie use? Provide a clear explanation why you are
recommending a particular decision rule.CLICK HERE TO ORDER THIS ESSAY!!!!
Page 2 of 5
*Note: For this question, the use of Excel is highly recommended (but not necessary) to create the appropriate
payoff matrix and solve the problem using the different criteria. Print outs from Excel are acceptable for this
question but make sure to demonstrate several example calculations of the cells in your payoff table. Please
make sure to have a concluding statement as shown in lecture or marks will be deducted. Do not include any
Excel formula printouts with your submission.
payoff matrix and solve the problem using the different criteria. Print outs from Excel are acceptable for this
question but make sure to demonstrate several example calculations of the cells in your payoff table. Please
make sure to have a concluding statement as shown in lecture or marks will be deducted. Do not include any
Excel formula printouts with your submission.
Question 2 – 15 Marks:
You and your friend have come up with an entrepreneurial idea that has great potential and you both are
trying to decide to invest in the project or not. Your initial investment for research and development (R&D) is
estimated to be $9000 total and there’s a 50-50 chance that it will be successful. If the results of the R&D
phase turn out to be successful, you will need a total of $20,000 to invest in the product’s development. If the
product goes through the development phase, uncertainty remains about the product’s demand on market and
thus uncertainty about the profit will be realized. You categorize the product demand as high, medium and
low with respective probabilities of 0.5, 0.3 and 0.2. Your best estimate of revenue projection under high
demand is $75000; at medium demand, revenue is projected at $55,000; and, at a low demand for the product,
revenue is projected at $21,000. Another option is that if the R&D phase is successful, you could sell the rights
of the product for an estimated $18,000 and not engage its development.
a) Develop the decision tree by hand and solve it according to the EMV decision criterion. State the
optimal decision according to the EMV decision criterion.
b) Create the decision tree using Treeplan.xla. Print it out and include it with your submission.
c) State the risk profile of the optimal decision according to the EMV criterion.
d) You and your friend would like to explore the sensitivity of your decision to the probability of the R&D
phase being successful or not. Create a sensitivity table (ie Data Table in Excel) showing how your
initial decision to invest $9000 might change (and its respective EMV) if the probability of a successful
R&D phase varies from 0% to 100% in steps 10%. Provide a clear statement of what the Data Table
means.CLICK HERE TO ORDER THIS ESSAY!!!!
You and your friend have come up with an entrepreneurial idea that has great potential and you both are
trying to decide to invest in the project or not. Your initial investment for research and development (R&D) is
estimated to be $9000 total and there’s a 50-50 chance that it will be successful. If the results of the R&D
phase turn out to be successful, you will need a total of $20,000 to invest in the product’s development. If the
product goes through the development phase, uncertainty remains about the product’s demand on market and
thus uncertainty about the profit will be realized. You categorize the product demand as high, medium and
low with respective probabilities of 0.5, 0.3 and 0.2. Your best estimate of revenue projection under high
demand is $75000; at medium demand, revenue is projected at $55,000; and, at a low demand for the product,
revenue is projected at $21,000. Another option is that if the R&D phase is successful, you could sell the rights
of the product for an estimated $18,000 and not engage its development.
a) Develop the decision tree by hand and solve it according to the EMV decision criterion. State the
optimal decision according to the EMV decision criterion.
b) Create the decision tree using Treeplan.xla. Print it out and include it with your submission.
c) State the risk profile of the optimal decision according to the EMV criterion.
d) You and your friend would like to explore the sensitivity of your decision to the probability of the R&D
phase being successful or not. Create a sensitivity table (ie Data Table in Excel) showing how your
initial decision to invest $9000 might change (and its respective EMV) if the probability of a successful
R&D phase varies from 0% to 100% in steps 10%. Provide a clear statement of what the Data Table
means.CLICK HERE TO ORDER THIS ESSAY!!!!
Question 3 – 20 Marks:
The City of Vancouver is considering whether or not to replace its fleet of gasoline-powered automobiles with
electric cars (true!!!). The manufacturer of electric cars claims that the city will experience significant cost
savings over the life of the fleet if it chooses to pursue the conversion. If the manufacturer is correct, the city
will save an estimated $1.2 million dollars. If the new technology within the electric cars is faulty, as some
critics suggest, the conversion to electric cars will cost the city $725,000. A third possibility is that less serious
problems will arise and the city will break even with the conversion. A consultant hired by the city estimates
the probabilities of these 3 outcomes are 0.40, 0.30 and 0.30 respectively. The city has an opportunity to
implement a pilot program that would indicate the potential cost or savings resulting from a switch to electric
cars. The pilot program involves renting a small number of electric cars for 3 months and running them under
typical conditions. The pilot program would cost the city $60,000. The city’s consultant believes that the
results of the pilot program would be significant but not conclusive; she provides the city with the following
compilation of probabilities based on her past experience consulting with other cities under the same
conditions. According to the consultant, the reliability for the pilot program in the past has been:
The City of Vancouver is considering whether or not to replace its fleet of gasoline-powered automobiles with
electric cars (true!!!). The manufacturer of electric cars claims that the city will experience significant cost
savings over the life of the fleet if it chooses to pursue the conversion. If the manufacturer is correct, the city
will save an estimated $1.2 million dollars. If the new technology within the electric cars is faulty, as some
critics suggest, the conversion to electric cars will cost the city $725,000. A third possibility is that less serious
problems will arise and the city will break even with the conversion. A consultant hired by the city estimates
the probabilities of these 3 outcomes are 0.40, 0.30 and 0.30 respectively. The city has an opportunity to
implement a pilot program that would indicate the potential cost or savings resulting from a switch to electric
cars. The pilot program involves renting a small number of electric cars for 3 months and running them under
typical conditions. The pilot program would cost the city $60,000. The city’s consultant believes that the
results of the pilot program would be significant but not conclusive; she provides the city with the following
compilation of probabilities based on her past experience consulting with other cities under the same
conditions. According to the consultant, the reliability for the pilot program in the past has been:
Actual City Outcomes of Electric Car Conversions
Savings Loss Breakeven
Pilot Predicted: Savings 0.601 0.10 0.40
Pilot Predicted: Loss 0.102 0.40 0.20
Pilot Predicted: Breakeven 0.30 0.50 0.40
1
For example, 0.60 in the table above represents the probability of the pilot predicting a savings, given that a conversion
to electric cars actually resulted in a savings of $1.2 million in other cities. 2Likewise, 0.10 represents the probability of
the pilot predicting a loss, given that a conversion to electric cars actually resulted in a savings of $1.2 million in other
cities. etc
Savings Loss Breakeven
Pilot Predicted: Savings 0.601 0.10 0.40
Pilot Predicted: Loss 0.102 0.40 0.20
Pilot Predicted: Breakeven 0.30 0.50 0.40
1
For example, 0.60 in the table above represents the probability of the pilot predicting a savings, given that a conversion
to electric cars actually resulted in a savings of $1.2 million in other cities. 2Likewise, 0.10 represents the probability of
the pilot predicting a loss, given that a conversion to electric cars actually resulted in a savings of $1.2 million in other
cities. etc
Page 3 of 5
a) Develop a decision tree for the City of Vancouver given the information above. Draw this decision tree by
hand and evaluate it using the EMV decision criterion. Provide a concluding statement with respect to the
optimal decision.
b) Use Treeplan.xla to evaluate the decision tree in part a). Print out your decision tree and include it with
your submission.
c) Would the optimal decision change if the pilot program only costs the city $35,000? If so, provide a
concluding statement with respect to the new optimal decision.
Instructions files attached:
hand and evaluate it using the EMV decision criterion. Provide a concluding statement with respect to the
optimal decision.
b) Use Treeplan.xla to evaluate the decision tree in part a). Print out your decision tree and include it with
your submission.
c) Would the optimal decision change if the pilot program only costs the city $35,000? If so, provide a
concluding statement with respect to the new optimal decision.
Instructions files attached:
Statistics
A Given a managerial problem and accompanying data set, construct graphs (following principles of ethical data presentation), calculate and interpret numerical summaries appropriate for the situation. Use the graphs and numerical summaries as aids in determining a course of action relative to the problem at hand.
B Given a managerial problem, utilize basic probability concepts, and standard probability distributions, e.g., binomial, normal, as is appropriate, to formulate a course of action which addresses the problem.
C Given a managerial problem and accompanying data set, for which application of a confidence interval is appropriate, construct an interval, assess its validity, and use the confidence interval in developing a course of action relative to a problem.
D Given a managerial problem and accompanying data set, for which the test of an hypothesis is appropriate, conduct an appropriate statistical test, assess the validity of the test, and use the test results to decide on a course of action relative to a problem.
E Given a managerial problem and accompanying data set, for which regression analysis—simple or multiple—is appropriate, fit a regression model to the data, determine the validity and utility of the model, and use the model, if appropriate, to determine a course of action intended to deal with a problem.
B Given a managerial problem, utilize basic probability concepts, and standard probability distributions, e.g., binomial, normal, as is appropriate, to formulate a course of action which addresses the problem.
C Given a managerial problem and accompanying data set, for which application of a confidence interval is appropriate, construct an interval, assess its validity, and use the confidence interval in developing a course of action relative to a problem.
D Given a managerial problem and accompanying data set, for which the test of an hypothesis is appropriate, conduct an appropriate statistical test, assess the validity of the test, and use the test results to decide on a course of action relative to a problem.
E Given a managerial problem and accompanying data set, for which regression analysis—simple or multiple—is appropriate, fit a regression model to the data, determine the validity and utility of the model, and use the model, if appropriate, to determine a course of action intended to deal with a problem.
Descriptive statistics and correlations:
1 describe the percentage of adolescents within Mental Health States (using a figure) and the relationships between variables.
2. A two way between groups Analysis of Variance: do scores on the PWB scale vary by gender at different ages?
3. Regression analysis: which of the PERMA measures best predict psychological well-being?
2. A two way between groups Analysis of Variance: do scores on the PWB scale vary by gender at different ages?
3. Regression analysis: which of the PERMA measures best predict psychological well-being?
Specific analyses required and research questions for the Level II practical 2013 are outlined below:
1. Descriptive statistics: describe the percentage of adolescents within Mental Health States (may use a figure).
2. Correlation analysis: is there a significant positive relationship between PWB and the measures of PERMA?
3. Paired Samples T-Test: are there sex differences in PWB and the PERMA measures?
The data file that will be used for the Level III and Level II psychology practicals will exclude data from the AHS. Data from all 10 scales will be used in subsequent analyses by the principal investigator. At this time, data from each collection point (2012 and 2013) will be combined and analysed using Structural Equation Modelling to determine relationships between variables.
2. Correlation analysis: is there a significant positive relationship between PWB and the measures of PERMA?
3. Paired Samples T-Test: are there sex differences in PWB and the PERMA measures?
The data file that will be used for the Level III and Level II psychology practicals will exclude data from the AHS. Data from all 10 scales will be used in subsequent analyses by the principal investigator. At this time, data from each collection point (2012 and 2013) will be combined and analysed using Structural Equation Modelling to determine relationships between variables.
Emerging trends – the use of technology for the benefit of society
Emerging trends – the use of technology for the benefit of society such as:- Bibliographic citation in the Harvard Referencing Style. ? Introduction ? Overview and scope of each text . ? A statement outlining the usefulness of each text in addressing the research topic. .. Having a similar paper …CLICK HERE TO ORDER THIS ESSAY!!!!
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