Statistics
Assessment item 3
Assignment 3
Value: 20%
Due date: 20-Sep-2016
Return date: 17-Oct-2016
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Alternative submission method
Task
QUESTION 1 Decision Analysis
Show all calculations to support your answers. You may follow the methods shown in the mp4 on Decision Analysis for a way to do part (b) of this question if you wish.
20 marks - 10 for (a), 10 for (b).
a) People frequently use three heuristics to assess probabilities and to predict values. Identify and describe these heuristics and identify and explain a bias to which each of these heuristics lead.
b) Martha Jones is considering investing money in three alternative investments over a one-year period. Below are the expected profits from each investment given assumptions about the state of the economy:
Decision Alternative Good Economy Poor Economy
Stock market $200,000 -$60,000
Bonds $80,000 $45,000
Term deposit $45,000 $35,000
i) If Martha is an optimist which investment should she choose?
ii) If Martha is a pessimist which investment should she choose?
iii) Following the criterion of regret which investment should she choose?
iv) If Martha believes that there is a 65% chance of a good economy which investment should she choose?
v) What is the expected value of perfect information about the state of the economy?
QUESTION 2 Value of information
Show all calculations to support your answers. You may follow the methods shown in the mp4 on
Value of info for a way to answer this question if you wish.
20 marks - 4 for (a), 8 for (b), 2 for (c), 6 for (d)
A manufacturer is trying to choose between two production methods (a1 and a2) for a new product. He considers that the probability of demand for the new product being good (s1) is 0.3 and the probability that demand will be poor (s2) is 0.7.
In evaluating the two production methods the manufacturer has calculated the following table of conditional profits:
s1 s2
a1 30,000 16,000
a2 10,000 24,000
a) Which production method should be used? Show calculations.
The manufacturer asks a marketing consult for an opinion as to whether demand will be good or poor. From previous experience when the consultant has indicated that demand will be good she has been right 80% of the time, and when she has indicated that demand will be poor she has been right 65% of the time.
b) Revise the prior probabilities in light of the consultant’s track record.
c) What is the posterior probability of good demand given that the consultant has indicated demand will be good?
d) What is the expected net gain or loss from engaging the consultant? Should the consultant be engaged? Explain the reasoning for your answer.
QUESTION 3 Simulation
This is a work integrated assessment item. The tasks are similar to what would be carried out in the workplace.
10 marks
A general practice has a nurse to attend patients with wounds and who need vaccinations. From an analysis of one week’s operation of the nursing service the following data were derived:
Time between arrivals Number of occasions
10 10
15 20
20 25
25 30
30 15
Service time (minutes) Number of occasions
10 40
15 20
20 20
30 10
30 10
Using Excel set up a simulation model to simulate about 2 hours (120 minutes) from time zero, and determine whether one nurse is sufficient or whether a second nurse is needed in the practice.
Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts
must show row and column numbers and be copied from Excel into Word. See Spreadsheet Advice in
Interact Resources for guidance.
QUESTION 4 Regression Analysis and Cost Estimation
20 marks - 4 for (a), 12 for (b), 4 for (c).
Quick Copy has recorded the following Maintenance Costs and two possible cost drivers over the last year.
Month Number of photocopies Hours of maintenance service Maintenance costs
January 80,000 525 4,710
February 68,000 505 4,310
March 69,000 310 2,990
April 64,000 495 4,200
May 90,000 315 3,000
June 85,000 485 4,215
July 55,000 315 2,950
August 85,000 405 3,680
September 62,000 475 4,100
October 82,000 345 3,250
November 60,000 350 3,260
December 70,000 335 3,015
a) Using the High-Low method of cost estimation and Number of Photocopies as the cost driver, what would be the resulting cost equation for Maintenance Costs?
b) Using Excel, perform three regression analyses to regress Maintenance Costs against Number of Photocopies, then against number of Hours of Maintenance Service, then against both of them simultaneously. Paste your results into Word. State the cost equation from each. Prepare a report to management including an analysis and comment on the results of each regression with a reasoned recommendation of the best cost driver to use in the future.
c) If the simple regression using Number of Photocopies were adopted, what would be the predicted overhead in a month when there were 85,000 photocopies and 500 hours of maintenance service?
QUESTION 5 CVP Analysis
20 marks - 4 for (a), 4 for (b), 4 for (c), 8 for (d).
A smart phone manufacturer makes two types of smart phones, Connect32 and Connect64. He has sales staff who sell the phones on commission. The following data are available:
Product Sales Price Variable Production Cost Sales Commission
Connect32 $600 $100 $20
Connect64 $850 $375 $35
Fixed costs per annum are $120,000.
a) Calculate the unit contribution margin for each product.
b) This year the manufacturer will specialise in making only Connect32 phones. How many does he need to sell to break even?
c) If Connect32 phones are still the only product what is the breakeven sales volume for the year in sales dollars?
d) He now decides to manufacture both phones this year in the ratio of 3 Connect64 to 1 Connect32.
i. How many of each phone must be sold to earn a profit of $195,000 before tax for the year?
ii. How many of each phone must be sold to earn a profit of $140,000 after tax (of 30c in the dollar) for the year?
Question 6 Forecasting
10 marks – 2 for (a), 2 for (b), 2 for (c) and 4 for (d).
Use Excel QM software to generate your answers to parts a), b) and c). Paste the results, both the answers and the formulas into your Word document. Both should show row and column numbers.
The following data has been collected for the demand for 20 kg bags of potting mix for the Grow-Well Garden Supplies Company.
Year Demand for potting mix (1,000 of bags)
1 4
2 6
3 4
4 5
5 10
6 8
7 7
8 9
9 12
10 14
11 15
a) Develop a 3 year moving average to forecast sales.
b) Estimate demand with a weighted moving average in which sales in the most recent year are given a weight of 2 and sales in the other 3 years are each given a weight of 1.
c) Develop a trend line for the demand for potting mix.
d) Which of the three methods above, 3 year moving average, a weighted moving average or a trend line would you use. Explain your answer.
Rationale
This assessment task covers topics 3,4,5,6 and 8: Decision analysis and value of information, simulation, correlation and regression analysis and CVP analysis. Specifically, it seeks to assess your ability to complete the following subject learning outcomes:
• apply decision theory to business situations
• use simulation in complex decisions
• demonstrate understanding of the application of statistical hypothesis testing in regression analysis
• apply CVP analysis to product mix decisions involving single and multiple products
Presentation
You should refer to the marking criteria for each the assessment item. You should also folow the directions given in each question..
Requirements:
1. Present answers in the same sequence as the questions set.
2. The front page of your assessment should consist of:
• subject code and subject name
• your name and student number
• assessment item number.
3. Other pages should include:
• statement of academic integrity
• list of questions attempted
• student name and number on each page submitted
• pages should be numbered
• bibliography on last page.
The following link provides study resources such as referencing, writing, grammar, punctuation and study planning:
http://student.csu.edu.au/study/resources
Requirements
This assignment must be submitted through Turnitin.
It is recommended that your name, student ID and page number are included in the header or footer of every page of the assignment. Further details about submission in Turnitin are provided in Appendix 1.