Assignment 2 Weighting: Worth 18% of final mark Final date for submission: 2 October 2020 Milestones: Auto-graded quiz for Module 2 material closes August 28th Auto-graded quiz for Module 3 material closes September 28th Place of submission: The manually-graded section should be submitted to the assignment dropbox on MyLO. The auto-graded sections are assessed via two MyLO quizzes which will remain open until the milestone dates listed above. The assignment has two major parts (worth 9% each). The first part of the assignment links to Learning Outcome 2: To demonstrate sound practices in sampling, data description and presentation in a business environment. It will use content covered in Module 2 (weeks 4-6 of the unit). The second part of the assignment links to Learning Outcome 3: Apply basic probability concepts, distributions, and statistical inference as an aid to business decision making. It will use content covered in Module 3 (weeks 8-10 of the unit).  Each major part of the assignment has both an auto-graded section and a manually-graded section.  For each part you may have multiple attempts at the auto-graded section.  The manually-graded section will be graded after the final due date.  Within each module, it is strongly suggested that you try and achieve full marks on the auto-graded section of the assessment before moving to the manually graded section. MODULE 2 - TOPIC 1 (EXPLORING DATA WITH PIVOT TABLES) Weight: This topic is worth 17 marks out of 68 (25% of the assignment 2 grade). Tools required: You should use the PivotTable tools that you learned about in computer lab 2. Suggested timeframe: The quiz for the auto-graded section will close at 5pm on August 28th. It is recommended that you have well-developed answers for the manually-graded part of the assignment by the end of week 7. Scenario. TerrificTrees is a franchise that specialises in planting and felling trees. They have two Tasmanian franchises. In the last quarter they had 200 customers. Data has been collected on the following attributes of the customers (see the file TerrificTrees.xls). CUSTOMER An identification number for the customer OWNER The owner of the franchise the customer used SERVICE The service that was provided (tree planting or tree felling) TREE SIZE Whether the tree was large or small SATISFACTION The customers satisfaction level (10 - extremely satisfied, 1 - extremely dissatisfied) The manager of TerrificTrees is concerned that Amy's customers have low satisfaction scores compared to Bob. However, it is possible that other variables maybe confounding this finding, your role is to investigate the data further. Auto-graded questions (submit answers via MyLO Quiz: Assignment 2 Milestones - Part 1) 1. What is the absolute value of the difference in average satisfaction for Amy's customers compared to Bob's? [1 mark] 2. Average satisfaction differs more by type of service provided (planting or felling) than it differs by tree size. [1 mark] 3. Amy did ____ tree plantings and ____ tree fellings, compared to Bob who did ____tree plantings and _____ tree fellings. [1 mark] 4. Amy had ____ small trees and ____ large trees, compared to Bob who had ____small trees and _____ large trees. [1mark] 5. Taking all the above into account, what two-way pivot table is most informative for assessing the manager's concerns? [1 mark] Questions for the manually-graded section of assignment 2 1. Based on your answer to (5), create an appropriately formatted table that has informative labels and a readable number of decimal places. The table should include an informative caption. [6 marks] 2. Reflecting on the summary statistics and tables you have created is there evidence that Amy is providing a lower quality of service than Bob? What do you think the manager should focus on to try and improve the overall customer satisfaction ratings for TerrificTrees customers? [4 marks] 3. What are the limitations of this sort of data for trying to establish cause and effect? [2 marks] MODULE 2 - TOPIC 2 (LINEAR REGRESSION) Weight: This topic is worth 17 marks out of 68 (25% of the assignment 2 grade). Tools required: You are encouraged to complete the calculations for the regression analysis using built in Excel functions (as covered in the lectures and in computer lab 3). Suggested timeframe: The quiz for the auto-graded section will close at 5pm on August 28th. It is recommended that you have well-developed answers for the manually-graded part of the assignment by the end of week 7. Scenario. The data set sydney2hobart.xls contains data on the time taken by the winning yacht in the Sydney to Hobart yacht race from 1945 to 1997. Your task is to develop a linear model that can predict the winning time based on year. Auto-graded questions (submit answers via MyLO Quiz: Assignment 2 Milestones - Part 1) 1. What is the explanatory variable (x-axis) and what is the response variable (y-axis)? [1 mark] 2. What is the best linear equation for predicting the winning time based on year? I.e. what are the intercept and slope terms? [1 mark] 3. What is the correlation between winning time and year? [1 mark] 4. How much of the variation in winning time is explained by year? I.e. what is the coefficient of determination, r2? [1 mark] 5. What is the standard error, se? [1 mark] Questions for the manually-graded section of assignment 2 1. About how many points would you expect to see more than 2se from the line? How many are there actually? [2 marks] 2. Create an appropriately formatted figure of the data, paying attention to labels and number formats. The figure should include an informative caption. [4 marks] 3. Linear regression makes some quite strong assumptions about the data. a. Points should be independent of each other b. The variation around the line, i.e. the error term, should be the same everywhere (we also assume the error term follows a normal distribution) c. The mean values of the response variable for different values of the explanatory variable should fall on a straight line How well do you think this data set meets the assumptions above? [3 marks] 4. What is your best prediction of the winning time in 2040? Discuss how accurate you expect this prediction to be. [3 marks] MODULE 3 - TOPIC 3 Weight: This topic is worth 34 marks out of 68 (50% of the assignment 2 grade). Tools required: You are encouraged to make use of built in Excel functions as appropriate. Suggested timeframe: The quiz for the auto-graded section will close at 5pm on September 28th. It is recommended that you have start working on your answers for the manually-graded part of the assignment during weeks 8-10. Grading: Questions shaded blue are part of the auto-graded section. Other questions are manually graded, to get full marks for the manually-graded questions you will need to show your working. Scenario. Eric runs a YouTube channel, DwarfPunk, where he gives tutorials on painting wargaming miniatures. Recently he has created a Patreon page where people have the option to make a monthly donation to support him. The Patreon page has 3 tiers: patrons in the "Hobbit" tier pay $1/month, patrons in the "Dwarf" tier pay $5/month and patrons in the "Elf" tier pay $10/month. Based on other data for similar content providers it has been found that:  80% of teenage patrons will opt for the Hobbit tier, 15% will opt for the Dwarf tier and 5% will opt for the Elf tier.  50% of working age patrons will opt for the Hobbit tier, 30% will opt for the Dwarf tier and 20% will opt for the Elf tier.  30% of retired patrons will opt for the Hobbit tier, 60% will opt for the Dwarf tier, and 10% will opt for the Elf tier. 1) Of Eric's subscribers 50% are teenagers, 20% are working age and 30% are retirees. a) What proportion of Eric's patrons are expected to fall into each tier? [1 mark] b) What is the expected value of each patron? [1 mark] c) Hannah is in the Elf tier, what is the probability that she is a retiree? [3 marks] 2) Eric's YouTube channel has 40,000 subscribers, each subscriber has a probability of 0.02 of becoming a patron. a) What distribution does the number of patrons follow? Give all relevant parameters. [2 marks] b) Explain why it would be appropriate to approximate the distribution above by a Normal distribution? [1 mark] c) Assuming it is okay, what parameters would you use for the mean and standard deviation? [1 mark] 3) To cover the costs of his time and materials Eric calculates that he needs to bring in $2400 / month. [Hint: first use the expected value from part 1b to work out how many patrons he needs] a) What is the probability that Eric can cover his costs? [1 mark] b) Draw a picture of a standard normal distribution that indicates the probability you calculated in part (a) and the corresponding z-value. [2 marks] 4) Eric has another strand to his DwarfPunk business where he sells painted wargaming miniatures to order. The following table shows the frequencies with which he has received different numbers of orders per week over the last 3 years. #orders 0 1 2 3 4 5 6 7 8 9 Frequency 5 13 27 23 34 27 11 10 4 2 E.g. there were 27 weeks where he received 2 orders. a) Out of a Normal distribution, Poisson distribution and Binomial distribution, which seems most appropriate as a model for the number of orders per week? [1 mark] b) By using this distribution to model the number of orders, what assumptions are we making? [2 marks] c) What is the mean number of orders per week? [1 mark] d) If Eric receives 4 or fewer orders per week then he has free time available to practice the harmonica, this irritates his flatmates. What is the probability that Eric will have time to play the harmonica? [1 mark] 5) Eric's flatmates decide to do a social media push about DwarfPunk in an attempt to boost his weekly orders. a) Assuming that the social media efforts make no difference to orders at all, how many orders would Eric expect to receive in a 4-week period? [1 mark] b) Do you think it would be appropriate to approximate the distribution of orders received in a 4-week period by a Normal distribution? If so, what parameters would you use for the mean and standard deviation? [3 marks] In the 4 weeks following the social media push Eric receives 23 orders. c) If the social media push had no effect (i.e. if the underlying rate of orders has not changed from what it was previously) then what would be the probability of receiving 23 orders or more in a 4-week period? [3 marks] [Note that the value you have calculated is known as a p-value, it is the chance of seeing some test-statistic (in this case the number of orders) or something more extreme given a null hypothesis (in this case that the social media campaign made no difference) is true.] d) Do you think the social media push made a difference to the number of orders? Give a reason to support your answer. [2 marks] 6) Eric has become concerned that the paints he uses may have too high a concentration of DC100 (a possible carcinogen). He decides to send some of his paint pottles off for testing but can only afford to send 8 out of the many hundreds of pottles he owns. a) How should Eric select he pottles that he sends for testing? [2 marks] Results come back as follows (in units of ppm): 10.7, 10.8, 11.3, 12.2, 12.4, 13.8, 13.8, 14.0 b) What is the mean level of DC100 for the sample? [1 mark] c) What is the sample standard deviation? [1 mark] d) The recommended safe level of DC100 is 13.5 ppm. How confident can Eric be that on average his collection of paints has a DC100 level below 13.5? Give a full explanation of what statistic you calculate and what distribution you compare it to. [4 marks] Assessment Guidelines The rubric below provides a guideline for students of the expectations with respect to key assessment criteria. Criteria Applies To Excellent Intermediate Poor Assumptions1 Questions or question parts  Identify and state any assumptions required to allow the use of a particular methodology.  No Penalty  Assumptions identified but misstated or misrepresented.  Penalty 0-1 marks  Failure to identify and state an assumption required to allow the use of a particular methodology, or use of a wrong assumption.  Penalty 1-2 marks Methodology  Student shows understanding of the problem.  Appropriate methodology chosen for the problem.  Enough detail in the answer for the marker to follow the logic of the student's approach. (As an example, the level of detail provided in examples in lecture notes.)  No Penalty  Student shows some understanding of the problem.  General approach basically correct, but some steps wrong or inappropriate.  Marker has some difficulty following student's approach and/or there are significant jumps of logic or missing details  Penalty <= 50% of marks available.  Student shows no understanding of the problem.  Totally inappropriate methodology employed.  Large or incorrect jumps of logic.  Marker cannot follow student's approach.  Important details missing.  Penalty >= 50% of marks available Evaluation  Answers are correct, given the values that the student started the problem (or problem part) with.2  No penalty.  Minor calculation and/or transcription errors leading to incorrect answers.  Penalty 1 mark.  Major and/or repeated errors.  Penalty 1-2 marks. Interpretation and reflection  Interpretations, when asked for are correct and complete.  Answers are feasible.  No penalty  Interpretations, when asked for, are partially correct or partially complete.  Answer is NOT feasible but the student identifies and explains why the answer can't be right.  Penalty 1 mark.  Interpretations, when asked for are either well off the mark or are missing.  Answer is NOT feasible but the student does not identify or explain this.  Penalty 2 marks. Presentation Whole Assignment  Submitted as a ".pdf" document, and has cover sheet.  Meet minimum standards expected of a business professional: o Pages numbered, questions and question parts assembled in order. o Prepared as a computer document (NOT a scanned hand written copy) using a clear readable font (9 to 12 point) o o Diagrams/Tables/Charts computer generated, labelled and appearing in correct sequence within an answer, and location clearly identified is this is not possible.3 o Mathematical expressions and equations presented using an equation editor or using fixed font approach as demonstrated in lecture 1. o Clear use of appropriate language and terminology. o Final answer to question parts presented in a sentence. For example, "R=427.51" is not an acceptable answer, but "The weekly deposit required is R=$427.51" is acceptable. o Cover sheet attached and completed.  No penalty Some of the following failings  Wrong file format -10%  Pages not numbered -2%  Inappropriate font -2%  Hand written (unless permission obtained beforehand) -10%  At least one diagram/table/chart unlabelled 1 to 2%  At least one diagram/table/chart out of sequence (or not referenced if in an appendix) 1 to 2%  Diagram/table/chart hand written (unless permission obtained beforehand) 1-2%  At least one expression not appropriately formatted 1 to 2%.  Language/terminology unclear or inappropriate 1-2%  Answers not expressed in sentences 1-2%  Cover sheet missing or incomplete - 2% (Items marked 1-2%, are 1% for single offence, 2% if there is more than one offence). Most of the failings listed in the previous column. Timeliness  Handed in on or before due date.  No penalty  As per unit outline  Handed in more than a week late, or not handed in, without prior arrangement and supporting documentation.  100% penalty 1 NB Sometimes questions may not need students to state any assumption as these may have been provided in the question. 2 If a student makes a mistake on a question part they will lose marks on that question part. If they then use a resulting incorrect number in a subsequent question part, as far as possible they will not penalised in that subsequent part, except where it should have become obvious to the student that an error was carried in. 3 For instance, if a diagram is required as part of an answer to part (b), it should be with the rest of part (b) and between parts (a) and (c). If a diagram is too large to fit into the answer sequence it should be included as an appendix at the end of the document, with a clear reference to it in the answer sequence. E.g. "see appendix 3 for the diagram associated with the answer". Guidelines for BEA140 Quantitative Methods Assignment Teams & Individuals  The assignment may only be completed and submitted by individuals. Team assignments are not allowed.  Whereas students are encouraged to discuss all elements of the unit, including the assignment, the preparation of the assignment must be an individual effort. For example, two or more students discussing how to attack question 2, for example, is acceptable. Two students working together to prepare a full solution to question 2 is NOT acceptable. A student presenting others' work as their own is NOT acceptable. A student allowing another student to copy all or part of their assignment is NOT acceptable. (See note about plagiarism at bottom of page.) Presentation  Assignments must be submitted with a completed cover sheet. If an assignment is submitted without, the assignment and mark will be withheld until the student submits it.  The assignment should be prepared on a word processor, and submitted as a ".pdf" document. It is imperative that students carefully read the Assessment Guidelines Rubric (previous page). Students are expected to show sufficient working such that the marker can establish the logic of their thoughts. (Typically, the amount of working in examples in the lectures is a good indication of what is an acceptable amount of detail.). Part marks will be available for incorrect answers, and will be allocated on the basis of the working. Preparation Methodology  Students are encouraged to check their answers, and ask themselves questions such as "does this make sense?", "how can I tell if this looks reasonable?" If a student gets an answer that is obviously wrong and can't figure out what has gone wrong, they are expected to at least comment that it does not look reasonable (and why).  Students are encouraged to complete assignment questions as the relevant topics are covered in class. (The "mad rush at the last minute" strategy is a dangerous one. See Problems below.) Problems  Assignments that are handed in late will be penalised, unless prior arrangement has been made with the lecturer. Assignments up to one week late will be penalised as described in the unit outline. Assignments more than one week late will not be marked.  In the event of sickness or other major disruption is likely to affect a student's ability to submit the assignment on time, the lecturer should be contacted a.s.a.p. Special consideration will require documentary evidence. (Medical certificate, memo on letterhead for participation in representative (Tas, or Aust) sport or for interstate work commitments, etc...)  Special consideration will most likely assume that the individual was working on the assignment as recommended in the Preparation Methodology section above. For example, if one is sick for the last week before the assignment is due, it may well be expected that all of the assignment that should have been prepared during previous weeks will be submitted on time, and that only the questions pertaining to the last week's work will be granted an extension.  If you have any other questions or problems contact your lecturer or workshop tutor - the earlier the better. Marking and Feedback  It will take a number of weeks to mark the assignment.  However, one week after the due date, a full and detailed set of solutions will be posted on mylo. Students are encouraged to keep a copy of their assignment which they can check against the solutions, and thus obtain feedback on their performance even before the assignments are marked. This strategy is designed to allow students to take maximum advantage of the assignment in their exam preparation study.  Upon return of marked assignments, teaching staff will be available for those students seeking more feedback. You should be aware that assignments will be checked for plagiarism. Plagiarism is punishable by reduction or cancellation of marks, and in the most serious cases, exclusion from a unit, a course or the University. This applies both to a student who submits somebody else's work as their own, AND to a student who willingly allows another to copy and submit their work.