BUMAN201A Business Maths And Statistics Assessment 4 Case Study Answer

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Question :

Subject Code: BUMAN201A

Subject Name: Business Maths and Statistics Semester 1, 2021

Assessment 4: Case Study

Case StudyTask instructions

This assessment contains two parts.

Part 1

You company in interested in purchasing a CNC textile cutting machine to increase the volume of clothing that can be manufactured, and to reduce the workload on the staff by automating the process. Your company requires you to find a recommendation for a loan to purchase the equipment and to determine the best method of depreciation of the asset for your business (see data on pg. 4).

Part 2

You have been tasked with advertising the new line of clothing/sports accessories. You have been instructed to consider two methods of marketing. 1st by running a standard 30 second advertisement on televised sporting events, and 2nd by sponsoring an athlete in a televised sporting event, specifically you want to supply clothing to a promising athlete for exposure

You are interested in 3 factors before you decide on what to advertise/who to sponsor.

  1. Are athletes improving over time? If so, you can market clothing/accessory technology as part of this reason and sell your apparel as the next breakthrough technology. This will be done by collecting Olympic data from a recent and historic Olympic event and determining to an appropriate confidence level whether one group was “better” than the other on average. (This data is not provided)
  2. Is there a correlation between the performance of a sponsored athlete and the exposure that athlete brings to a televised sporting event? This will be done by analysing the televised exposure percentage that the top 20 golfers received during 6 tournaments and determining if the data is correlated using a scatter plot and linear regression. (This data is provided)
  3. Is the expected exposure time the athlete would bring worth more than their sponsorship cost compared to running advertisements for the same amount of time?

You have an opportunity to sponsor a golfing athlete at a cost of $299,000. They are going to be playing in an upcoming televised tournament. The cost of a televised advertisement in this event is $39,000 per minute. The tournament is televised for 2 hours with 30 minutes of advertising in that 2-hour timeslot.

You wish to know if the potential sponsorship of the athlete would be worth more than the cost of their sponsorship. That is, is paying for advertisements for the same amount of time the athlete is expected to bring in exposure more or less expensive than the cost of sponsorship? From this provide feedback as to whether you recommend sponsoring the athlete. (This data is provided)

Note: This is a business report and needs to be written as such. However, your statistical analysis and the method you used to analyse the data must be part of the report.

Analysis Instructions

This section is to help you in the analysis. These are not questions. Your report must be business advice based on your findings after performing the following analysis.

Part 1


The CNC textiles cutting table your company is interested in purchasing is valued at $29,000. The expected purchase date is the 1st October. According to the Australian taxation office (ATO) the working life of this equipment is 15 years.

You have two options for a loan to purchase this equipment.

  1. A bank loan with 4.75% PA interest, with monthly repayments, compounded month, paid over a term of 4 years. This loan contains a $500 setup fee.
  2. A manufacturer loan with an interest rate of 5.95% P.A with quarterly repayments, compounded quarterly, paid over 5 years. This loan contains a $100 setup fee.

Provide advice as to which loan you recommend.


Determine the depreciation schedule for the life of the CNC table using both the prime cost and diminishing value method, given the intended purchase date is the 1st October 2021.

Provide advice as to which depreciation method you recommend for your company. Show the differences graphically.

Part 2

Factor 1: Are athletes improving over time?

You are to collect time data from a recent Olympic games (2000-2016 Olympic games) of an individual event (i.e. not a team event). The data you collect must be in terms of time required to finish or total points etc. You will need a minimum of 30 data points. This could be achieved by collecting the times from the quarter finalists (or semi-finals etc) in that Olympic event. An example could be 100m sprinting time, high jump height, etc.

You will then find the same data from an Olympic games that was at least 30 years before the recent Olympics games you selected above. Your data must not be older than 1952.

Your analysis of this data is to determine an appropriate confidence interval of the mean times (or heights, points etc) for both data sets. Determine if the recent athletes outperformed on average the historic athletes by looking at your confident intervals (Hint: do they overlap or not? If they overlap you cannot analyse this data using confidence intervals, so include a statement about why further analysis would be required).

Discuss your findings. Is the claim that athletes are improving over time due to technology reasonable to include in your advertising? Could there be other factors that may have impacted this result? Provide advice.

Factor 2: Does the performance of an athlete correlate with the exposure time of that athlete on a televised sporting event?

You have been provided with data outlining the amount of exposure the top 20 athletes in 6 golfing tournaments have received as a percentage of the total time the tournaments aired on television. To analyse this there will be several steps. Ensure that you address each step in your response.

  1. Graph this data in a meaningful way to visualise any trend in the mean exposure time.
  2. Of the top 20 golfers, only the top 5 will be analysed. (Explain why you want to do this)
  3. Using a scatter plot, is there a correlation between the position the golfer finished with the amount of exposure that athlete received in the top 5?
  4. Is this correlation statistically significant?
  5. Using a linear regression, determine the equation of the line of best fit, and examine the slope. How much more exposure time does each subsequent finishing position provide according to your regression line?

Factor 3: Should you sponsor someone?

You have been provided with data on the most recent 50 finishing results of a golfing athlete that your company is considering sponsoring in an upcoming golf tournament. The cost of sponsoring them is in the data provided on the Moodle. You need to determine whether the likely value of exposure they bring is worth more than the cost of their sponsorship, given advertising in the tournament is $39,000 per minute. The tournament is televised for 2 hours, which includes 30 minutes of advertising.

  1. Determine the amount of television exposure time and hence exposure percentage, the athlete would need to be worth more than their sponsorship compared to running an advertisement for the same period of time in the upcoming tournament.
  2. Determine the athlete’s mean finishing position and the standard deviation based on their provided previous finishing results. What does this data tell you about the athlete?
  3. Using your linear regression from part 2, determine what position you expect the athlete will need to finish so that they receive the exposure time you determined in 1. above.
  4. What is the probability that the athlete will finish in this position or higher based on their previous results?
  5. Look closely at your data and discuss your findings

Do you recommend sponsoring this athlete? Provide advice. You do not need to analyse this data any further

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