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On January 31, 2014, the number of registered motor vehicles in the Newcastle local government area (LGA) was 110985. This figure comprises of a mix of cars, trucks, buses and motorcycles. The table b

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On January 31, 2014, the number of registered motor vehicles in the Newcastle local government area (LGA) was 110985. This figure comprises of a mix of cars, trucks, buses and motorcycles. The table below provides a summary of the number of registered vehicles in the area and can be accessed online via the following Australian Bureau of Statistics website http://stat.abs.gov.au/itt/r.jsp? RegionSummary&region=15900&dataset=ABS_REGIONAL_LGA&geoconcept=REGION &maplayerid=LGA2014&measure=MEASURE&datasetASGS=ABS_REGIONAL_ASGS& datasetLGA=ABS_REGIONAL_LGA&regi...

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On January 31, 2014, the number of registered motor vehicles in the Newcastle local government area (LGA) was 110985. This figure comprises of a mix of cars, trucks, buses and motorcycles. The table below provides a summary of the number of registered vehicles in the area and can be accessed online via the following Australian Bureau of Statistics website http://stat.abs.gov.au/itt/r.jsp? RegionSummary®ion=15900&dataset=ABS_REGIONAL_LGA&geoconcept=REGION &maplayerid=LGA2014&measure=MEASURE&datasetASGS=ABS_REGIONAL_ASGS& datasetLGA=ABS_REGIONAL_LGA®ionLGA=REGION®ionASGS=REGION The data are also available in the SPSS file Assignment 2 Vehicle – T1 2017 available in the list of SPSS files on Blackboard (under Resources/HELP) a) To help gain an understanding of what this data tells us, an informative tool is to graphically summarise the data. With that in mind, create and provide the appropriate chart for the data. (2 marks) b) Write a brief report on your findings by observing • any important points you found from your graphical summary, and • the data given to you in the above table. Note: A comprehensive response should require less than 100 words (2 marks) Vehicle Type Number Passenger Vehicles 88716 Campervans 276 Light Commercial Vehicles 13668 Light Rigid Trucks 1045 Articulated Trucks 251 Non-freight Carrying Trucks 33 Buses 340 Motorcycles 5882 Total 110985 2 STAT1060: Business Decision Making Assignment 2 3 STAT1060: Business Decision Making Assignment 2 For Questions 2, 3, 4 and 5 the scenario, and data, below are relevant. Please answer these three questions with this scenario and data at the forefront of your mind You are part of the group of consultants that provides professional advice to senior executives of an adhesive manufacturing company. The group is responsible for helping the executives make decisions about the quality of a variety of adhesive products that the company makes. The most financially lucrative, and high profile, product is an adhesive that is used to attach heat shield tiles to rockets that delivery payload to the international space station In the past, you and your group have observed (through a formal process of analysis and review) that the quality of the current adhesive is declining – the quality of the product is assessed by examining (amongst other important features) the drying time of the adhesive. Therefore, the executives are also concerned since any reduction in the quality of the adhesive compromises safety of the future missions to the space station. So, the executives have asked their research and development (R&D) lab to produce a new adhesive that will address their concerns by producing an adhesive that has a shorter, and more consistent, drying time. However, because of pressures imposed by those who transport the payload to the international space station, the drying time of the new adhesive must be no more than 5 hours. In fact, the R&D lab have vowed that they can reduce the drying time of a new adhesive by 2 hours when compared with the drying time of the current adhesive. To test the new adhesive product, 20 tiles are randomly selected and attached to a section of a replica rocket using the old adhesive and another 20 are randomly selected tiles are attached using the new adhesive product. If the new adhesive product reduces the drying time so that the tiles remain fixed on the rocket, the executives will manufacture the new adhesive instead of the current adhesive. The executives would like to see the drying time of the new adhesive is no more than 5 hours, while the R&D lab states that the new adhesive will reduce the required drying time by 2 hours To compare the drying time of the current adhesive and the new adhesive, the data collected from the manufacturing company is included in the SPSS file called Assignment 2 Adhesive – T1 2017 which is available in the list of SPSS files on Blackboard (see the Resources/ HELP link). Answer Questions 2, 3, 4 and 5 using this scenario. 4 STAT1060: Business Decision Making Assignment 2 Question 2 (27 marks) a) A key variable of the data is Adhesive_Type with Current Adhesive and New Adhesive being the two possible options. The second variable is the Drying Time of the adhesive. Identify each variable type and give a brief, but clear, reason for your decision. (2 marks) b) To help make a decision about whether the executives order that the new adhesive replace the current adhesive, they require some evidence-based findings to help guide them. One of the simplest pieces of evidence is to provide them with a graphical summary of the Drying Time of the two adhesives. Therefore, to help them in their decision making process, use SPSS to construct SEPARATE histograms of Drying Time for the Current Adhesive and the New Adhesive. (5 marks) Ensure that your histograms • Have a common scale along the horizontal axis. Set the minimum value to 0 and the maximum value to 10. • Have a common scale along the vertical axis. Set the minimum value to 0 and the maximum value to 8. • Are vertically aligned. • Have a bin (interval) width 1 c) For the histograms that you constructed in part b), give one reason why it is important to ensure that the scaling along each of the histogram’s axes is consistent for comparing them. State the importance of this scaling for helping make informed decisions or recommendations to the executives. (2 marks) d) For each of the histograms you obtained in part b), compare the shape, centre and spread of the two types of adhesives. Comment on what this tells you about the drying time of the new adhesive when compared with the current adhesive. (4 marks) e) Construct a side-by-side boxplot of the drying time of the two adhesives. From this boxplot, comment on the distribution of Drying Time for the new adhesive product and the current adhesive product. How do these features of Drying Time compare with what you saw in part d)? (5 marks) f) The graphical summaries of the adhesive’s drying time help paint a picture for the executives how to compare the quality of the current adhesive when compared with the new adhesive. However, they want some “hard” numbers. Use SPSS to find the mean, median, standard deviation and interquartile range of New Adhesive and Current Adhesive separately. DO NOT simply just provide SPSS output. (4 marks) 5 STAT1060: Business Decision Making Assignment 2 g) Identify why it would be suitable to use all of the above four summary measures to describe the distribution of Drying Time. (2 marks) h) Now that you have provided the executives with some visual and numerical summaries that allow them to compare the drying time of the new adhesive and the current adhesive, this has helped them better understand how they compare. Given these summaries, the executives now feel they would like to see the drying time of the new adhesive to be no more than 5 hours. Use the empirical rule to (approximately) estimate the probability of the drying time of the new adhesive being less than 5 hours. Show all your working. DO NOT use the computer to estimate this probability. Explain your answer in terms of the question. (3 marks) Question 3 (21 marks) The executives now wish to determine the mean drying time of the New Adhesive. Such a measure will allow them to compare the current adhesive with the new developed adhesive (note that further comparisons of the two for the company will be made in Question 4). a) Given the mean value of drying time you found for the new adhesive in Question 2, use SPSS to find the 95% confidence interval of this mean value. Include the SPSS output from where you obtained this interval. However, do not just provide SPSS output. (2 marks) b) By providing a brief statement, interpret the 95% confidence interval you found in part a). Ensure you relate this interval to the scenario concerning the drying time of the new adhesive. (4 marks) c) Recall that the executives would like to see the drying time of the new adhesive be less than 5 hours. Suppose the executives wish to see the drying time being equal to 5 hours. Explain, using the supporting evidence from your 95% confidence interval, whether there is evidence to confirm the executives wishes. (5 marks) d) Use SPSS to conduct a formal hypothesis test, using a 5% significance level, of whether the population mean drying time of the new adhesive is meeting the executive’s expectations of drying in 5 hours. Apply the five steps that were outlined in the lecture and include the SPSS output from where you obtain the p-value. Remember: ensure the marker can understand any decisions you make. Use the SPSS file with the name Assignment 2 New_Adhesive – T1 2017. (10 marks) Question 4 (10 marks) 6 STAT1060: Business Decision Making Assignment 2 In Question 3, you provided the executives with some information concerning the drying time of the new adhesive. However, before they make a final decision about whether they should go ahead with the new adhesive, it is prudent for them to compare the drying time of the new adhesive with the drying time of the current adhesive. So you have been asked to make such a comparison and provide them with an appropriate report concerning whether the company should continue with producing the current adhesive for the rockets or commence full production of the new adhesive. a) To help the executives of the company to make a final decision, use SPSS to obtain a 95% confidence interval for the difference in the mean drying time of the current adhesive and the new adhesive. i) State the 95% confidence interval (that is, simply give the lower and upper limits). Include the SPSS output from where you obtained this interval. However, do not just provide SPSS output. (2 marks) ii) Interpret the 95% confidence interval (that is, give a statement) in terms of whether there is a difference in the drying time of the two adhesives. Reminder: ensure you accurately word your response. (3 marks) b) Recall that R&D lab vowed that they could reduce the drying time of the new adhesive by 2 hours when compared with the drying time of the current adhesive. Explain, using the supporting evidence from the 95% confidence interval, what you would conclude about such a vow. (5 marks) Question 5 (18 marks) Using the evidence that you generated from the R&D lab, what professional advice would you report to the senior executives that helps them make a decision about the choice of adhesive? Provide two positive impacts this choice will have on the company’s decision to manufacture an adhesive and their commitment to producing a product that ensures that a payload is delivered safely to the international space station. Keep your response to no more than 200 words. This evidence needs to consist of outcomes • About the centre, spread and shape of the data, including outcomes from the graphical and numerical summaries • That stem from a description of the population mean drying time of the new adhesive. • That come about from the comparison of the population mean drying time of the current adhesive and new adhesive. 7

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The above graph shows that the “passenger vehicles” is the most registered vehicle in the Newcastle local government area followed by “light commercial vehicles”. The bar of
“non freight carrying trucks” is minimal followed by “articulated trucks” and “campervan”. As per the data, while there were total 110985 vehicles registered but there
were only 110211

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