Tony Lau is considering opening a business, either near his home in Sydney, or on the Central Coast where he would like to semi-retire within a few years. Tony has asked you to analyse ABS and other data, to assist him with making his decision. Tony has asked you to answer three questions. Part 1 - Employment and Incomes i. Tony wants to know how many people living in each region are of working age (15-64 years] and whether this is growing over time. Tony asks that you include graphs showing this population change over recent years ii. Tony also asks you to use regression (least-squares) to predict the working age population in 2023 for both regions. Comment on the reliability of your prediction. Tony is also interested in the average (mean) employee income earned by people working in these two regions, and asks that you include graphs showing any changes over recent years. iv. Finally, Tony is interested in how many employees are in each region. He asks you to provide the mean and median number of employees, for 2013-2017, for each region, and to also report the range of employee numbers for each region for those five years. Part 2 - Business Ownership and Wealth Indicators Tony is convinced that business owners earn more money than employees, and that he can predict future business growth by measuring certain measurements of wealth. Tony feels this will help his to decide on the best location for his business. i. Tony asks you to calculate the relationship (correlation] between the number of people in each region that own a business, and the median total income for individuals in that region (excluding Government pensions). Tony also asks you to calculate the relationship between mean capital gains and the number of business owners. Tony wants you to report these correlations for each region. ii. Include your comments on the results, and the significance (if any) for Tony. Part 3 - Product Choice Part of Tony's business idea involves selling low profile sports sedan tyres for expensive cars such as Mercedes and BMW. Tony intends to stock either the Triomphe brand, from France, or the Palio brand, from Italy. Tony has negotiated exclusive arrangements with both brands, so whichever brand he chooses he will be the only outlet in the Sydney geographic basin. Palio has offered Tony a profit margin 8% higher than Triomphe. For both brands, Tony will offer customers a free replacement under warranty, if a tyre lasts less than two years. ABS and RMS data reveals that residents of the Central Coast and North Sydney regions travel 10,000km per year on average. The tyre manufacturers have provided Tony with the following production data: Triomphe: 28,000km mean tyre life; standard deviation 2500km. Palio: 28,000km mean tyre life; standard deviation 6500km. The data from each brand forms an approximate normal curve. Required: i. ii. iii. For each brand, Tony asks you to calculate: a. the probability that a tyre will last more than 32,000km. b. the probability that a tyre will last more than 26,000km but less than 31,000km. c. the likely proportion of tyres Tony will need to replace for free under his warranty. Based on part i. advise Tony on which brand you think he should sell. Justify your choice. Tony is keen on Palio's higher profit margin, but very worried about their quality control and variability, so he tested a random sample of 60 Palio tyres, finding a sample mean tyre life of 22,164km. Construct a 99% confidence interval for the mean Palio tyre life. Explain for Tony the meaning of the confidence interval calculated in part iii. iv. Tony Lau is considering opening a business, either near his home in Sydney, or on the Central Coast where he would like to semi-retire within a few years. Tony has asked you to analyse ABS and other data, to assist him with making his decision. Tony has asked you to answer three questions. Part 1 - Employment and Incomes i. Tony wants to know how many people living in each region are of working age (15-64 years] and whether this is growing over time. Tony asks that you include graphs showing this population change over recent years ii. Tony also asks you to use regression (least-squares) to predict the working age population in 2023 for both regions. Comment on the reliability of your prediction. Tony is also interested in the average (mean) employee income earned by people working in these two regions, and asks that you include graphs showing any changes over recent years. iv. Finally, Tony is interested in how many employees are in each region. He asks you to provide the mean and median number of employees, for 2013-2017, for each region, and to also report the range of employee numbers for each region for those five years. Part 2 - Business Ownership and Wealth Indicators Tony is convinced that business owners earn more money than employees, and that he can predict future business growth by measuring certain measurements of wealth. Tony feels this will help his to decide on the best location for his business. i. Tony asks you to calculate the relationship (correlation] between the number of people in each region that own a business, and the median total income for individuals in that region (excluding Government pensions). Tony also asks you to calculate the relationship between mean capital gains and the number of business owners. Tony wants you to report these correlations for each region. ii. Include your comments on the results, and the significance (if any) for Tony. Part 3 - Product Choice Part of Tony's business idea involves selling low profile sports sedan tyres for expensive cars such as Mercedes and BMW. Tony intends to stock either the Triomphe brand, from France, or the Palio brand, from Italy. Tony has negotiated exclusive arrangements with both brands, so whichever brand he chooses he will be the only outlet in the Sydney geographic basin. Palio has offered Tony a profit margin 8% higher than Triomphe. For both brands, Tony will offer customers a free replacement under warranty, if a tyre lasts less than two years. ABS and RMS data reveals that residents of the Central Coast and North Sydney regions travel 10,000km per year on average. The tyre manufacturers have provided Tony with the following production data: Triomphe: 28,000km mean tyre life; standard deviation 2500km. Palio: 28,000km mean tyre life; standard deviation 6500km. The data from each brand forms an approximate normal curve. Required: i. ii. iii. For each brand, Tony asks you to calculate: a. the probability that a tyre will last more than 32,000km. b. the probability that a tyre will last more than 26,000km but less than 31,000km. c. the likely proportion of tyres Tony will need to replace for free under his warranty. Based on part i. advise Tony on which brand you think he should sell. Justify your choice. Tony is keen on Palio's higher profit margin, but very worried about their quality control and variability, so he tested a random sample of 60 Palio tyres, finding a sample mean tyre life of 22,164km. Construct a 99% confidence interval for the mean Palio tyre life. Explain for Tony the meaning of the confidence interval calculated in part iii. iv