1. AuCement produces many types of cement products at its factory in Sydney and sells them in Sydney, Brisbane, Canberra, and Melbourne. Six month ago, the company established a new cement facility to load a new 20Kg packaged cement. The company sells this new product in a competitive price and has boosted its sales with this option. In every contract the price of the product is paid based on its delivery time and customer satisfaction. To investigate more about the sales, they surveyed the customers who have purchased this kind of cement and a sample of 50 receipts was selected from the previous sales. For better comparison, they scaled the delivery time with dividing the hours spent for delivering the product by the travelled kilometres. AuCement file contains data showing the customer’s location, the payment type, the delivery time, the amount of customer satisfaction, and the price of sales paid for every tonne of this product by each of the 50 customers.

AuCement would like to use the sample data to determine whether customers who receive their package earlier and are more satisfied about the quality also pays higher prices. The company would also like to investigate the effect that the customer location and the payment type have on sales.

Managerial Report

Use the methods of descriptive statistics to learn about the customers who purchase in higher prices. Include the following in your report:

• Graphical and numerical summaries for the length of delivery time, the customer satisfaction factor, and the average amount gained per sale. Discuss what you learn about AuCement’s new product sales based on this data. (5 marks)

(Hint: for the graphical summaries show histograms for each variable and for the numerical summaries draw a table listing mean, median, standard deviation, min, max and range for each variable)

• Summarise the frequency, the average sale price, average delivery time, and average customer satisfaction for each city. Discuss the observations you can make about AuCement’s business based on the destination city of the sales? (2 marks)
• Develop a scatter diagram, and compute the sample correlation coefficient to explore the relationship between the delivery time and the selling price. Use the horizontal axis for the delivery time of the new product. Discuss your findings. (2 marks)
• Develop a scatter diagram, and compute the sample correlation coefficient to explore the relationship between the delivery time and the customer satisfaction. Use the horizontal axis for the delivery time of the new product. Discuss your findings. (2 marks)
• Develop a scatter diagram, and compute the sample correlation coefficient to explore the relationship between the customer satisfaction and the sale price of new product. Use the horizontal axis to represent the customer satisfaction. Discuss your findings.(2 marks)

2. Ambulance Victoria has an official Response Time (RT) targets: Respond to incidents within 15 minutes for 85% of incidents state-wide. Response times are an important measure of the service they provide. The response times are measured from the receipt of the triple zero (000) call until paramedics arrive on scene. Response times are influenced by many factors including traffic, distance required to travel, availability of ambulances and demand for the services. They designate those patients that require urgent paramedic and hospital care as “Code 1,” and these patients receive a “lights and sirens” response. The AmbulanceVictoria file provides information about their Code 1 response time performance by Local Government Area (LGA) in the 3^rd quarter of the financial year 2015-2016.

Managerial Report

Use the data-visualization methods presented in this chapter to explore these data and discover relationships between the variables. Include the following in your report:

• Create a scatter chart to examine the relationship between the average response time and the total number of incidents. Include a trend line for this scatter chart with its formula. What does the scatter chart indicate about the average response time over the total number of incidents for these Victoria’s LGAs? (2 marks)
• Create a scatter chart to examine the relationship between the percentage of less than 15 minutes response times and the average response time. What does this scatter chart indicate about the relationship between the percentage of less than 15 minutes response times and the average response time? (2 marks)
• Create frequency distributions, percent frequency distributions and intervals in a table for the number of incidents using bin size of 250 incidents. Then, draw a histogram for the frequencies. Interpret the results. Do any data points appear to be outliers in this distribution? (3 marks)
• Create a PivotTable for these data. Use the PivotTable to generate a cross tabulation for LGA categories and rating. Determine which combinations of LGA categories and rating are most represented in the Ambulance Victoria data. Now filter the data to consider only area with average response time more than 15 minutes (900 seconds). What combinations of LGA categories and rating are most represented? What does this indicate about how the ranking of the LGAs may be defined for the other quarters of the year? (3 marks)
• Use the PivotTable to display the average incidents happened in each combination of category-rating pair of areas in the data set. Interpret the results.(2 marks)

                                                                 SAMPLE SOLUTION

1. AuCement produces many types of cement products at its factory in Sydney and sells them in Sydney, Brisbane, Canberra, and Melbourne. Six month ago, the company established a new cement facility to load a new 20Kg packaged cement. The company sells this new product in a competitive price and has boosted its sales with this option. In every contract the price of the product is paid based on its delivery time and customer satisfaction. To investigate more about the sales, they surveyed the customers who have purchased this kind of cement and a sample of 50 receipts was selected from the previous sales. For better comparison, they scaled the delivery time with dividing the hours spent for delivering the product by the travelled kilometres. AuCement file contains data showing the customer’s location, the payment type, the delivery time, the amount of customer satisfaction, and the price of sales paid for every tonne of this product by each of the 50 customers.

AuCement would like to use the sample data to determine whether customers who receive their package earlier and are more satisfied about the quality also pays higher prices. The company would also like to investigate the effect that the customer location and the payment type have on sales.

Managerial Report

Use the methods of descriptive statistics to learn about the customers who purchase in higher prices. Include the following in your report:

• Graphical and numerical summaries for the length of delivery time, the customer satisfaction factor, and the average amount gained per sale. Discuss what you learn about AuCement’s new product sales based on this data. (5 marks).

Graphical Summaries