Reference no: EM132335651

Assignment -

OBJECTIVE OF THE ASSIGNMENT - To apply the concepts of inference statistics through the application of appropriate testing methods on a real case scenario and draw appropriate conclusions.

CASE STUDY - You are the owner of a warehouse business. You are actively looking for opportunities to expand into the delivery services as part of your business expansion strategy. Recently, you met a close friend, Paul from your Polytechnic studies. He is also the owner of local small parcel delivery company, SPEEDY PTE LTD. Paul has indicated to you his intention to sell this delivery business so that he can migrate to Australia to be together with his family. In the discussion, Paul provided the following information on SPEEDY:

a. The population mean number of trips made by each driver is 20.5 trips per day. In fact, Paul insisted that this figure is quite understated as his drivers are generally making more than 20.5 trips per day.

b. Based on historical data, the mean number of drivers on medical leave is 6 per day.

c. The operating environment is extremely competitive and in Dec 2017, the company implemented a new delivery system that helped them to optimize the number of delivery trips made by each driver. Hence, the mean daily number of trips per driver has improved after the implementation of the new delivery system.

d. For the last 2 years, the daily business volume is independent of the day of the week.

Based on your initial discussion, you thought it could be a good business opportunity. However, you are mindful that any discussion for you to take-over Paul's business will depend on 2 factors:

a. Although Paul is a friend, you are not sure whether he can be fully trusted and hence, there is a need to validate the claims that he had indicated to you. Being new to the delivery business, you felt the trustworthiness of Paul is an important consideration in your decision making.

b. Based on a research study conducted by the local Supply Chain Institute, a delivery company has to achieve a minimum of 20 trips per driver per day in order to breakeven. You want to have at least 95% chance of breaking even before considering to acquire the business.

Since you expressed interest in acquiring the business, Paul provided randomly selected information on the delivery data for the year 2017 and 2018 for your analysis. The details of this information are given in the data file which will be sent to your TP student email account by your tutor. He will provide the financial statements only after you have confirmed your interest in the business. Apply all the inference statistical concepts and tools that you have learnt from Unit 6-9 to answer the following questions:

Question 1 - Calculate the sample mean, sample variance and sample standard deviation for the following measures shown in the table below.

	Number of Delivery Trips Per Day Per Driver (2017)	Number of Delivery Trips Per Day Per Driver (2018)	Average No. of Delivery staff on MC per day
Sample Mean
Sample Std Dev
Sample Variance

Question 2 - Assuming the information provided on the population mean daily number of trips made by each driver at 20.5 trips is correct, you would like to know the following:

2a) Based on the data provided for 2018, what is the probability of breaking even?

2b) If you take over the business, you would like to reward 10% of delivery drivers who made the most number of daily delivery trips for the year 2018. Based on the 2018 sample data provided, what is the minimum number of daily delivery trips a driver has to make in order to qualify for the $500 cash award?

Question 3 - Construct the 95% confidence interval for population mean daily number of delivery staff on MC. Can you agree with the information provided by Paul that the mean number of delivery drivers on MC is 6 per day? Explain statistically.

Question 4 - At the 5% level of significance, can you agree with the claim made by the Paul that the mean number of deliveries made by each driver per day (based on 2018 performance) is more than 20.5? You are required to use Microsoft EXCEL to determine the p-value.

Question 5 - At the 5% level of significance, can you agree with Paul that the mean number of trips made by each driver per day has improved after the implementation of the new delivery system? State any assumptions made. (Hint : This is a Z-Test: Two Sample for Means)

Question 6 - You remembered Paul saying that the daily volume of business is the same regardless of the day of the week and this has not changed in the last 2 years.

6a) Calculate the mean number of trips made by each driver per day for each day of the week and summarise your results in a contingency table as shown below: (Leave your answers in 4 decimal places.)

Day	Mean Number of Trips per Driver per Day (2017)	Mean Number of Trips per Driver per Day (2018)	Total
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Total

6b) At the 5% level of significance, can you agree with Paul that the daily volume of business (in terms of mean number of deliveries made) is independent to the day of the week? (Note: Leave your answers in 8 decimal places for your p-value. For your expected frequency table, leave your answers in 4 decimal places.)

Question 7 - Summarise your conclusions. Specifically, will you proceed to have further discussions with Paul on the takeover of the business? Explain statistically using the results obtained from question (1) to (6).