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OBJECTIVE
1. To apply the concepts of inference statistics through the application of appropriate  testing methods on a real case scenario and draw appropriate conclusions. (Unit 6 - 9).


CASE STUDY


2. 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.
3. 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 marking.


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.


4. 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


(Leave your answers in 4 decimal places.)
Calculate the sample mean, sample variance and sample standard deviation for the
following measures shown in the table below. (6 marks)

 

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
(Leave your answers in 4 decimal places.)
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?
(6 marks)
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
2b)

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?
(6 marks)


Question 3
(Leave your answers in 4 decimal places.)
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. (10 marks)


Question 4
(Leave your answers in 4 decimal places.)
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.  (17 marks)

Question 5
(Leave your answers in 8 decimal places for your p-value.)
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)
(20 marks)

 

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 :

(5 marks)


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? (20 marks)

(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). (10 marks)

Down load the Data for the project.

 

Question five

Let’s assume that population 1 is Average No. of Delivery trips per day per driver (2018) and population 2 is Average No. of Delivery trips per day per driver (2017). The level of significance is 5%.

The P value is 0.00000012. Since the p value is less than the significance level the null hypothesis is rejected. I can 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.

Conclusion:

I would proceed to have further discussions with Paul in regard to the delivery business. This is because, based on the data provided, it was determined that the  mean number of deliveries made by each driver per day (based on 2018 performance) is more than 20.5.  This value is greater than the minimum value of 20 given by previous research in order to breakeven. The analysis has also revealed that the mean number of trips made by each driver per day has improved after the implementation of the new delivery system. It has also been determined that the daily volume of business (in terms of mean number of deliveries made) is independent to the day of the week. However, there are a few key points to note such as the probability of breaking even was too low, or almost non-existent. Financial statements would be useful to shed more light on this issue. The analysis showed that an average of 6 drivers per day on MC is not accurate. This average is higher than Paul let on.

 

 

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Solutions for this project have been prepared in an Excel Sheet, Therefore, most calculations and obtaining of the p - values were done using the Excel functions.  The first problem is about descriptive analysis. Remember the  = average() and the Stdev() functions in Excel and the = Var Function?

Answers to Question 1      
       
  Number of Delivery Trips per Day per Driver (2017) Number of Delivery Trips per Day per Driver (2018) Average Number of Delivery Staff on MC per day
Sample Mean 19.4467 21.2525 6.9690
Sample Standard Deviation 2.2915 2.2325 0.7013
Sample Variance 5.2511 4.9842 0.4918

Questions 2:

The second question is on hypothesis testing, that is finding the probability of a mean of 20 or more.

a)      The sample is assumed to be normal since the sample size is large enough, that is, it is greater than 30. A delivery company needs a minimum of 20 trips per driver per day in order to break even. We hence need to find the probability that the mean number of trips per day is 20 trips per driver per day or more.

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