Apply the Concepts of Inference Statistics Through the Application of Appropriate Testing Methods on a real case Scenario: Business Statistics Assignment, TP, Singapore

OBJECTIVE OF THE ASSIGNMENT
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. Driven by his passion for food and his “You Only Live Once” attitude, David decided to give up his full-time security job to become a hawker some years ago. David started his first Mala Hotpot hawker stall in Bedok. Two years later, he started his second Mala Hotpot hawker stall in Jurong. Both stalls sell identical food with the same pricing and operating hours. All his business decisions are made based on his gut feel.

3. Recently, you met David who was once your close friend from your secondary school days. David heard that you are taking a Business Program diploma and he seek your assistance to give him some professional inputs into his existing business. You agreed to help.

4. To help you with the analysis, you asked David to track the daily revenue collected and the number of customers served at both hawker stalls for 3 months. At the end of the 3 months, David sent the details of this information to you in a data file to your chat in MS Team. Apply all the inference statistical concepts and tools that you have learnt from Unit 6-9 to help him 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.

Question 2: (Leave your answers in 4 decimal places.)
Based on some market research information, the population mean the amount that each customer spent at hawker stall eating Mala Hotpot is $8.60 per visit. David would like to reward his staff operating the stalls if they can get customers to spend more per visit. He is prepared to give a reward of $500 for each staff if the average amount spent per customer for the month is more than $9.00. However, he is unsure if this is a realistic target that will motivate the staff. Help David by calculating the following:

2a) What is the probability for staff operating the Bedok stall to get the reward?

2b) What is the probability for staff operating the Jurong stall to get the reward?

Question 3: (Leave your answers in 4 decimal places.) According to David, there is another Mala Hotpot stall operating within the same vicinity as his Bedok stall. This Mala Hotpot stall which sells identical food and has similar pricing is in direct competition with David’s Bedok stall. His competitor has been boosting to him that his Mala Hotpot business is generating $2200 of revenue daily.

David is unsure whether to believe him or not. Construct the 98% confidence interval for the population mean daily revenue for the Bedok Mala stall. Is there any grounds to doubt the claim made by David’s competitor? Explain statistically.

Question 4: (Leave your answers in 4 decimal places.)
David believes that the Jurong stall is making more than $2080 of revenue daily. At the 5% level of significance, can you agree with the claim made by David?

Question 5: (Leave your answers in 8 decimal places for your p-value.) With the direct competition at Bedok stall, David believes that the business at his
Jurong stall is now performing better than his Bedok stall. At the 5% level of
significance, can you agree with David that the mean daily revenue from Jurong stall is better than the mean daily revenue from Bedok stall? State any assumptions made.

Question 6: You remembered David saying that the daily number of customers eating at both the Mala Hotpot stalls is the same regardless of the day of the week.

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

6b) At the 5% level of significance, can you agree with David that the daily number of customers served at each of the Mala Hotpot stalls is independent to the day of the week?