Question 1

a. Construct the frequency distribution for the number of customers served for both Bedok stall and Jurong stall using a class interval of 20 with 200 as the lower limit of the first class. (Use 4 decimal place for relative frequency)

b. Construct a histogram for each stall from the frequency distribution table generated in part a. Comment on the shape of the histogram.

c. Calculate the sample mean, sample variance and sample standard deviation for the following measures shown in the table below.
(Suggest to use 4 decimal places)

Question 2

“Based on his gut feel, David assumed that as more customers are served each day, more revenue would be earned each day too.”

a. From the above statement, identify the independent and dependent variable.

b. Based on David’s assumption, what is the type of relationship that you expect from the 2 variables you identified in part (a). (2 marks)

c. Plot scatter diagrams for the 2 variables identified in this relationship for each stall. Use the scatter diagram to either support or refute the assumption made by David.

Question 3

a. David is wondering if the daily revenue at his Bedok stall is dependent on the average amount spent per customer. Can you determine whether David is correct? Use the appropriate correlation analysis techniques to help David to verify this.

b. David would now like to develop a linear regression model that helps him to determine the daily revenue for his Bedok Stall. Construct a linear regression equation for the Bedok Stall and explain the value of b in the equation statistically.

c. Using the linear regression equation constructed in part (b), estimate the daily revenue if the average amount spent per customer is $8.50.

Question 4

Based on some market research information, the population mean amount that each customer spent per visit on Mala Hotpot at the hawker stall is $8.60. 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:

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

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

Question 5

According to David, another Mala Hotpot stall operates 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 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 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 6

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 7
Summarise your findings to share with David.