STA60104 Quantitative Methods for Business Assignment Discuss whether the two options increase the number of items purchased.
Question 1 (17 marks)
A store manager wants to increase the number of items each customer buys. The current probability distribution for the number of items purchased is given in a table. Two options for increasing the number of items purchased are being considered: offering more discounts to customers (Option 1) or reconfiguring the store layout (Option 2). The revised probability distribution for these options is also provided in a table.
- (a) Discuss whether the two options increase the number of items purchased. (6 marks)
- (b) Determine and justify which option is more effective in increasing the number of items purchased. (2 marks)
- (c) Discuss whether the two options increase the variability in the number of sales. (9 marks)
Question 2 (13 marks)
The government of a country is designing a subsidy policy based on the income of its citizens. The income is normally distributed with a mean of RM5000 and a standard deviation of RM1000. Citizens are divided into three groups with subsidies given as follows: Group I (lowest 30%) receives RM6000, Group II (middle 50%) receives RM3000, and Group III (highest 20%) receives no subsidy.
- (a) Determine the approximate range of incomes for each group. (8 marks)
- (b) Evaluate the mean and standard deviation of the amount of subsidy per year. (5 marks)
Question 3 (19 marks)
A retail owner wants to compare the monthly revenue of two outlets. The monthly revenue for 4 years is given in a table. The following tasks are required:
- (a) Identify the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum for the monthly revenue for both outlets. Use the Excel function QUARTILE.EXC to find Q1, Q2, and Q3. (5 marks)
- (b) Compute the lower and upper outlier limits for the revenue of both outlets. Determine if there are any outliers. (4 marks)
- (c) Based on the quartiles and outlier limits, produce box and whisker plots for both outlets and compare them in terms of the median, spread, and shape. (5 marks)
- (d) From the box and whisker plots, is it reasonable to conclude that Outlet A typically shows higher monthly revenue than Outlet B? (2 marks)
- (e) The owner speculates that the revenue for Outlet A correlates with the revenue for Outlet B. Discuss whether this speculation is valid. (3 marks)
Question 4 (21 marks)
A retail company with 45 outlets is collecting data on variables that might affect weekly sales. The attached Excel file contains data on the weekly sales and corresponding variables. (This question requires further analysis in Excel.