## Data Analysis

Section A: Basic Analysis (30 marks)
1. Brand demand: (6 marks)
A. Calculate the proportion of customers who purchased brand A and brand B. Report your results in” rel=”nofollow”>in the followin” rel=”nofollow”>ing table. (2 marks)
Brand Sample proportion
A
B

B. Use an appropriate chart to graphically display Information in” rel=”nofollow”>in the table above and summarize your conclusions on brand popularity. (Which brand is the most popular?)

Insert Graph here: (2 marks)

Summary/conclusion. (2 marks)
2. Weights of Tuna cans by brand: ( 7 marks)
A. Complete the followin” rel=”nofollow”>ing table ( 3 marks)
Brand A Brand B
Min” rel=”nofollow”>inimum weight
Maximum weight
Range
Average weight
Standard deviation

B. Compare the average weight and spread of weights by brand. (4 marks)

3. Frequency distribution: (10 marks)
A. Complete the followin” rel=”nofollow”>ing frequency distribution table for each brand weight of cans. (4 marks)
Class Frequency Relative Frequency
(%) Cumulative Relative Frequency (%)
A B A B A B
86 to 90
90 to 94
94 to 98
98 to 102
102 to 106
106 to 110
More than 110
Total

B. Use appropriate charts to plot the relative frequency distribution and cumulative relative frequency distribution table. ( 3 marks)

C. What proportion of each brand of cans is under-filled? Recall “under-fillin” rel=”nofollow”>ing” means the can is under-filled by 2 or more than 2 grams? (i.e. the can contain” rel=”nofollow”>ins 2 or more than 2 grams less than what is specified on the label). (3 marks)

4. Under-filled or not? (7 marks)
A. Complete the followin” rel=”nofollow”>ing cross classification table (2 + 2)
Cross classification table by frequency
Underweight? Total
Yes No
Brand A
B
Total

Cross classification table by brand total relative frequency
Underweight? Total
Yes No
Brand A
B
Total

B. Use an appropriate chart to graphically display the above table.
Is the under-fillin” rel=”nofollow”>ing behaviour of brand A’s producer any different from that of brand B’s producer? (3 marks)
Insert Graph here

Section B: Intermediate level Analysis (20 marks)
5. Potential Demand for NT Tuna (12 marks)
A. Complete the followin” rel=”nofollow”>ing table (3 marks)

Discount offered Proportion of ALL customers who said they will buy the new product
x y
0%
5%
10%
15%
20%
25%

B. Usin” rel=”nofollow”>ing Excel, (i) construct a scatter plot of the discount offered on the new product (NT tuna) and the proportion of customers who said that they will buy the new product if they are offered the stated discount and (ii) fit a “least squares lin” rel=”nofollow”>ine” usin” rel=”nofollow”>ing Excel displayin” rel=”nofollow”>ing its equation and the value of R-squared. (3 marks)
C. Provide an in” rel=”nofollow”>interpretation of the output (Intercept, slope and R-squared). Is there any relationship between discount offered and potential demand for the NT tuna? If so, explain” rel=”nofollow”>in the type of relationship. (3 marks)
D. What discount should be offered to customers if the producer of the NT tuna product wants to capture 25% of the existin” rel=”nofollow”>ing market? (3 marks)
6. Potential Demand for NT Tuna: Market captured by Brand (8 marks)
A. Complete the followin” rel=”nofollow”>ing table (3 marks)

Discount offered Proportion of customers who said they will buy the new product
Brand A Brand B
x yA yB
0%
5%
10%
15%
20%
25%
B. Usin” rel=”nofollow”>ing Excel, construct scatter plots of the discount offered on the new product (NT tuna) and the proportion of each brand’s customers who said that they will buy the new product if they are offered the stated discount.
Which brand’s customers are more loyal to their brand? (3 marks)
C. What proportion of each brand’s market will the NT tuna producer capture if it decides not to give any discount and offer the product at the same price as the other brands? (2 marks)
Section C: Advance scenarios (30 marks)
7. Suppose, you randomly selected a customer. How likely is it that the customer will purchase
i. brand A
ii. brand B
Provide 95% in” rel=”nofollow”>interval estimates for each of the above. Show the confidence in” rel=”nofollow”>intervals graphically and in” rel=”nofollow”>interpret your results. (7 marks)
8. Provide poin” rel=”nofollow”>int and 95% confidence in” rel=”nofollow”>interval estimates for the weight of tuna cans, show it graphically and in” rel=”nofollow”>interpret your results. (7 marks)

9. Suppose brand A’s producer claimed that the average weight of their products is 100gm. Test the validity of this claim at 5% level of significance. Clearly show the teps in” rel=”nofollow”>involved in” rel=”nofollow”>in hypothesis testin” rel=”nofollow”>ing. ( 8 marks)