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Question:

Below are some hints to help you with the evaluation of the survey method

Is the method of data collection consistent with random sampling? (overall data collection not the random sample that you have selected).

Should we be concerned about the fact that the data was collected at one location only (Northland Shopping centre) on multiple days?

Can this data be representative of all customers in Melbourne/Australia?

What should we do to reduce the concern you might have raised in your critical analysis?

 

Answer:

Introduction

Nowadays, there is a very common issue that is gaining the attention of the media. This is under weighing of canned products. It is claimed that the contents in the can have a net weight which is less than the weight specified on its label. This issue has been investigated in Australia on Tuna cans. Tuna cans are available in the market in two cans. These are Brand A and Brand B. Both the brands are of 100 gm net weight as per the label. Analysis has been conducted to test the claim of under weighing if the canned goods.

645 customers in total participated in the survey. From all the participants, a sample of 80 participants has been selected randomly to conduct this research.

Data Analysis

Basic Analysis

Brand Demand

The proportion of customers buying brand A and Brand B of Tuna cans are given in table 2.1 and illustrated graphically in figure 2.1. It can be seen clearly from the figure that The Brand B of Tuna cans have a popularity higher than that of Brand A of Tuna cans.

 


Table 2.1: Proportion of Customers Purchasing brands of Tuna cans

Brand

Sample proportion

A

0.35

B

0.65

Figure 2.1: Proportion of Customers Purchasing brands of Tuna cans

Weights of Tuna Cans by Brand

Table 2.2 shows the summary of the weights of Tuna cans of each brand. It can be seen from the table that the average weight of Tuna cans of Brand A is 101.66 gm whereas the average weight of Tuna cans of Brand B is 99.23 gm. Both the weights are close to 100 gm but not exactly 100 gm. This indicates that there are variations in the weights from the labelled weights. The standard deviations of the weights are very less. This indicates that most of the weights are close to the average weight.

Table 2.2: Table showing the Summary of the Weights of Two Brands of Tuna Cans

 

Brand A

Brand B

Minimum weight

94.3

90.4

Maximum weight

111.8

107.6

Range

17.5

17.2

Average weight

101.66

98.23

Standard deviation

3.73

4.08

Frequency Distribution

The frequency, relative frequency and the cumulative relative frequency for each of the brands are given in the following table 2.3. A can is said to be under filled if the weight of the tuna in the can is less than 100 gm by 2 grams or more than 2 grams. From the cumulative relative frequencies, it is found that the proportion of Tuna cans of brand A that is under filled is 0.14 and the proportion of Tuna cans of brand B that is under filled is 0.44.s

Table 2.3: Frequency Distribution table of Weights of Tuna Cans

Class

Frequency

Relative Frequency

(%)

Cumulative Relative Frequency (%)

 

A

B

A

B

A

B

86 to 90

0

0

0

0

0

0

90 to 94

0

8

0

0.15

0

0.15

94 to 98

4

15

0.14

0.29

0.14

0.44

98 to 102

12

20

0.43

0.38

0.57

0.83

102 to 106

10

7

0.36

0.13

0.93

0.96

106 to 110

1

2

0.04

0.04

0.96

1

More than 110

1

0

0.04

0

1

1

Total

28

52

1

1

 

 

Figure 2.2: Relative Frequency of the Weights of Tuna Cans

Figure 2.3: Cumulative Frequency of the Weights of Tuna Cans

Under-filled or Not

It can clearly be understood from the illustration provided in figure 2.4 that the producer of Brand B Tuna cans has a higher tendency of under filling the cans than the producer of the Tuna cans of Brand A.

Table 2.4: Cross classification table by frequency

 

 

Underweight?

Total

 

 

Yes

No

Brand

A

4

24

28

B

23

29

52

Total

27

53

80

Table 2.5: Cross classification table by brand total relative frequency

 

 

Underweight?

Total

 

 

Yes

No

Brand

A

0.05

0.3

0.35

B

0.29

0.36

0.65

Total

0.34

0.66

1

Figure 2.4: Frequency of Under Filled Tuna Cans

Intermediate Level Analysis

Potential Demand for NT Tuna

Table 2.6 shows the proportion of customers who would buy the new product (NT tuna), if the respective discounts were applied. With the help of the scatter plot in figure 2.5, relationship between the discounts and the proportion of people getting the new product is shown.

It can be seen clearly from the figure that with the increase in the discount percentage, the proportion of people buying the new product increases. The r squared value is found to be 0.90, indicating that the model is correct to 90 percent of the time. Further, it can be said that in the absence of discount, the proportion of people buying the new product is 0.22. With each percent increase in the discount on the new product, the proportion of people getting the new product increases by 1.46 percent.

If the producer of NT Tuna wants to capture 25 percent of the existing market, the discount offered on the product should be

Discount Offered = (0.25 – 0.22) / 1.46 = 2%

Table 2.6: Proportion of Customers buying the New Product with Discount

Discount offered

Proportion of ALL customers who said they will buy the new product

x

y

0%

0.18

5%

0.29

10%

0.44

15%

0.48

20%

0.50

25%

0.55

Figure 2.5: Scatterplot of Discount Offered

Potential Demand for NT Tuna: Market captured by Brand

By comparing the proportion of customers of each brand buying the new product with discount, it can be seen that there has not been much change in the proportion of customers of brand B buying the new product with the changes in the discount. Thus, it can be said from here that the customers of Brand B are more loyal to their brand.

From table 2.7, it can also be seen that if no discounts are offered and the same price is offered, then 0 percent of the market will be captured by Brand A and 27 percent of the market will be captured by Brand B.

Table 2.7: Proportion of Customers buying the New Product with Discount for each Brand

Discount offered

Proportion of customers who said they will buy the new product

 

Brand A

Brand B

x

yA

yB

0%

0

0.27

5%

0.14

0.37

10%

0.46

0.42

15%

0.5

0.46

20%

0.57

0.46

25%

0.68

0.48

Figure 2.6: Scatterplot of Discount offered for each Brand

Advance Scenarios

If a customer is selected randomly, it can be said from table 2.1 that the probability that the person will buy Brand A is 0.35 and the probability that the person will purchase Brand B is 0.65. It can be said with 95 percent confidence that the probability that a randomly selected customer will buy brand A will be between 0.25 and 0.45 and the probability that a randomly selected customer will buy brand B will be between 0.55 and 0.75.

 

Summary and Discussion

Thus, this assignment has been based on testing the under filled proportion of Tuna cans for the two brands that are present in the market. A new brand of Tuna was also introduced in the market. The existing customers of the old two brands were asked to weight their old Tuna cans and try the new brand.

It has been observed from the analysis so far that the proportion of under filled Tuna cans are higher for Brand B than from Brand A. Yet the customers of Brand B are more loyal to their brand and less proportion of existing brand B customers are interested in buying the new product even if significant discounts are provided. It has also been observed that Brand B has a more capture over the market than Brand A. Thus, Brand B is a more popular Brand than Brand A.

Hence, it will be a challenge for the new Brand of Tuna to capture the market over the existing Brand B. It has already been observed that the with the increase in the discounts, the customers of brand A are switching towards the new Brand. Hence, it will not be much problem to draw the Brand A customers. To draw the Brand B customers, some other policies has to be developed. The quality of the product has to be better than brand B and the price must be less. This can cause the customers to switch the brand.

OR

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