INSTRUCTIONS
The survey can be used to answer many interesting questions but for this assignment you are required to focus on the specific questions listed below.
Your report must follow the format below.

You MUST use the word document (which will be provided to you on Moodle as a separate file) to insert your answers.

 
Due Dates:

Your sample of 100 (Excel file) to be submitted through Turn it in by 1st April, 5:30pm

 

Your Report (word file) to be submitted through Turn it in by 14th May 11:55pm. In addition to this, a hard copy (printed copy) of your report is to be submitted to your teacher.

 

 
Cover Page
 
An investigation into the under-filling of tuna cans and the demand for a new product
 
Teacher’s  Name:             _________________________________
 
Classs (e.g. Class 3)          :_________________________________
 
 

Student No
Name
Student contribution*
(%)
Student Signature

 
 
 
 

 
 
 
 

 
 
 
 

 
 
*We expect all group members to exert an equal amount of effort on all questions of the assignment. Students are not allowed to divide sections.
If a student has contributed to only some sections, the contribution of the student should be equal to the marks it carries. A student with less than 100% contribution will receive marks proportional to their contribution.
YOU MUST ATTACH a signed copy of this cover sheet to the assignment complete with each student’s contribution to the assignment.
 
 
 
I.                  Introduction: (5% marks)
Provide a brief introduction to what this assignment is about and how your sample was selected?
 
 

 

Data Analysis (80 marks):

This section must answer the following specific questions
Section A: Basic Analysis (30 marks)

Brand demand: (6 marks)
Calculate the proportion of customers who purchased brand A and brand B. Report your results in the following table. (2 marks)

Brand
Sample proportion

A
 

B
 

 

Use an appropriate chart to graphically display Information 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)
 
 
 
 
 

Weights of Tuna cans by brand: ( 7 marks)

Complete the following table ( 3 marks)

 
Brand A
Brand B

Minimum weight
 
 

Maximum weight
 
 

Range
 
 

Average weight
 
 

Standard deviation
 
 

 

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

ANSWER
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Frequency distribution: (10 marks)
Complete the following 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
 
 
 
 
 
 

 
 
 
 

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

 
ANSWER:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

What proportion of each brand of cans is under-filled? Recall “under-filling” means the can is under-filled by 2 or more than 2 grams? (i.e. the can contains 2 or more than 2 grams less than what is specified on the label).  (3 marks)

ANSWER:
 
 

 

Under-filled or not? (7 marks)
Complete the following 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
 
 
 

 

Use an appropriate chart to graphically display the above table.

Is the under-filling behaviour of brand A’s producer any different from that of brand B’s producer? (3 marks)
ANSWER:
Insert Graph here
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Insert your Comment here
 
 
 
 
Section B: Intermediate level Analysis (20 marks)

Potential Demand for NT Tuna (12 marks)

Complete the following 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%
 

 

Using 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 line” using Excel displaying its equation and the value of R-squared. (3 marks)

ANSWER:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Provide an 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 the type of relationship.   (3 marks)

ANSWER:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

What discount should be offered to customers if the producer of the NT tuna product wants to capture 25% of the existing market? (3 marks)

ANSWER:
 
 
 
 
 
 
 
 
 
 
 

Potential Demand for NT Tuna: Market captured by Brand (8 marks)

Complete the following 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%
 
 

Using 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)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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)

ANSWER:
 
 
 
 
 
Section C: Advance scenarios (30 marks)

Suppose, you randomly selected a customer. How likely is it that the customer will purchase

brand A
brand B

Provide 95% interval estimates for each of the above. Show the confidence intervals graphically and interpret your results. (7 marks)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Provide point and 95% confidence interval estimates for the weight of tuna cans, show it graphically and interpret your results. (7 marks)

ANSWER:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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 involved in hypothesis testing. ( 8 marks)

ANSWER:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Suppose brand B’s producer claimed that less than 20% of their cans are under-filled. Test the validity of this claim at 5% level of significance. Clearly show the steps involved in hypothesis testing. (8 marks)

ANSWER:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

Summary and discussion (15 marks):

Summarize your results and critically evaluate the survey method used in this assignment.
Some Examples:

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

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