# Stats

STATS1900Business Statistics

Major Assignment

Date Due:

Refer to Course Description

Total Marks:40

Worth: 20%

of final assessment

This assignment

requires a considerable amount of computer work and written comment. You may

need to seek guidance from your tutor along the way. Do not leave things until

too late. Each question carefully describes what you are required to do, so

please follow these carefully.

In this

assignment, you will again examine data from afruit and vegetable market that supplies fresh produce

to supermarket outlets in NSW and Victoria. The market is conducting an

evaluation of customers in Sydney and Melbourne.Thefruit and vegetable marketwants toexamine the%

of produce damage at each of the outletsand is particularly

interested in the relationship between% produce damagewith: the

type of produce; the customer; and,quantity (sold per day).

The data collected is contained in a file called ‘Fruit and Veggie Market.xls’and the

columns of the file contain the following information:

Column

Name

Description

A

ID Number

Customer

Number

B

Customer

1= Coles

2=Private

3= Safeway

C

City

1= Sydney

2= Melbourne

D

Produce

1= Apple

2= Orange

3= Potato

4= Tomato

E

Quantity

(sold/day)

Total

quantity of produce sold per day

F

Price$/kg

Price in

dollars per kilogram

G

% of produce

damage

Percentage

of produce damaged

Use your random

sample of 200 customersfrom the minor assignment. Your answers to the assignment tasks

below are to be based on your sample

of200 customers. Make sure you keep a safe copy of your sample, since you cannot

use Random Sample Generator to reproduce the first sample. (If necessary, talk

to your tutor about generating a new sample.)

Assignment Tasks

For each task below, you must submit all of

the required printouts, graphs, tables and summaries required.

NB:Each graph and table should have a

heading and each axis should have a label!!

1. Introduction and Variable List:Give a brief introduction to your report,

setting out the nature of the data.[1

mark]

2. Data:

Provide a printout of the data in your sample, sorted in ascending order based

oncustomer number.

[1 mark]

3. Pivot Table:Prepare

a contingency table (cross-classification) using the Pivot Table option in

Excel that compares types ofproduceand customers. You may use counts or

percentages as the basis of comparison. Compare any similarities or differences

in the types ofproducesold, betweenColes and Safeway.[2 marks]

4. Pivot Table:Prepare

another contingency table that shows the average

(mean) price$/kgand average (mean) %

of produce damaged, classified bycustomerand

the type ofproduce. Compare any

similarities or differences among the customers

with regard to prices, and damagedapples, oranges and tomatoes:

a) Which customerhas

the highestaverage (mean) price$/kgfor

apples, and which for oranges?

b) Which customer has the highest mean % of produce damagedfor tomatoes,

and which for apples? [4 marks]

5. T-Test:The

market wants to investigate the % of produce damaged atColes’

stores in Sydney and Melbourne so they can make a comparison with other states.

The current data will be used as a typical representation of the % of

produce damaged.

a) Determine the mean, standard

deviation and standard error for the % of produce damaged at Coles’

stores in your sample.[2 marks]

b) The market has found that, on

average, there is no more than 5% produce damage at Coles’ stores in other

states. Based on this information carry out a t-test to see if the average % of

produce damaged at Coles stores in Sydney and Melbourne is more than 5%. Mention any assumptions, include relevant

hypotheses and report the result and conclusion in the conventional manner.[6 marks]

6.

Obtain

a scatterplot of the % of produce damaged and price$/kg for all customers.Think carefully about which variable should go on the

vertical axis. Remember, it is the independent variable that goes on the

horizontal axis (i.e. the x-axis). Make

sure you label your axes properly and that your graph has an appropriate title.

[3 marks]

7. Briefly describe the

nature of the relationship between these two variables (Hint: mention strength

and direction).[2 marks]

8. Use Excel to carry out a

regression analysison two variables: % of produce damaged(independent

variable) and price$/kg (dependent

variable).

a) Copy the output into your

assignment and then use it to determine the answer to the following questions.[2 mark]

b) Write down the regression

equation. [1 mark]

c) State the R-squared value and the

standard error and explain what they mean with respect to the data. [4 marks]

d) Write down the value of the

gradient of the regression line and explain what it means in the context of this

question. [3 marks]

e) Are the values for the constant

and intercept (slope coefficient) significant in this case? Justify your answer

using values from the output.[3marks]

f) Do you think this regression model

is a good model? Justify your answer using the regression output.[3 marks]

9. Using the information obtained for

your analyses write a short conclusion about what you found out about the relationship

between the % of produce damagedand price$/kg,

and how this relates to customerand

the type of produce. [3

marks]

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