Stats

| October 22, 2018

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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