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.The fruit and vegetable market wants toexamine the % of produce damage at each of the outletsand is particularly interested in the relationship between % produce damage with: 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:

Use your random sample of 200 customersfrom the minor assignment. Your answers to the assignment tasks below are to be based on your sample of 200 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]

1. Data: Provide a printout of the data in your sample, sorted in ascending order based oncustomer number.                                                                  [1 mark]

1. 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 ofproduce sold, betweenColes and Safeway.[2 marks]

1. 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 damaged for tomatoes, and which for apples?                                           [4 marks]

1. 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]

1. 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]

1. Briefly describe the nature of the relationship between these two variables (Hint: mention strength and direction).[2 marks]

1. 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]

1. 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 customer and the type of produce.      [3 marks]

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