Assessment Type 2: Folio

Assessment Type 2: Folio

Topic 4: Statistics Is it a good buy?

The Task

You wish to purchase a used car. You want to use your maths knowledge to investigate if there is a connection between the number of kilometres that a car has travelled and its selling price, and determine if one brand of car appears to hold its value better than another.

Part 1: Population of cars

Choose two different brands/models of cars, and the year of manufacture that you wish to investigate. Using car sale websites (such as www.carsales.com.au ) or newspapers or other sources, collect data for the second hand cars for sale for the two brands/models you have chosen. When collecting your data, make sure that the population is large enough that you can choose an appropriate sample. Also make sure that you keep the two sets of data separate.

From these two populations of cars choose the one that you would like to purchase. Looking at the data that you have collected predict if this car that you would like to purchase has a good price when considering the number of kilometres that it has travelled.

Part 2: Getting a sample

Explain what sampling technique you will use (Stratified, Simple random or Systematic) and take an appropriate sized sample from the two populations. These samples will now be used for all further calculations.

A copy of both populations should be placed in the appendix.

Part 3: Linear correlation

For the two models of car for which you have collected data, investigate if there is a correlation between the kilometres travelled by the vehicles and the selling price.

In your mathematical investigations you may choose to consider:

effect of sample size used

outliers and their effect on the result

using the least squares regression line to make predictions.

Part 4: Analysis/Discussion

Critically analyse your results for the two models of car that you have investigated. You should consider:

is there a strong enough relationship for your sets of data for you to be able to make predictions

the appropriateness of the size of the samples used

the validity of any selling price predictions made using the least squares regression line you have determined for each car model

any assumptions and limitations of the investigation.

Part 5: Was your prediction about the car you chose correct?

Does the correlation that you determined for the model of the car you wished to purchase confirm your prediction about it being a good buy when considering the number of kilometres it has travelled?

The Response

Introduction

Read the whole task and write an introduction that outlines the task in your own words. Include what car you would like to purchase.

Mathematical Investigations

Complete Parts 2 and 3 and include your mathematical investigations in your response. If you cannot fit all of your correlation investigations in the main body of the response, consider including them in your appendices. Make sure that you refer to the results of any correlation investigations that are included in the appendices in the main body of your response, and include discussion of what each extra investigation shows.

Discussion and conclusion

Complete Parts 4 and 5.

Appendix

Include evidence such as:

population of cars.