This assignment consists of 2 problems and 1 essay and will test your understanding of what you have learned in Quantitative Methods. You will also demonstrate your use of statistical software like Minitab or Excel.
In assignments, always show all your working, making sure that your methods are fully explained. Your diagrams should be neat, accurate and large enough to see the details. All diagrams and graphs must have an explanation of what they show.
Two printed and stapledcopies of your assignment need to be handed in(including a standard INTO front sheet on both copies) and an electronic copy mustbesent to Carolyn van Lottum.
Show all work and justify your answers. Explain the meaning of any statistics included in your assignment.
Problem 1: What influences the price of a second hand car?
Marks available in question: 50
There are many variables that affect the price of a second hand car, for example, engine size, age, mileage etc. The aim of this study is to select 2 variables that could influence price and to analyse their effect on price using regression and correlation.
Before you start your data collection it is important to consider the issue of confounding.
i) In your assignment explain what a confounding variable is. Consider what confounding variables could be present in this problem. Think about how you could avoid confounding and explain any steps that you take to deal with confounding variables. Discuss any unwanted factors in your sample that it was not possible to avoid.
ii) Collect a sample of car data (price and your two variables) to analyse. You can find the price of a range of second hand cars on websites such as Autotrader.co.uk.
Analysis of your data
iii) Use Graphs (such as scatter plots) with Regression and Correlation to analyse both of your chosen variables.
iv) Interpret the analysis results
v) Explain whether or not your selected factors are good predictors of price. If they are not good predictors, explain why you think that might be the case. How could the predictions be improved?
• Selecting sensible factors, explaining confounding factors, identifying potential confounding factors in the analysis, explaining the sample selection(12 marks)
• Using appropriate graphs and making relevant comments about eachgraph (10 marks)
• Calculating a regression lines and correlation coefficients (8 marks)
• Analysing the data using regression and correlation (individually for both variables) and making appropriate comments about the regression and correlation results and the validity of the regression equations (20marks)
Size for Problem 1: Maximum 6 sides of A4, including graphs (excluding data tables which should be added as an appendix).
Problem 2: Is the machine set correctly?
Marks available in question: 20
A manufacturer makes small colourful fruit flavoured sweets. Each packet of sweets contains a mix of colours, red, green, yellow, orange, purple
Through extensive market research the manufacturer found out that the best mix of colours in a packet is as follows;
Red Green Yellow Orange Purple
25% 15% 20% 25% 15%
This is the combination that customers prefer.
The company uses a machine that mixes the coloured sweets together according to how many of each colour should be in the packet. The company are concerned that the machine is not working correctly (a recent sample showed a low number of yellow sweets in the mix). You will be given a sample of sweets to test. You need to determine if the count of each colour in the sample matches what is expected. You need to decide whether or not the machine is working correctly. To do this you must use a hypothesis test.
• Well designed and reported hypothesis test, which follows and describes all the key steps of a hypothesis test (16 marks)
• Appropriate advice given to the manufacturer taking into consideration issues such as the outcome of the hypothesis test and whether there is the possibility of errors (4 marks).
Size for Problem 2: Maximum 3 sides of A4, including data table.
II. Essay: Using the Normal Distribution in Business
800 words – Marks available in question: 30
When you write your essay you should look for secondary data and resources to help you. Use at least 3 books and/or e-journals. In addition to the books and e-journals you may also use websites; but only those provided by sources from which you can reasonably expect valid expert opinion,high quality and up-to-date information (for example, government, university and professional association websites). Reference all sources of information fully.
In statistics we talk a lot about normally distributed data. Explain where and how the normal distribution is used in real life, in business. Use at least three examplesfrom business to illustrate how it can be practically applied. However, not all business data is normally distributed, discuss a circumstance where the normal distribution cannot be used.
• Where and how the distribution can be used with a minimum of three applications (referenced from sources) within business (20marks)
• When can the normal distribution not be used (6 marks)
• General essay structure (including introduction, conclusion, references) (4 marks)