Order Description
A note on how grades will be awarded:
Three of the four questions below relate to performing tests of statistical significance on data. In these questions marks will be awarded for the computations performed, and, the presentation of the workings. In order to get full marks in these questions, you will need to:
? State the null and alternative hypothesis;
? State the test statistic and how this statistic will be distributed if the null hypothesis is true;
? Calculate the value of the test statistic;
? Calculate the p-value associated with this test statistic;
? State whether the null hypothesis can be rejected at an appropriate significance level (in
order to do this, state the significance level you are applying and why).
? Illustrate this in a sketch of the distribution and the resulting test statistic.
MBUMD1BAN Ayodeji Oguntona BA2_219
?
Question 1
?Below are the quarterly returns on investment (in £000s) of two different investment projects which had the same initial outlay. There is a sample of 16 quarters of returns and your manager has asked you to investigate the relative performance of each project. In particular, your manager suspects that ‘Investment B’ outperforms ‘Investment A’ and she would like you to test this hypothesis. Perform an appropriate statistical test that incorporates your manager’s hypothesis.
Hint: in this question you will need to calculate the mean and standard deviation of each investment, assume that both returns come from independent samples, are both normally distributed and that the true (but unknown) variances are not the same.
[25 marks]
?????Quarter
Investment A
???Investment B
??2012Q1
89
??94
??2012Q2
86
??87
??2012Q3
96
??120
??2012Q4
94
??101
??2013Q1
94
??99
??2013Q2
98
??107
??2013Q3
92
??90
??2013Q4
86
??106
??2014Q1
101
??97
??2014Q2
90
??79
??2014Q3
92
??116
??2014Q4
88
??101
??2015Q1
93
??102
??2015Q2
89
??96
??2015Q3
90
??123
??2015Q4
93
???102
????????????????
Question 2
?The table below represents the results from 100 different marketing campaigns performed over three different products; the table splits between the products (Product A, B and C), and between the success of the marketing campaign, segregating between those which demonstrate: no increase in sales before and after the campaign; and, an increase in sales compared to before the campaign.
Your manager thinks that the success of the marketing campaigns is different across different products, but she does not know if this result is statistically significant. Test this hypothesis with an appropriate statistical test.
[20 marks]
Question 3
The head office of a large retailer feels that one of its stores is outperforming the overall sales of their UK shops in general. They would like to promote this fact, and further, try to learn and understand more about their success. However, they want to know that this result is a fair interpretation of the data, and ask you to perform a test of statistical significance on this result.
The national monthly sales for the retailer are normally distributed with a mean of £57,000 and a standard deviation of £9,500. For the individual store in question, there are data for 12 months of sales which has a sample mean of £68,000. Perform a statistical test on the claim that the store is outperforming the UK average, assuming that monthly sales are normally distributed.
[15 marks]
Question 4
For one of the questions above, prepare a short report on the results. Do this assuming a wide audience with differing levels of knowledge in the area of statistics and hypothesis testing (therefore, explain the processes involved in simple but formal language). In particular, discuss the following:
? The idea behind hypothesis testing and why this is important;
? The process performed in order to get the results, the key assumptions in this process, and
the appropriateness of these assumptions to the question;
? The result, how to interpret the result, and the meaning of the p-value.
Within this, feel free to bring in other knowledge you have from the question which you did not apply in previous questions that you feel would best describe the process and result to a wide audience (for example, calculating other factors from the numbers and/or graphs). This is meant to be a (very brief) report which you would happily present in a business format.
Although there is no formal word limit, 500 words is a good length in order to bring together all arguments required for this question.
[40 marks]
Product A
Product B
Product C
No increase in sales
6
21
35
Increase in sales
9
9
20