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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]

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