Need Help With statistic work. Hypothesis testing

#1
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 90 100
2012Q2 84 99
2012Q3 92 95
2012Q4 87 98
2013Q1 88 88
2013Q2 97 99
2013Q3 96 92
2013Q4 85 96
2014Q1 97 102
2014Q2 94 91
2014Q3 89 103
2014Q4 89 106
2015Q1 92 120
2015Q2 86 106
2015Q3 90 97
2015Q4 94 110

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.

Product A Product B Product C
No increase in sales 5 14 49
Increase in sales 15 11 6

[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 £51,000 and a standard deviation of £10,000. For the individual store in question, there are data for 12 months of sales, which has a sample mean of £54,000. Perform a statistical test on the claim that the store is outperforming the UK average, assuming that monthly sales are normally distributed.
[15 marks]