# Business Analysis Assignment 2

**Paper, Order, or Assignment Requirements**

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

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