Business Information Analysis Assessment 1 Assignment Help: Probability Tree
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Business Information Analysis
Assessment 1 Instructions
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If easier to do, scanning in hand-written work using university printers (Select the ‘Workflow scanning’ option from the home menu of the Xerox photocopiers). Alternatively, placing hand-written work into word-processed documents using photo images is acceptable.
Marking criteria:
Question 1 Measures of Central Tendency [30 marks]
Table 1. Communication Methods
To survey methods of communications with their clients, a company records the number of times post and telephones were used (Table 1).
- Summarise this data in an appropriate chart. [5 marks]
- Calculate the measures of central tendency (mean, median, and mode), including measures of dispersion (standard deviation and range). [20 marks]
- Use the measures calculated in (c) to describe and compare the two methods. [5 marks]
Question 2 Probability [15 marks]
Probability Trees are closely related to decision trees, which are used in finance and other fields in business.
A survey states that 65% of a product is manufactured by Cilico and AUM manufactures 35%. 8 % of the products from Cilico are defective. 12% of the products from AUM are defective.
a. Produce a tree diagram to represent this information. [6 marks]
ii. A person purchases a new product.
b. What is the probability that the product was from Cilico?
c. What is the probability that the product was from AUM? [2 marks]
iii. The product is tested for defects.
d. What is the probability that a defective product was from Cilico?e. What is the probability that a defective product was from AUM? [4 marks]f. What is the probability that a product is defective in general? [3 marks]
Question 3 Binomial Probability [25 marks]
You own your own consulting firm in Business Information Analytics. You charge $350 and hour.
A small tourist resort has a weekend traffic problem and is considering whether to provide emergency services to help mitigate the congestion that results from an accident. Past records show that the probability of an accident on any given day of a four-day weekend is 0.25. The cost to the community caused by congestion from an accident is as follows:
- a weekend with 1 accident day costs £20,000
- a weekend with 2 accident days costs £30,000
- a weekend with 3 accident days costs £60,000
- a weekend with 4 accident days costs £125,000
As part of its contingency planning, the resort needs to know:
a. The probability that a weekend will have no accidents [5 mark]
b. The probability that a weekend will have at least two accidents [10 marks]
c. The expected cost that the community will have to bear for an average weekend period [7 marks]
d. Whether or not to accept a tender from a private firm for emergency services of £20,000 for each weekend during the season. [3 marks]
(Hint: Assume the accidents are independent events.)
Question 4 Hypothesis Testing [35 marks]
Table 2. Quarterly returns on investment (in £000s)
The quarterly returns on investment (in £000s) of two different investment projects that 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. She 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 the same.
Prepare a short report of the results and discuss the following:
- Is hypothesis testing important? Explain in detail. [10 marks]
- Explain the process to get the results, the key assumptions in this process and report back to your manager. [25 marks]
(Word limit: approximately 500 words)
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