# Statistic

**Topics:**Net present value, Regression analysis, English-language films

**Pages:**6 (863 words)

**Published:**April 15, 2013

Please use BLOCK CAPITALS: First name Last name Student number ……….……….……….……….……….………. ……….……….……….……….……….………. ……….……….……….……….……….……….

Instructions You have 50 minutes to complete the test. Attempt ALL questions. Answers must be provided on the test paper. The paper is worth 30 marks. The available marks are indicated alongside each question. Incorrect answers and questions left blank will score zero. Calculators are permitted. No books or paperwork are permitted.

1

1. The following Box plots show the salaries of the top 50 tennis players and the top 50 basketball players in 2004. The amounts shown are to the nearest £100,000.

a) From the Box plots, estimate: i. ii. The Five Figure Summary for the tennis players and The Five Figure Summary for the basketball players.

[4 marks] b) Use the Box plots and the Five Figure Summaries to compare the salaries received by the tennis players and the basketball players.

[3 marks]

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2. Your financial adviser offers you the opportunity to invest ion a financial project, Abekus. It requires you to put up an amount of £10,000 now. The interest rate, i, is assumed to be 12% throughout the life of the project. The following excel table shows the estimated inflows and outflows of cash for the next six years of the project. Partial Net Present Value (NPV) calculations are also shown in this table. Year 0 1 2 3 4 5 6 Inflow 0 £14,000 £11,000 £10,000 £8,000 £4,000 £3,000 Outflow 10,000 £4,000 £3,000 £4,000 £3,000 £1,000 £1,000 Net Cash Flow (A) -10,000 10,000 8,000 6,000 X 3,000 2,000 24,000 a) Calculate the value of X. [1 mark] Discount factor (df) 1 0.892857 Y 0.71178 0.635518 0.567427 0.506631 Present Value (P) -10000 8928.57 6377.55 4270.68 3177.59 Z 1013.26

df

b) Calculate the value of Y using

1 (1 i)n

.

[1 mark]

P

c) Calculate the value of Z using

A (1 i) n

.

[2 mark] d) Evaluate the Net Present Value of the Project

[1 mark] e) You are also offered the opportunity to invest in a second project, Belarus. It also requires you to put up an amount of £10,000 now. The NPV for this project is £13,822.17. Which project would you invest in? Explain your answer. 2 marks] 3

3. An estate agent in a large city would like to be able to predict the monthly rental costs (£) for flats based on the size of the flat as defined by square footage. Data is available for 25 flats and a regression analysis produced the following output. Scatterplot of Rent vs Size

2000 1800 1600

Rent

1400 1200 1000

600

800

1000

1200 Size

1400

1600

1800

Rent = 283 + 0.945 Size Predictor Constant Size Coef 283.1 0.9448 SE Coef 166.7 0.1440 T 1.70 6.56 P 0.103 0.000

S = 185.330

R-Sq = 65.2%

R-Sq(adj) = 63.7%

a) What does the scatter plot tell you about the nature of the relationship between Rent and Size? [1 mark] b) Write down the equation of the regression line of Rent on Size. [1 mark] c) Interpret the coefficient of Size in your regression line. [1 mark] d) Write down and interpret the value of the Coefficient of Determination. [2 marks] e) Estimate the rent for a flat with 1500 square feet. Comment on the reliability of your estimate. [2 marks]

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4. A manufacturer makes two products, X and Y. The usage of resources and the unit profit on each product is given by the following table: X (time in hrs) 5 3 1 30 Y (time in hrs) 12 4 5 100 Total time available (hrs) 2400 1200 800

Resource ASSEMBLY SPRAYING FINISHING PROFIT

The related graph is

350

300

250

200 B 150

A

C

100

50

D 0 0 100 200 300 400 500 600 700 800 900 1000

Use the above information to answer the following three questions. i) On the graph, shade the feasible region. [2 mark]

ii)

Write down the expression for the profit function by completing the following equation:

P

[1 mark] 5

iii) The following table shows these four points, with their coordinates and the profits at the points...

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