FIN10002 Final Examination Sem 1 2019 PDF

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Examination Cover Sheet SEMESTER 1, 2019 EXAMINATION DETAILS Faculty: Business, Design and Arts

Unit Code: FIN10002 Unit Title: Financial Statistics Duration: 180 min

Reading time: 10 min

50% of overall assessment covered by this exam

CANDIDATE DETAILS Student to complete (do not use pencil) Surname:

ID:

Given:

CANDIDATE DECLARATION • • • •

I am the person stated above I agree to obey the Examination Supervisors instructions for proper conduct of the exam I have read and understood the Instructions to Candidates provided (see back of this exam paper) I understand that it is my responsibility to ensure that I have been correctly enrolled for the above subject and that I am fully liable for any outstanding fees and charges • I am aware that I am not allowed to present for any special examination unless approval has been granted by the appropriate Swinburne or external authority

STUDENT SIGNATURE:

DATE:

INSTRUCTIONS TO CANDIDATES Material/equipment that is not on this list is unauthorised material. Where a student is found in possession of any unauthorised material: 1. That material will be removed as soon as it is detected; and 2. The Student Academic Misconducts Regulations and Student Administration Regulations will be implemented.

Materials Allowed: Students are NOT permitted to have any other material, including pencil cases, calculator cases, notes of any description, and any books.

Answering Instructions: 1. This exam is worth 50% of the available marks for this semester. 2. This exam paper consists of 100 marks. 3. This exam paper consists of two (2) sections: SECTION A (10 questions) SECTION B (5 questions) 4. Answer ALL questions in both sections. (i) Answer SECTION A in the Multiple-Choice Objective Answer Table on page 2. (ii) Answer SECTION B in the space of question booklet provided. Show the relevant steps for maximum marks. 5. There are 23 printed pages in this exam paper including the first page and instructions. 6. A seven-page Appendix is provided on pages 17 to 23. If you complete this exam before the set exam duration time, you may be asked to enter your time of departure. This information will have no bearing on your result.

SECTION A: MULTIPLE-CHOICE QUESTIONS [10 marks] Use the following Multiple-Choice Answer Table, write letter A, B, C or D that gives the correct answer to each question.

(1)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

A statistics professor asked students in a class their ages. Based on this information, the professor states that the average age of all the students in the university is 21 years. This is an example of: A. B. C. D.

(2)

a census descriptive statistics an experiment statistical inference

Weights of students in a school is a(n) _______________ level of measurement. A. B. C. D.

(3)

nominal ordinal interval ratio

A list of 5 pulse rates is: 70, 64, 80, 74, 92. What is the median for this list? A. B. C. D.

(4)

74 76 77 80

A researcher has collected the following sample data. The mean is: 5 A. B. C. D.

(5)

12

6

8

5

6

7

5

12

4

5 6 7 8

The most frequently occurring value of a data set is called the: A. B. C. D.

mean median mode range

FIN10002 Financial Statistics Final Examination Semester 1, 2019

Page 2 of 23

(6)

Which one of these statistics is unaffected by outliers? A. B. C. D.

(7)

One way to measure the spread is to calculate the difference between the third and first quartile. This measure is called: A. B. C. D.

(8)

Interquartile range Mean Range Standard deviation

differential quartile interquartile range mid quartile range second quartile

The mean of a distribution is 23, the median is 24, and the mode is 25.5. It is most likely that this distribution is: A. B. C. D.

asymptotic negatively skewed positively skewed symmetrical

(9) Assumption in calculating annuity is that every payment is: A. B. C. D.

different equal marginal nominal

(10) Interest rate per year is 16% and compounding occurs every quarter. Then, interest rate per compounding period is: A. B. C. D.

0.04% 0.4% 4% 40%

FIN10002 Financial Statistics Final Examination Semester 1, 2019

Page 3 of 23

SECTION B: STRUCTURAL QUESTIONS [90 marks] Use the space provided, show your workings to each sub-question. QUESTION 1

[24 marks]

(a) The demand for canned sardine, which is specialty of Salim Industries, varies greatly from month to month. Based on the past two years of data, the following probability distribution shows the company’s monthly demand. Unit Demand (canes) 300 400 500 600

Probability 0.20 0.30 0.35 0.15

(i) If the company prepares monthly production based on the expected value of the monthly demand, what quantity of canned sardine should Salim Industries prepare? (2 marks)

(ii) Assume that each unit of canned sardine demanded generates $70 in revenue and that each can of sardine produced costs $50. How much will the company gain or loss if its monthly production is based on your answer from (a) and the actual demand for the product is 300 canes. (3.5 marks)

(iii) What is the standard deviation of the monthly demand?

FIN10002 Financial Statistics Final Examination Semester 1, 2019

(2.5 marks)

Page 4 of 23

(b) An automobile insurance company classifies drivers as class A (good risks), class B (medium risks), and class C (poor risks). Among the drivers who apply insurance from the company, 30% are from class A, 50% from class B, and the rest from class C. the probability that a class A driver will have accidents in any 12-month period is 0.01, the probability for a class B driver is 0.03, and for a class C driver is 0.10. (i) Draw a tree diagram with probabilities for the above situation.

(3 marks)

(ii) Find the probability that a driver had an accident within 12 months.

(2 marks)

(iii) Mr Wilson applies an insurance policy from this company. If he had an accident within 12 months, what is the probability that he is a class B driver? (3 marks)

FIN10002 Financial Statistics Final Examination Semester 1, 2019

Page 5 of 23

(c) Psychologists tend to believe that there is a relationship between aggressiveness and order of birth. To test this belief, a psychologist chose 500 elementary school students at random and administered to each test design to measure the student’s aggressiveness. Each student was classified according to one of four categories. The percentages of students falling in the four categories are shown below. Categories Aggressive Not Aggressive Total

Firstborn 75 125 200

Not Firstborn 75 225 300

Total 150 350 500

Based on the data in the table above, answer the following questions and round your answer to 3 decimal places. If one student is chosen at random, (i) What is the probability that the student is aggressive?

(2 marks)

(ii) What is the probability that the student is aggressive or firstborn?

(2 marks)

(iii) What is the probability that the student is aggressive given that the student is firstborn? (2 marks)

(iv) Let A be the event as a student selected is aggressive, and let B be the event as student selected is firstborn. Are A and B independent? Justify your answer. (2 marks)

FIN10002 Financial Statistics Final Examination Semester 1, 2019

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QUESTION 2

[10 marks]

The Cosmo Wire Company makes wires for fencing. The population mean thickness for the wires is 0.45 cm with a population standard deviation of 0.03 cm. The measurements are assumed to be normally distributed. (a) What is the probability that a randomly chosen wire has a thickness less than 0.42 cm? (3 marks)

(b) Find the percentage of wires rejected if wires with thickness outside the range between 0.42 cm and 0.47 cm are to be rejected? (4 marks)

(c) Find k, if it is found that 2.5% of the wires have a thickness greater than k.

(3 marks)

FIN10002 Financial Statistics Final Examination Semester 1, 2019

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QUESTION 3

[14 marks]

(a) A manufacturer of light bulbs has found that the lifetime of its 60-watt bulbs is normally distributed with an average of 166 days and a standard deviation of 18 days. The manufacturer wants to test a sample of 60-watt bulbs. He has selected 40 bulbs at random. Determine the:

(i) standard error of the sample mean lifetime of the bulbs.

(1 mark)

(ii) probability that the average lifetime of the sample bulbs will be greater than 160 days. (3 marks)

(iii) probability that the average lifetime of the sample bulbs will be less than 163 days. (2 marks)

(iv) 95% confidence interval for the average lifetime of the sample bulbs.

FIN10002 Financial Statistics Final Examination Semester 1, 2019

(3 marks)

Page 8 of 23

(b) A questionnaire was sent to a large number of people asking for their opinions about a proposal to alter an examination syllabus. Of the 180 replies received, 134 were in favour of the proposal. Assume that the people replying were a random sample from the population. Determine the 90% confidence interval for the population proportion of people who are in favour of the proposal. (5 marks)

FIN10002 Financial Statistics Final Examination Semester 1, 2019

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QUESTION 4

[24 marks]

(a) The labour cost for manufacturing a unit of table should be $20. The management accountant selected a sample of 12 units, and found that the sample mean labour cost is $23, with a standard deviation of $2.089. (i) At the 5% level of significance, test whether the sample indicates that the labour cost per unit exceeds $20. (6 marks)

(ii)What assumption do we have to make in order to carry out the test in (i)?

FIN10002 Financial Statistics Final Examination Semester 1, 2019

(1 mark)

Page 10 of 23

(b) A supermarket chain is wanting to increase its turnover by attracting new customers. It is proposing to do this by a voucher scheme. In a pilot study, 9 supermarkets are selected for the introduction of the vouchers. Their turnover is measured in the week before the promotion and again in the week after the promotion. The results are summarised in the table below.

Turnover ($000)

Store Week 1 Week 2

1 340 412

2 367 375

3 423 435

4 417 426

5 395 428

6 324 341

7 310 360

8 305 347

9 426 429

Using the correct EXCEL output from the tables below, does the promotion make a significant different to the weekly turnover of the stores in the pilot study at 5% significance level? (5 marks) t-Test: Paired Two Sample for Means

t-Test: Two-Sample Assuming Equal Variances

Week 2

Week 1

Week 2

Week 1

Mean

394.7778

367.4444

Mean

394.7778

367.4444

Variance

1492.444

2446.278

Variance

1492.444

2446.278

9

9

9

9

Observations Pearson Correlation Hypothesized Mean Difference df t Stat P(T...