questions

3

Grading Criteria

Criteria 70%-100% 60-69% 50-59% 0 to 49% Fail

Generic skills: communication and

presentation.

Comprehensive and correctly structured assessment. Style of writing is very fluent and develops a coherent and logical argument. Excellent referencing.

Well structured report which follows appropriate format but some aspects of layout and referencing could be improved. Style of writing is fairly fluent. Good referencing.

Good report in most aspects but suffers from variations in quality and the layout contains some inadequacies. Style of writing is satisfactory. Referencing needs improving.

Very poor report which is incorrectly structured and contains major errors and omissions. Style of writing lacks coherence and fluency. Poor referencing.

Knowledge & Understanding

Demonstrates excellent knowledge of theory and provides critical theoretical underpinning. Very good interpretations and summarising of main themes.

Wide range of knowledge demonstrated and evidence of good understanding of the topic. Ability to interpret and summarise succinctly.

Good range of knowledge demonstrated but weaknesses in key areas. Some understanding displayed of the topic. Summary and interpretation are satisfactory.

Very poor range of knowledge demonstrated and there are major weaknesses evident in interpretation and understanding. No clear interpretation of main themes.

Analysis

Excellent use of theoretical and conceptual models to guide analysis linked with a critical discussion of main themes. Deconstructs the major themes used in the argument.

Very good use of the theoretical and conceptual models with good critical discussion and application. Good evidence of deconstruction.

Use of theory and concepts limited but relevant. Application could be improved and there is a tendency towards description. Must provide more evidence of deconstruction.

Very poor use of theory and very little application of concepts. Very little description with not much evidence of analysis.

Synthesis/ Creativity/ Application

Logical presentation of themes with appropriate examples being demonstrated. Very good demonstration of synthesis. Models have been clearly applied to the argument.

Very good account of main themes with sound application. Good attempt at applying models to the argument. .Fairly good attempt at synthesising the salient points.

Good account of main themes with some attempt at application. Limited evidence of synthesis.

Very poor account of main themes with little or no application. No links between models and argument.

Evaluation

Shows clear evidence of in-depth critical reflection and evaluation of the argument by providing a robust defence of the opinions presented in the assessment.

Shows evidence of critical reflection and evaluation and a fairly cohesive defence of the argument

Shows some evidence of critical reflection but could have been developed.

Shows little or no evidence of critical reflection and needs to be much more developed. There is no defence of the opinions presented.

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Your Task

QUESTION 1

The managing partner for Westwood One Investment Managers Inc. gave a public seminar in

which she discussed a number of issues, including investment risk analysis. In that seminar, she

reminded people that the coefficient of variation can often be used as a measure of risk of an

investment. To demonstrate her point of view, she used two hypothetical stocks as examples. She

let x equal the change in assets for a $1,000.00 investment in stock1 and y reflect the change in

assets for a $1,000.00 investment in stock2. She showed the seminar participants the following

probability distributions:

x P(x) y P(y)

-$1,000 0.1 -$1,000 0.2

$0 0.1 $0 0.4

$500 0.3 $500 0.3

$1,000 0.3 $1,000 0.05

$2,000 0.2 $2,000 0.05

a. Compute the expected values for the random variables x and y. (2 marks)

b. Compute the standard deviations for the random variables x and y.(3 marks)

c. Compute the coefficient of variation for each random variable. (2 marks)

d. Referring to part c, suppose the seminar director said that the first stock was riskier since

its standard deviation was greater than the standard deviation of the second stock. How

would you respond to her assertion? (3 marks)

QUESTION 2

MainStay Investments is one of the investment vehicles used by New York Life Investment

Management (NYLIM). The respondents to a survey conducted by NYLIM and who are aged

between 26 and 82 indicated that 66% of seniors, 61 % of baby boomers, and 58% of Generation

X expect Individual Retirement Accounts (IRAs) to be their primary source of income in

retirement. The margin of error was given as ±5 percentage points.

a. Calculate a 95% confidence interval for the proportion of seniors who expect IRAs to be

their primary source of income in retirement. (5 marks)

b. Although the sample size for the entire survey was listed, the sample size for each of the

three generations was not given. Assuming the confidence level was 95%, determine the

sample size for each of the three generations. (5 Marks)

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QUESTION 3

About 74% of Freddie Mac-owned loans were refinanced in the second quarter of 2005 (USA

Today, Lifeline, August 3, 2005), resulting in new mortgages carrying loan amounts at least 5%

above the original mortgage balance. The median loan refinanced in the second quarter was 2.6

years old. If a sample size of 2,500 was used to obtain this information,

a. Determine if the sample size for the test is large enough to warrant approximating the

sample proportion’s distribution with a normal distribution. (5 marks)

b. Use this information to determine if less than 75% of new mortgages had a loan amount at

least 5% above the original mortgage balance. Use a test statistic approach with a = 0.025.

(5 marks)

QUESTION 4

Before the unprecedented decline in home sales that started in late 2008, the National Association

of Realtors profile of home buyers and sellers indicated that the percentage of home buyers who

are single women has more than doubled since 1981, whereas the percentages of home buyers

who are single men has declined. This occurred despite evidence indicating that women’s salaries

still lag behind those of men. The Association’s profile states that the median income for men

and women home buyers was $58.939 and $47,315, respectively. Assume the respective standard

deviations and sample sizes were $10,000 and $9,000, and 200 and 302.

a. Conduct a hypothesis test to determine if the median income for men buying homes is

more than $10,000 larger than that of women. Use a significance level of 0.05. (5 marks)

b. Describe any additional assumptions required to validate the results of the hypothesis test

in part a. (5 marks)

QUESTION 5

In conjunction with the housing foreclosure crisis of 2009, many economists expressed

increasing concern about the level of credit card debt and efforts of banks to raise interest rates on

these cards. The banks claimed the increases were justified. A Senate sub-committee decided to

determine if the average credit card balance depends on the type of credit card used. The cards

under consideration are Visa, MasterCard, Discover, and American Express. The sample sizes to

be used for each level are 25, 25, 26, and 24, respectively.

a. Describe the parameter of interest for this analysis. (1 mark)

b. Determine the factor associated with this experiment. (2 marks)

c. Describe the levels of the factor associated with this analysis. (1 mark)

d. State the number of degrees of freedom available for determining the between-samples

variation. (2 marks)

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e. State the number of degrees of freedom available for determining the within-samples

variation. (2 marks)

f. State the number of degrees of freedom available for determining the total variation. (2

marks)

QUESTION 6

A senior analyst working for Ameritrade has reviewed purchases his customers have made over

the last six months. He has categorized the mutual funds purchased into eight categories:

Aggressive Growth (AG) - Growth (G) - Growth-Income (G-I) - Income Funds (IF) -

International (I) - Asset Allocation (AA) - Precious Metal (PM) - Bond (B).

The percentage gains (%) accrued by 3 randomly selected customers (C1, C2 and C3) in each

group are as follows:

Mutual Fund AG G G-I IF I AA PM B

C1 6 7 5 1 14 -3 5 -1

C2 7 -2 6 0 13 7 7 3

C3 12 0 2 6 10 7 5 2

a. Develop the appropriate ANOVA table to determine if there is a difference in the average

percentage gains accrued by his customers among the mutual fund types. Use a

significance level of 0.05. (5 marks)

b. Use the Tukey-Kramer procedure to determine which mutual fund type has the highest

average percentage gain. Use an experiment-wide error rate of 0.05. (5 marks)

QUESTION 7

A study was conducted to determine if there is a difference between the investing preferences of

mid-level managers working in the public and private sectors in New York City. A random

sample of 320 public sector employees and 380 private sector employees was taken. The sampled

participants were then asked about their retirement investment decisions and classified as being

either “aggressive,” if they invested only in stocks or stock mutual funds, or “balanced,” if they

invested in some combination of stocks, bonds, cash, and other. The following results were

found:

Agressive Balanced

Public 164 156

Private 236 144

a. State the hypothesis of interest and conduct the appropriate hypothesis test to determine

whether there is a relationship between employment sector and investing preference. Use

a level of significance of 0.01. (3 marks)

b. State the conclusion of the test conducted in part a. (3 marks)

c. Calculate the p-value for the hypothesis test conducted in part a. (4 marks)

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QUESTION 8

During the recession that began in 2008, not only did some people stop making house payments,

but they also stopped making payments for local government services such as trash collection and

water and sewer services. The following data have been collected by an accountant who is

performing an audit of account balances for a major city billing department. The population from

which the data were collected represents those accounts for which the customer had indicated the

balance was incorrect. The dependent variable, y, is the actual account balance as verified by the

accountant. The independent variable, x, is the computer-generated account balance.

x 233 10 24 56 78 102 90 200 344 120 18

y 245 12 22 56 90 103 85 190 320 120 23

a. Compute the least squares regression equation. (2 marks)

b. If the computer-generated account balance was 100, what would you expect to be the

actual account balance as verified by the accountant? (2 marks)

c. The computer-generated balance for Timothy Jones is listed as 100 in the computer-

generated account record. Calculate a 90% interval estimate for Mr. Jones’s actual

account balance. (3 marks)

d. Calculate also a 90% interval estimate for the average of all customers’ actual account

balances in which a computer-generated account balance is the same as that of Mr. Jones

(part c). Interpret your results. (3 marks)

QUESTION 9

A real estate agent wishes to determine the selling price of residences using the size (square feet),

and whether the residence is a condominium or a single-family home. A sample of 20 residences

was obtained with the following results:

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Price ($) Type Square Feet

199,700 F 1,500

211,800 C 2,085

197,100 F 1,450

228,400 F 1,836

215,800 F 1,730

190,900 C 1,726

312,200 F 2,300

313,600 C 1,650

239,000 F 1,950

184,400 C 1,545

200,600 C 1,375

208,000 C 1,825

210,500 F 1,650

233,300 F 1,960

187,200 C 1,360

185,200 C 1,200

284,100 F 2,000

207,200 F 1,755

258,200 F 1,850

203,100 F 1,630

F: Single-Family Home

C: Condomnium Residence

a. Produce a regression equation to predict the selling price for residences using a model of

the following form: (2 marks)

0 1 1 2 2    

i y β β x β x ε

Where,



Square Footage

1, if a condomnium

0, if a single-family home

x

x





1

2

b. Interpret the parameters β1, and β2 in the model given in part a. (2 marks)

c. Produce an equation that describes the relationship between the selling price and the

square footage of (1) condominiums and (2) single-family homes. (3 marks)

d. Conduct a test of hypothesis to determine if the relationship between the selling price and

the square footage is different between condominiums and single-family homes. (3

marks)

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QUESTION 10

A major brokerage company has an office in Miami, Florida. The manager of the office is

evaluated based on the number of new clients generated each quarter. The following data reflect

the number of new customers added during each quarter between 2006 and 2009.

2006 2007 2008 2009

1st Quarter 218 250 244 229

2nd Quarter 190 220 228 221

3rd Quarter 236 265 263 248

4th Quarter 218 241 240 231

a. Plot the time series and discuss the components that are present in the data. (1 mark)

b. Referring to part a, fit a linear trend model to the data for the years 2006- 2008. Then use

the resulting model to forecast the number of new brokerage customers for each quarter in

the year 2009. Compute the MAD and MSE for these forecasts and discuss the results. (2

marks)

c. Using the data for the years 2006-2008, determine the seasonal indexes for each quarter.

(2 marks)

d. Develop a seasonally unadjusted forecast for the four quarters of year 2009. (2 marks)

e. Using the seasonal indexes computed in part d; determine the seasonally adjusted forecast

for each quarter for the year 2009. Compute the MAD and MSE for these forecasts. (2

marks)

f. Examine the values for the MAD and MSE in parts b and e. Which of the two forecasting

techniques would you recommend the manager to use in order to forecast the number of

new clients generated each quarter? Support your choice by explaining your rationale. (1

mark)

Total 100 marks

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