QUESTION 1

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.
b. Determine the factor associated with this experiment.
c. Describe the levels of the factor associated with this analysis.
d. State the number of degrees of freedom available for determining the between-samples variation.
e. State the number of degrees of freedom available for determining the within-samples variation.
f. State the number of degrees of freedom available for determining the total variation.

QUESTION 2

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:

(1) Aggressive Growth (AG)

(2) Growth (G)

(3) Growth-Income (G-I)

(4) Income Funds (IF)

(5) International (I)

(6) Asset Allocation (AA)

(7) Precious Metal (PM)

(8) Bond (B).

The percentage gains (%) accrued by 3 randomly selected customers (C1, C2 and C3) in each group are as follows:

(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.

(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.

QUESTION 3

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.

a. Compute the least squares regression equation.

b. If the computer-generated account balance was 100, what would you expect to be the actual account balance as verified by the accountant?

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.

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.

QUESTION 4

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:

(a). Produce a regression equation to predict the selling price for residences using a model of the following form:

Where,

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

(c). Produce an equation that describes the relationship between the selling price and the square footage of (1) condominiums and (2) single-family homes.

(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.

QUESTION 5

a) A manufacturer of snow chain is considering building a new production plant to cope with growing demand. A tyre firm is interested in investing in the company and has been provided with the following quarterly sales figures:

1. Calculate the trend line using the moving average method.
2. Estimate and then eliminate the season variation component. In other words find the deseasonalised data.

QUESTION 6

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.

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

(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.

(c. Using the data for the years 2006-2008, determine the seasonal indexes for each quarter.
(d. Develop a seasonally unadjusted forecast for the four quarters of year 2009.

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.

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.

QUESTION 7

a) Kahn and Rudd (1995) examined whether historical performance predicts future performance for a sample of mutual funds that included 300 actively managed U.S. domestic equity funds. One approach they used involved calculating each funds' exposure to a set of style indexes (the term style captures the distinctions of growth/value and large-capitalisation/mid-capitalisation/small-capitalisation). After establishing a style benchmark (a comparison portfolio marched to the fund's style) for each fund, Kahn and Rudd computed the fund's selection return for two periods. They defined selection return as fund return minus the fund's style-benchmark return. The first period was October 1990 to March 1992. The top 50 percent of funds by selection return for that period were labelled winners; the bottom 50 percent were labelled losers. Based on selection return in the next period, April 1992 to September 1993, the top 50 percent of funds were tagged as winners and the bottom 50 percent as losers for that period. An excerpt from their results is given in following table. The winner-winner entry, for example, shows that 70 of the 150 first-period winners fund were also winners in the second period (52.7%= 79/150). Note that the dour entries in parentheses in the table can be viewed as conditional probabilities.

Based on the four events needed to define the four conditional probabilities.
• State the four entries of the table as conditional probabilities using the form P(this event | that event) = number
• Are the conditional probabilities in Part 2 empirical, a priori, or subjective probabilities?
• Using the information in the table, calculate the probability of the event a fund is a loser in both Period 1 and Period 2. (Note that because 50 percent of funds are categorised as loser in each period, the unconditional probability that a fund is labelled a loser in either period is 0.5)

b) You have a portfolio of two mutual funds, A and B, 75 percent invested in A, as shown in following table:

1. Calculate the expected return of the portfolio.

Calculate the correlation matrix for this problem. Carry out the answer to two decimal places.

2. Compute portfolio standard deviation of return.

QUESTION 8

The following are annual rate of return for US government T-bills and UK common stocks:

a. Compute the arithmetic mean rate of return and the standard deviation of rates of return for the two series - Discuss these two alternative investments in terms of their arithmetic average rates of return, their absolute risk, and their relative risk.

b. Compute the geometric mean rate of return for each of these investments. Compare the arithmetic mean return and the geometric mean return for each investment, and discuss this difference between mean returns as related to the standard deviation of each series.

QUESTION 9

a) Suppose an investment analyst takes a random sample of U.S equity mutual funds and calculates Sharp Ratio. The sample size is 100, and the average sharp ratio is 0.45. The sample has a standard deviation of 0.30. Calculate and interpret the 90 percent confidence interval for the population mean of all U.S. equity mutual funds by using a reliability factor based on the standard normal distribution.

b) A money manager wants to obtain a 95 percent confidence interval for fund inflows and outflows over the next six months for his existing clients. He begins by calling a random sample of 10 clients and inquiring about their planned additions to and withdrawals from the fund. The manager then computes the change in cash flow for each client sampled as a percentage change in total funds placed with the manager. A positive percentage indicates a net cash inflow to the client's account, and a negative percentage change indicates a net cash outflow from the clients account. The manager weights each response by the relative size of the account within the sample and then computes a weighted average.

As a result of this process, the money manager computes a weighted average of 5.5 percent. Thus, a point estimate is that the total amount of funds under management will increase by 5.5 percent in the next six months. The standard deviation of the observations in the sample is 10 percent. A histogram of past data looks fairly close to normal, so the manager assumes the population is normal.

Calculate a 95 percent confidence interval for the population mean and interpret your findings.

• Using the sample mean of 5.5 percent and standard deviation of 10 percent, compute the confidence interval for sample sizes of 20 and 30.

Interpret your results from Part a and Part b.

QUESTION 10

Using a source of international statistics (OECD, IMF, or their respective Central Bank's Statistical Database), compare the percentage change in the following economic data for Japan, Germany, Canada and the United States for the last five (5) years:
1. Aggregate output (GDP).
2. Inflation.
3. Money Supply Growth.

Compare the differences and analyse which country or countries differed most from the United States.