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mathematics
statistics
Questions and Answers of
Statistics
Identify the theoretically correct test statistic to use for a hypothesis test concerning the mean of a single population under the following conditions: A. The sample comes from a normally
Willco is a manufacturer in a mature cyclical industry. During the most recent industry cycle, its net income averaged $30 million per year with a standard deviation of $10 million (n = 6
Investment analysts often use earnings per share (EPS) forecasts. One test of forecasting quality is the zero-mean test, which states that optimal forecasts should have a mean forecasting error of 0.
Variable X takes on the values shown in the following table for five observations. The table also shows the values for five other variables, Y1 through Y5. Which of the variables Y1 through Y5 have a
Industry automobile sales should be related to consumer sentiment. The following table provides a regression analysis in which sales of automobiles and light trucks (in millions of vehicles) are
Use the following information to create a regression model:A. Calculate the sample mean, variance, and standard deviation for X and for Y. B. Calculate the sample covariance and the correlation
The bid-ask spread for stocks depends on the market liquidity for stocks. One measure of liquidity is a stock's trading volume. Below are the results of a regression analysis using the bid-ask spread
An economist collected the monthly returns for KDL's portfolio and a diversified stock index. The data collected are shown below:The economist calculated the correlation between the two returns and
Diet Partners charges its clients a small management fee plus a percentage of gains whenever portfolio returns are positive. Cleo Smith believes that strong incentives for portfolio managers produce
Kenneth McCoin, CFA, is a fairly tough interviewer. Last year, he handed each job applicant a sheet of paper with the information in the following table, and he then asked several questions about
Kenneth McCoin, CFA, is a fairly tough interviewer. Last year, he handed each job applicant a sheet of paper with the information in the following table, and he then asked several questions about
Kenneth McCoin, CFA, is a fairly tough interviewer. Last year, he handed each job applicant a sheet of paper with the information in the following table, and he then asked several questions about
Kenneth McCoin, CFA, is a fairly tough interviewer. Last year, he handed each job applicant a sheet of paper with the information in the following table, and he then asked several questions about
Kenneth McCoin, CFA, is a fairly tough interviewer. Last year, he handed each job applicant a sheet of paper with the information in the following table, and he then asked several questions about
Use the data sample below to answer the following questions.A. Calculate the sample mean, variance, and standard deviation for X. B. Calculate the sample mean, variance, and standard deviation for
Kenneth McCoin, CFA, is a fairly tough interviewer. Last year, he handed each job applicant a sheet of paper with the information in the following table, and he then asked several questions about
Howard Golub, CFA, is preparing to write a research report on Stellar Energy Corp. common stock. One of the world's largest companies, Stellar is in the business of refining and marketing oil. As
Howard Golub, CFA, is preparing to write a research report on Stellar Energy Corp. common stock. One of the world's largest companies, Stellar is in the business of refining and marketing oil. As
Howard Golub, CFA, is preparing to write a research report on Stellar Energy Corp. common stock. One of the world's largest companies, Stellar is in the business of refining and marketing oil. As
Howard Golub, CFA, is preparing to write a research report on Stellar Energy Corp. common stock. One of the world's largest companies, Stellar is in the business of refining and marketing oil. As
Howard Golub, CFA, is preparing to write a research report on Stellar Energy Corp. common stock. One of the world's largest companies, Stellar is in the business of refining and marketing oil. As
Howard Golub, CFA, is preparing to write a research report on Stellar Energy Corp. common stock. One of the world's largest companies, Stellar is in the business of refining and marketing oil. As
Statistics for three variables are given below. X is the monthly return for a large-stock index, Y is the monthly return for a small-stock index, and Z is the monthly return for a corporate bond
Home sales and interest rates should be negatively related. The following table gives the number of annual unit sales for Packard Homes and mortgage rates for four recent years. Calculate the sample
The following table shows the sample correlations between the monthly returns for four different mutual funds and the S&P 500. The correlations are based on 36 monthly observations.The funds are
Bouvier Co. is a Canadian company that sells forestry products to several PacificRim customers. Bouvier's sales are very sensitive to exchange rates. The following table shows recent annual sales (in
Julie Moon is an energy analyst examining electricity, oil, and natural gas consumption in different regions over different seasons. She ran a regression explaining the variation in energy
You are examining the results of a regression estimation that attempts to explain the unit sales growth of a business you are researching. The analysis of variance output for the regression is given
The first table below contains the regression results for a regression with monthly returns on a large-cap mutual fund as the dependent variable and monthly returns on a market index as the
With many US companies operating globally, the effect of the US dollar's strength on a US company's returns has become an important investment issue. You would like to determine whether changes in
You are examining the effects of the January 2001 NYSE implementation of the trading of shares in minimal increments (ticks) of $0.01 (decimalization). In particular, you are analyzing a sample of 52
You are analyzing if institutional investors such as mutual funds and pension funds prefer to hold shares of companies with less volatile returns. You have the percentage of shares held by
In estimating a regression based on monthly observations from January 1987 to December 2002 inclusive, you find that the coefficient on the independent variable is positive and significant at the
The book-to-market ratio and the size of a company's equity are two factors that have been asserted to be useful in explaining the cross-sectional variation in subsequent returns. Based on this
You are analyzing the variables that explain the returns on the stock of the Boeing Company. Because overall market returns are likely to explain a part of the returns on Boeing, you decide to
You are analyzing the cross-sectional variation in the number of financial analysts that follow a company (also the subject of Problems 3 and 8). You believe that there is less analyst following for
You have noticed that hundreds of non-US companies are listed not only on a stock exchange in their home market but also on one of the exchanges in the United States. You have also noticed that
Gary Hansen is a securities analyst for a mutual fund specializing in small-capitalization growth stocks. The fund regularly invests in initial public offerings (IPOs). If the fund subscribes to an
Gary Hansen is a securities analyst for a mutual fund specializing in small-capitalization growth stocks. The fund regularly invests in initial public offerings (IPOs). If the fund subscribes to an
Gary Hansen is a securities analyst for a mutual fund specializing in small-capitalization growth stocks. The fund regularly invests in initial public offerings (IPOs). If the fund subscribes to an
One of the most important questions in financial economics is what factors determine the cross-sectional variation in an asset's returns. Some have argued that book-to-market ratio and size (market
Gary Hansen is a securities analyst for a mutual fund specializing in small-capitalization growth stocks. The fund regularly invests in initial public offerings (IPOs). If the fund subscribes to an
Gary Hansen is a securities analyst for a mutual fund specializing in small-capitalization growth stocks. The fund regularly invests in initial public offerings (IPOs). If the fund subscribes to an
Gary Hansen is a securities analyst for a mutual fund specializing in small-capitalization growth stocks. The fund regularly invests in initial public offerings (IPOs). If the fund subscribes to an
Adele Chiesa is a money manager for the Bianco Fund. She is interested in recent findings showing that certain business condition variables predict excess US stock market returns (one-month market
Adele Chiesa is a money manager for the Bianco Fund. She is interested in recent findings showing that certain business condition variables predict excess US stock market returns (one-month market
Adele Chiesa is a money manager for the Bianco Fund. She is interested in recent findings showing that certain business condition variables predict excess US stock market returns (one-month market
Adele Chiesa is a money manager for the Bianco Fund. She is interested in recent findings showing that certain business condition variables predict excess US stock market returns (one-month market
Adele Chiesa is a money manager for the Bianco Fund. She is interested in recent findings showing that certain business condition variables predict excess US stock market returns (one-month market
Adele Chiesa is a money manager for the Bianco Fund. She is interested in recent findings showing that certain business condition variables predict excess US stock market returns (one-month market
There is substantial cross-sectional variation in the number of financial analysts who follow a company. Suppose you hypothesize that a company's size (market cap) and financial risk (debt-to-equity
In early 2001, US equity marketplaces started trading all listed shares in minimal increments (ticks) of $0.01 (decimalization). After decimalization, bid-ask spreads of stocks traded on the NASDAQ
The "neglected-company effect" claims that companies that are followed by fewer analysts will earn higher returns on average than companies that are followed by many analysts. To test the
Some developing nations are hesitant to open their equity markets to foreign investment because they fear that rapid inflows and outflows of foreign funds will increase volatility. In July 1993,
Both researchers and the popular press have discussed the question as to which of the two leading US political parties, Republicans or Democrats, is better for the stock market.A. Write a regression
Problem 3 addressed the cross-sectional variation in the number of financial analysts who follow a company. In that problem, company size and debt-to-equity ratios were the independent variables. You
You believe there is a relationship between book-to-market ratios and subsequent returns. The output from a cross-sectional regression and a graph of the actual and predicted relationship between the
The civilian unemployment rate (UER) is an important component of many economic models. Table 1 gives regression statistics from estimating a linear trend model of the unemployment rate: UERt = b0 +
A. The AR(1) model for the civilian unemployment rate, ΔUER t = −0.0405 − 0.4674ΔUERt −1, was developed with five years of data. What would be the drawback to using the AR(1) model to predict
Figure 4 shows monthly observations on the natural log of lightweight vehicle sales, ln (Sales t), for the period January 1992 to December 2000.FIGURE 4 Lightweight Vehicle SalesA. Using the figure,
Figure 5 shows a plot of first differences in the log of monthly lightweight vehicle sales over the same period as in Problem 11. Has differencing the data made the resulting series, Îln
Using monthly data from January 1992 to December 2000, we estimate the followingequation for lightweight vehicle sales: Îln (Sales t) = 2.7108 + 0.3987Îln
Figure 6 shows the quarterly sales of Cisco Systems from 1Q:1991 to 4Q:2000.FIGURE 6 Quarterly Sales at CiscoTable 6 gives the regression statistics from estimating the model Îln (Sales
Figure 7 shows the quarterly sales of Avon Products from 1Q:1992 to 2Q:2002. Describe the salient features of the data shown.FIGURE 7 Quarterly Sales at Avon
Table 7 following shows the autocorrelations of the residuals from an AR(1) model fit to the changes in the gross profit margin (GPM) of The Home Depot, Inc.TABLE 7 Autocorrelations of the Residuals
Suppose we decide to use an autoregressive model with a seasonal lag because of the seasonal autocorrelation in the previous problem. We are modeling quarterly data, so we estimate Equation 15: (ln
Describe how to test for autoregressive conditional heteroskedasticity (ARCH) in the residuals from the AR(1) regression on first differences in the civilian unemployment rate, ΔUER t = b0 + b1ΔUER
Suppose we want to predict the annualized return of the five-year T-bill using the annualized return of the three-month T-bill with monthly observations from January 1993 to December 2002. Our
Figure 1 compares the predicted civilian unemployment rate (PRED) with the actual civilian unemployment rate (UER) from January 1996 to December 2000. The predicted results come from estimating the
You have been assigned to analyze automobile manufacturers and as a first step in your analysis, you decide to model monthly sales of lightweight vehicles to determine sales growth in that part of
Figure 3 shows a plot of the first differences in the civilian unemployment rate (UER) between January 1996 and December 2000, ÎUER t = UER t UERt1.FIGURE 3
Table 2 gives the regression output of an AR(1) model on first differences in the unemployment rate. Describe how to interpret the DW statistic for this regression.TABLE 2 Estimating an AR(1) Model
Assume that changes in the civilian unemployment rate are covariance stationary and that an AR(1) model is a good description for the time series of changes in the unemployment rate. Specifically, we
Suppose the following model describes changes in the civilian unemployment rate: ΔUER t = −0.0405 − 0.4674ΔUERt −1. The current change (first difference) in the unemployment rate is 0.0300.
Table 3 gives the actual sales, log of sales, and changes in the log of sales of Cisco Systems for the period 1Q:2001 to 4Q:2001.Forecast the first- and second-quarter sales of Cisco Systems for 2002
Table 4 gives the actual change in the log of sales of Cisco Systems from 1Q:2001 to 4Q:2001, along with the forecasts from the regression model Îln (Sales t) = 0.0661 +
Compare the assumptions of the arbitrage pricing theory (APT) with those of the capital asset pricing model (CAPM)?
Last year the return on Harry Company stock was 5 percent. The portion of the return on the stock not explained by a two-factor macroeconomic factor model was 3 percent. Using the data given below,
Assume that the following one-factor model describes the expected return for portfolios:Also assume that all investors agree on the expected returns and factor sensitivity of the three highly
Which type of factor model is most directly applicable to an analysis of the style orientation (for example, growth vs. value) of an active equity investment manager? Justify your answer.
Suppose an active equity manager has earned an active return of 110 basis points, of which 80 basis points is the result of security selection ability. Explain the likely source of the remaining 30
Address the following questions about the information ratio. A. What is the information ratio of an index fund that effectively meets its investment objective? B. What are the two types of risk an
A wealthy investor has no other source of income beyond her investments and that income is expected to reliably meet all her needs. Her investment advisor recommends that she tilt her portfolio to
A researcher is investigating the effectiveness of a treatment for adolescent boys who are taking medication for depression. A group of 30 boys is selected and half receive the new treatment in
A researcher would like to evaluate the claim that large doses of vitamin C can help prevent the common cold. One group of participants is given a large dose of the vitamin (500 mg per day), and a
A research study comparing alcohol use for college students in the United States and Canada reports that more Canadian students drink but American students drink more (Kuo, Adlaf, Lee, Gliksman,
Oxytocin is a naturally occurring brain chemical that is nicknamed the "love hormone" because it seems to play a role in the formation of social relationships such as mating pairs and parent-child
For each of the following, determine whether the variable being measured is discrete or continuous and explain your answer. a. Social networking (number of daily minutes on Facebook) b. Family size
Four scales of measurement were introduced in this chapter: nominal, ordinal, interval, and ratio. a. What additional information is obtained from measurements on an ordinal scale compared to
In an experiment examining the effects of humor on memory, Schmidt (1994) showed participants a list of sentences, half of which were humorous and half were non-humorous. The participants
Explain why shyness is a hypothetical construct instead of a concrete variable. Describe how shyness might be measured and defined using an operational definition?
Ford and Torok (2008) found that motivational signs were effective in increasing physical activity on a college campus. Signs such as "Step up to a healthier lifestyle" and "An average person burns
For the following scores, find the value of each expression: a. (X b. (X2 c. ((X)2 d. ((X - 1) X 4 2 1 5
For the following set of scores, find the value of each expression:a. (Xb. (X2c. ( (X + 1)d. ((X + 1)2X46032
Define the terms parameter and statistic. Be sure that the concepts of population and sample are included in your definitions?
For the following set of scores, find the value of each expression: a. (X b. (X2 c. ( (X + 4) X - 4 - 2 0 - 1 - 1
Two scores, X and Y, are recorded for each of n = 4 subjects. For these scores, find the value of each expression.a. ΣXb. ΣYc. ΣXY
Use summation notation to express each of the following calculations: a. Add 1 point to each score, then add the resulting values. b. Add 1 point to each score and square the result, then add the
For the following set of scores, find the value of each expression:a. ΣX2b. Σ(X)2c. Σ(X - 2)d. Σ(X - 2)2X1052
Statistical methods are classified into two major categories: descriptive and inferential. Describe the general purpose for the statistical methods in each category?
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