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Statistics For Business And Economics 12th Edition James T. McClave, P. George Benson, Terry T Sincich - Solutions

Recall that simple linear regression was used to model y = mass of the spill as a function of x = elapsed time of the spill.a. Find a 99% confidence interval for the mean mass of all spills with an elapsed time of 15 minutes. Interpret the result.b. Find a 99% prediction interval for the mass of a
Managers are an important part of any organization's resource base. Accordingly, the organization should be just as concerned about forecasting its future managerial needs as it is with forecasting its needs for, say, the natural resources used in its production process (North craft and Neale,
The reasons given by workers for quitting their jobs generally fall into one of two categories: (1) worker quits to seek or take a different job, or (2) worker quits to withdraw from the labor force. Economic theory suggests that wages and quit rates are related. The table below lists quit rates
a. Use a 90% confidence interval to estimate the mean useful life of a brand A cutting tool when the cutting speed is 45 meters per minute. Repeat for brand B. Compare the widths of the two intervals and comment on the reasons for any difference.b. Use a 90% prediction interval to predict the
Prices of recycled materials (e.g., plastics, paper, and glass) are highly volatile due to the fact that supply is constant, rather than tied to demand. An exploratory study of the prices of recycled products in the United Kingdom was published in Resources, Conservation, and Recycling (Vol. 60,
Refer to the International Conference on Web Intelligence and Intelligent Agent Technology (2010) study of how social media (e.g., Twitter.com) may influence the products consumers buy, Recall that opening weekend box office revenue (in millions of dollars) and tweet rate (average number of tweets
The importance of having employees with a healthy work-life balance has been recognized by U.S. companies for decades. Many business schools offer courses that assist MBA students with developing good work-life balance habits, and most large companies have developed work-life balance programs for
Consider the following sample data:a. Construct a scatter plot for the data. b. It is possible to find many lines for which ˆ‘(y - ) = 0. For this reason, the criterion ˆ‘(y - ) = 0 is not used for identifying the "best-fitting" straight line. Find two lines that have
Consider the following 10 data points:a. Plot the data on a scatter plot.b. Calculate the values of r and r2.c. Is there sufficient evidence to indicate that x and y are linearly correlated? Test at the Î± = .10 level of significance.
Effective management of one's own career requires a skill set that includes adaptability, tolerance for ambiguity, self-awareness, and ability to identify change. Management professors at Pace University (New York) used correlation coefficients to investigate the relationship between these "meta
Emotional exhaustion, or burnout, is a significant problem for people with careers in the field of human services. Regression analysis was used to investigate the relationship between burnout and aspects of the human services professional's job and job-related behavior (Journal of Applied
Individuals who report perceived wrongdoing of a corporation or public agency are known as whistle-blowers. Two researchers developed an index to measure the extent of retaliation against a whistle-blower (Journal of Applied Psychology, 1986). The index was based on the number of forms of reprisal
Write a first-order model relating E(y) to a. Two quantitative independent variables. b. Four quantitative independent variables. c. Five quantitative independent variables.
Recall that opening weekend box office revenue data (in millions of dollars) were collected for a sample of 24 recent movies. In addition to each movie's tweet rate, i.e., the average number of tweets referring to the movie per hour 1 week prior to the movie's release, the researchers also computed
An article in the Community Mental Health Journal (Aug. 2000) used multiple regression analysis to model the level of community adjustment of clients of the Department of Mental Health and Addiction Services in Connecticut. The dependent variable, community adjustment (y), was measured
Recall that the Harvard Business School professors used regression to model the relative optimism (y) of the analysts' 3-month horizon forecasts as a function of x1 = {1 if the analyst worked for a buy-side firm, 0 if the analyst worked for a sell-side firm} and x2 = number of days between forecast
Recall that multiple regression was used to model an employee's intention to leave (y) as a function of bullying (x1, measured on a quantitative scale) and perceived organizational support (measured qualitatively as "low POS," "neutral POS." or "high POS"). In Exercise 12.91b, you wrote a model for
Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of a high-pressure inlet fogging method for a gas turbine engine. Exercise 12.19. Consider a model for heat rate (kilojoules per kilowatt per hour) of a gas turbine as a function of cycle speed (revolutions per minute)
Recall that y = task performance score (measured on a 30-point scale) was modeled as a function of x1 = conscientiousness score (measured on a scale of -3 to +3) and x2 = {1 if highly complex job, 0 if not) using the complete model E(y) = β0 + β1x1 + β2(x1)2 + β3x2 + β4x1x2 + β5(x1)2x2a.
Recall that psychologists modeled desire to have cosmetic surgery (y) as a function of gender (x1), self-esteem (x2), body satisfaction (x3), and impression of reality TV (x4). The psychologists theorized that one's impression of reality TV will "moderate" the impact that each of the first three
"Moonlighters" are workers who hold two jobs at the same time. What are the factors that impact the likelihood of a moonlighting worker becoming aggressive toward his/her supervisor? This was the research question of interest in the Journal of Applied Psychology (July 2005). Completed
The researchers modeled mean income, E(y), as a function of both agreeableness score (x1) and a dummy variable for gender (x2 = 1 if male, 0 if female). Suppose the researchers theorize that for either gender, income will decrease at a decreasing rate as agreeableness score increases. Consequently,
You fit a complete second-order model for E(y) as a function of region and sales volume. a. Conduct a nested-model F-test to determine whether the quadratic terms in the model are statistically useful for predicting sales price (y). Use α = .05. b. Based on the result, part a, which of the nested
Because glass is not subject to radiation damage, encapsulation of waste in glass is considered to be one of the most promising solutions to the problem of low-level nuclear waste in the environment. However, chemical reactions may weaken the glass. This concern led to a study undertaken jointly by
Recall that a Mach rating score was determined for each in a sample of accounting alumni of a large southwestern university. For one portion of the study, the researcher modeled an accountant's Mach score (y) as a function of age, gender, education, and income. Data on n = 198 accountants yielded
There are six independent variables, x1,x2,x3,x4,x5, and x6. that might be useful in predicting a response y. A total of n = 50 observations is available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to be useful. The software fits all
In Economic Policy (January 2011), researchers from the London School of Economics conducted a cross-country analysis of the relationship between teacher's pay and pupils' performance. Data collected for 39 countries were used to model y = the country's average standardized score of its pupils. The
Benefits Quarterly (First Mil Quarter, 1995) published a study of entry-level job preferences. A number of independent variables were used to model the job preferences (measured on a 10-point scale) of 164 business school graduates. Suppose stepwise regression is used to build a model for job
Corn is high in starch content; consequently, it is considered excellent feed for domestic chickens. Does corn possess the same potential in feeding ducks bred for broiling? This was the subject of research published in Animal Feed Science and Technology (April 2010). The objective of the study was
Recall that psychologists modeled desire to have cosmetic surgery (y) as a function of gender (x1), self-esteem (x2), body satisfaction (x3), and impression of reality TV (x4). Suppose you want to determine which subset of these four independent variables is best for predicting one's desire to have
Bus Rapid Transit (BRT) is a rapidly growing trend in the provision of public transportation in America. The Center for Urban Transportation Research (CUTR) at the University of South Florida conducted a survey of BRT customers in Miami (Transportation Research Board Annual Meeting, Jan. 2003).
A marine biologist was hired by the EPA to determine whether the hot-water runoff from a particular power plant located near a large gulf is having an adverse effect on the marine life in the area. The biologist's goal is to acquire a prediction equation for the number of marine animals located at
Consider fitting the multiple regression modelE(y) = Î²0 + Î²1x1 + Î²2x2 + Î²3x3 +Î²4x4 +Î²5x5A matrix of correlations for all pairs of independent variables is given below. Do you detect a multicollinearity problem? Explain.
During new product development, companies often involve "lead users," i.e., creative individuals who are on the leading edge of an important market trend. Creativity and Innovation Management (Feb. 2008) published an article on identifying the social network characteristics of lead users of
Identify the problem(s) in each of the residual plots shown below.
Some states permit only licensed firms to sell funeral goods (e.g., caskets, urns) to the consumer, while other states have no restrictions. States with casket sales restrictions are being challenged in court to lift these monopolistic restrictions. A paper in the Journal of Law and Economics (Feb.
Monthly data (n = 252 months) were collected for several variables in an attempt to model the number of females in managerial positions (y).The independent variables included the number of females with a college degree (x1), the number of female high school graduates with no college degree (x2),
The Professional Geographer (Feb. 2000) published a study of urban and rural counties in the western United States. Six independent variables total county population (x1), population density (x2), population concentration (x3), population growth (x4), proportion of county land in farms (x5), and
Simulated data for the study is saved in the file. In Exercise 12.17, you fit the first-order model. E(y) = β0 + β1x1 + β2x2 + β3x3 + β4x4,where y = desire to have cosmetic surgery, x1 is a dummy variable for gender, x2 = level of self-esteem, x3 = level of body satisfaction, and x4 =
Recall that the researchers modeled mean income, E(y), as a function of both agreeableness score (x1) and a dummy variable for gender (x2 = 1 if male, 0 if female). Use the data saved in the file to analyze the residuals of the model. E(y) = β0 + β1x1 + (β2x1)2 + β3x2 What model modifications,
Suppose you have developed a regression model to explain the relationship between y and x1, x2, and x3. The ranges of the variables you observed were as follows: 10 ≤ y ≤ 100, 5≤ x1 ≤ 55, .5 ≤ x2 ≤ 1, and 1,000 ≤ x3 ≤ 2,000. Will the error of prediction be smaller when you use
When a multiple regression model is used for estimating the mean of the dependent variable and for predicting a new value of y. which will be narrower the confidence interval for the mean or the prediction interval for the new y value? Why?
Suppose you fit the model y = β0 + β1x1 + β2x21 + β3x2 +β4x22 +β5x1x22 + ε to n = 25 data points with the following results: a. Is there sufficient evidence to conclude that at least one of the parameters β1,β2,β3 or β4 is nonzero? Test using a = .05. b. Test H0:β1 = 0 against Ha : β1
Suppose you used Minitab to fit the modely = Î²0 + Î²1x1 + Î²2x2 + Îµto n = 15 data points and obtained the printout shown below.a. What is the least squares prediction equation? b. Find R2 and interpret its value. c. Is there sufficient evidence to
Write a model relating E(y) to one qualitative independent variable that is at four levels. Define all the terms in your model.
It is desired to relate E(y) to a quantitative variable x1 and a qualitative variable at three levels.a. Write a first-order model.b. Write a model that will graph as three different second-order curves-one for each level of the qualitative variable.
Explain why stepwise regression is used. What is its value in the model-building process? Discuss.
In Chance (Fall 2000), statistician Scott Berry built a multiple regression model for predicting total number of runs scored by a Major League Baseball team during a season. Using data on all teams over a 9-year period (a sample of n = 234), the results in the following table were obtained.a. Write
Consider relating E(y) to two quantitative independent variables x1 and x2.a. Write a first-order model for E(y).b. Write a complete second-order model for E(y).
To model the relationship between y, a dependent variable, and x, an independent variable, a researcher has taken one measurement on y at each of three different x values. Drawing on his mathematical expertise, the researcher realizes that he can fit the second-order modelE(y) = β0 + β1x +
Suppose you fit the regression modelE(y) = β0 + β1x1 + β2x2 + β3x22 +β4x1x2 +β5x1x22to n = 35 data points and wish to test the null hypothesis H0: β4 = β5 = 0.a. State the alternative hypothesis.b. Explain in detail how to compute the F-statistic needed to test the null hypothesis. c. What
According to the Chronicle of Higher Education Almanac, 4-year private colleges charge, on average, five times as much for tuition and fees than 4-year public colleges. In order to estimate the true difference in the mean amounts charged for an academic year, random samples of 40 private colleges
Research scientists at the Educational Testing Service (ETS) used multiple regression analysis to model y, the final grade point average (GPA) of business and management doctoral students. A list of the potential independent variables measured for each doctoral student in the study follows:(1)
The Florida Citrus Commission is interested in evaluating the performance of two orange juice extractors, brand A and brand B. It is believed that the size of the fruit used in the test may influence the juice yield (amount of juice per pound of oranges) obtained by the extractors. The commission
Scientists believe that a major cause of global warming is higher levels of carbon dioxide (C02) in the atmosphere. In the Journal of World-Systems Research (Summer 2003), sociologists examined the impact of foreign investment dependence on C02 emissions in n = 66 developing countries. In
A matrix giving the correlation (r) for each pair of independent variables is shown above. Identify the independent variables that are highly correlated. What problems may result from including these highly correlated variables in the regression model?For Information: Refer to Exercise 12.146.
Recall that the dependent variable (y) is measured as relative error of the effort estimate of a software development task. A total of eight independent variables were evaluated as potential predictors of relative error. Each of these was formulated as a dummy variable, as shown in the table
Electronic commerce (or "e-commerce") describes the use of electronic networks to simplify a business operation. With e-commerce, retailers now can advertise and sell their products easily over the Web. In Internet Research: Electronic Networking Applications and Policy (Vol. 11, 2001), Canadian
To meet the increasing demand for new software products, many systems development experts have adopted a prototyping methodology. The effects of prototyping on the system development life cycle (SDLC) was investigated in the Journal of Computer Information Systems (Spring 1993). A survey of 500
Can a corporation's annual profit be predicted from information about the company's CEO? Each year Forbes publishes data on company profit (in $ millions), CEO's annual income (in $ thousands), and percentage of the company's stock owned by the CEO. Consider a model relating company profit (y) to
Numerous "sun safety"' products exist on the market to prevent excessive exposure to solar radiation. But many people do not practice "sun safety" or recognize the effectiveness of these products. A group of University of Arizona researchers examined the feasibility of educating preschool (4- to
A supermarket chain is interested in exploring the relationship between the sales of its store-brand canned vegetables (y), the amount spent on promotion of the vegetables in local newspapers (x1) and the amount of shelf space allocated to the brand (x2). One of the chain's supermarkets was
Industrial engineers at the University of Florida used regression modeling as a tool to reduce the time and cost associated with developing new metallic alloys (Modeling and Simulation in Materials Science and Engineering, Vol. 13. 2005). To illustrate, the engineers built a regression model for
Fluorocarbon plasmas are used in the production of RADCAL semiconductor materials. In the Journal of Applied Physics (Dec. 1. 2000). electrical engineers at Nagoya University (Japan) studied the kinetics of fluorocarbon plasmas in order to optimize material processing. In one portion of the study,
Traffic forecasters at the Minnesota Department of Transportation MNOOT (MDOT) use regression analysis to estimate weekday peak-hour traffic volumes on existing and proposed roadways. In particular, they model y, the peak-hour volume (typically, the volume between 7:00 and 8:00 A.M.), as a
Multiple regression was used to estimate the effect of coaching on SAT-Mathematics scores. Data on 3,492 students (573 of whom were coached) were used to fit the model, E(y) = β0 + β1x1 + β2x2, where y = SAT-Math score, x1 = score on PSAT, and x2 = {1 if student was coached, 0 if not}.a. The
Environmental Science & Technology (Jan. 2005) reported on a study of the reliability of a commercial kit to test for arsenic in groundwater. The field kit was used to test a sample of 328 groundwater wells in Bangladesh. In addition to the arsenic level (micrograms per liter), the latitude
An operations manager is interested in modeling E(y), the expected length of time per month (in hours) that a machine will be shut down for repairs, as a function of the type of machine (001 or 002) and the age of the machine (in years). The manager has proposed the following model:E(y) =
To determine whether extra personnel are needed for the day, the owners of a water adventure park would like to find a model that would allow them to predict the day's attendance each morning before opening based on the day of the week and weather conditions. The model is of the formE(y) = Î²0 +
The owners of the water adventure park are advised that the prediction model could probably be improved if interaction terms were added. In particular, it is thought that the rate at which mean attendance increases as predicted high temperature increases will be greater on weekends than on
A Minneapolis. Minnesota, real estate appraiser used regression analysis to explore the relationship between the sale prices of apartment buildings and various characteristics of the buildings. The file contains data for a random sample of 25 apartment buildings. Note: Physical condition of each
A firm that has developed a new type of light bulb is interested in evaluating its performance in order to decide whether to market it. It is known that the light output of the bulb depends on the cleanliness of its surface area and the length of time the bulb has been in operation. Use the data in
A large research and development firm rates the performance of each member of its technical staff on a scale of 0 to 100, and this merit rating is used to determine the size of the person's pay raise for the coming year. The firm's personnel department is interested in developing a regression model
The data in the table on the next page were collected for a random sample of 26 households in Washington, DC An economist wants to relate household food consumption, y. to household income, x1, and household size,x2. with the first-order modelE(y) = Î²0 + Î²1x1
Recall that data collected for a sample of 1,437 funerals were used to fit the model, E(y) = β0 + β1x1 + β2x2 + β3x1x2, where y is the price (in dollars) of a direct burial, x1= {1 if funeral home is in a restricted state, 0 if not), and x2 = {1 if price includes a basic wooden casket, 0 if no
A medium-sized automobile insurance company is interested in developing a regression model to help predict the monthly collision claims of its policyholders. A company analyst has proposed modeling monthly collision claims (y) in the middle Atlantic states as a function of the percentage of claims
Many colleges and universities develop regression models for predicting the GPA of incoming fresh men. This predicted GPA can then be used to make admission decisions. Although most models use many independent variables to predict GPA, we will illustrate by choosing two variables:x1 = Verbal score
How much influence does the media, especially reality television programs, have on one's decision to undergo cosmetic surgery? This was the question of interest to psychologists who published an article in Body Image: An International Journal of Research (March 2010). In the study, 170 college
The Bell Curve (Free Press, 1994), written by Richard Herrnstein and Charles Murray(H&M), is a controversial book about race, genes, IQ, and economic mobility. The book heavily employs statistics and statistical methodology in an attempt to support the authors' positions on the relationships
The U.S. Army Corps of Engineers data on fish contaminated from the toxic discharges of a chemical plant located on the banks of the Tennessee River in Alabama. Recall that the engineers measured the length (in centimeters), weight (in grams), and DDT level (in parts per million) for 144 captured
Recall that the heat rate (kilo-joules per kilowatt per hour) was measured for each in a sample of 67 gas turbines augmented with high-pressure inlet fogging. In addition, several other variables were measured, including cycle speed (revolutions per minute), inlet temperature (°C), exhaust gas
Minitab was used to fit the modelE(y) = Î²0 + Î²1x1 + Î²2x2 to n = 20 data points, and the printout shown on the next page was obtained.a. What are the sample estimates of Î²1, Î²2, and Î²3?b. What is the least squares prediction equation?c. Find SSE, MSE, and s. Interpret the standard
In the oil industry, water that mixes with crude oil during production and transportation must be removed. Chemists have found that the oil can be extracted from the water/oil mix electrically. Researchers at the University of Bergen (Norway) conducted a series of experiments to study the factors
An important goal in occupational safety is "active caring." Employees demonstrate active caring (AC) about the safety of their coworkers when they identify environmental hazards and unsafe work practices and then implement appropriate corrective actions for these unsafe conditions or behaviors.
Because the coefficient of determination R2 always increases when a new independent variable is added to the model, it is tempting to include many variables in a model to force R2 to be near 1. However, doing so reduces the degrees of freedom available for estimating σ2, which adversely affects
The vineyards in the Bordeaux region of France are known for producing excellent red wines. However, the uncertainty of the weather during the growing season, the phenomenon that wine tastes better with age, and the fact that some Bordeaux vineyards produce better wines than others encourage
Refer to the Creativity and Innovation Management (Feb. 2008) study of lead users of children's computer games, Exercise 12.12. Recall that the researchers modeled lead-user rating (y, measured on a 5-point scale) as a function of gender (x1 = 1 if female, 0 if male), age (x2, years), degree of
Refer to the Chance (Fall 2000) study of runs scored in Major League Baseball games, Exercise 12.14. Multiple regression was used to model total number of runs scored (y) of a team during the season as a function of number of walks (x1), number of singles (x2), number of doubles (x3), number of
Recall that psychologists used multiple regression to model desire to have cosmetic surgery (y) as a function of gender (x1), self-esteem (x2), body satisfaction (x3), and impression of reality TV (x4). The SPSS printout below shows a confidence interval for E(y) for each of the first five students
Fit the first-order model, E(y) = Î²0 + Î²1x1 + Î²2x2 + Î²3x3.To the data, where y = DDT level (parts per million), x1 = number of miles upstream, x2 = length (centimeters), and x3 = weight (grams). Use the Excel/XLSTAT printout above to predict, with 90%
Recall that you fit a first-order model for heat rate (y) as a function of speed (x1), inlet temperature (x2), exhaust temperature (x3), cycle pressure ratio (x4), and airflow rate (x5). A Minitab printout with both a 95% confidence interval for E(y) and prediction interval for y for selected
Suppose you fit the multiple regression modely = β0 + β1x1 + β2x2 + β3x3 + εto n = 30 data points and obtain the following result: = 3.4 - 4.6x1 + 2.7x2 + .93x3The estimated standard errors of 2 and 3 are 1.86 and .29, respectively.a. Test the null hypothesis H0: β2 = 0 against the
Refer to the Environmental Science & Technology (Jan. 2005) study of the reliability of a commercial kit to test for arsenic in groundwater, Exercise 12.16. You fit a first-order model for arsenic level (y) as a function of latitude, longitude, and depth. Based on the model statistics, the
Forbes magazine's "Executive Compensation Scoreboard." Forbes (April 13, 2011) determined which CEOs are worth their pay based on a comparison of the firm's stock performance and the CEO's annual salary. Data for 175 of the top performers are saved in the file. Some of the variables measured for
Refer to Exercise 12.20 and the study on separating water from oil. The researchers concluded that "in order to break a water-oil mixture with the lowest possible voltage, the volume fraction of the disperse phase (x1) should be high, while the salinity (x2) and the amount of surfactant (x5) should
In a production facility, an accurate estimate of man-hours needed to complete a task is crucial to management in making such decisions as the proper number of workers to hire, an accurate deadline to quote a client, or cost-analysis decisions regarding budgets. A manufacturer of boiler drums wants
Write an interaction model relating the mean value of y, E(y) to a. Two quantitative independent variables b. Three quantitative independent variables
Suppose the true relationship between E(y) and the quantitative independent variables x1 and x2 is E(y) = 3 + x1 + 2x2 - x1x2 a. Describe the corresponding three-dimensional response surface. b. Plot the linear relationship between y and x2 for x1 = 0, 1, 2, where 0 ≤ x2 ≤ 5. c. Explain why the
Suppose you fit the interaction modely = β0 + β1x1 + β2x2 + β3x1x2 + εto n = 32 data points and obtain the following results:SSyy = 479SSE = 213 = 10s3 = 4a. Find R2 and interpret its value.b. Is the model adequate for predicting y? Test at α = .05.c. Use a graph to explain the contribution

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