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Questions and Answers of Statistics

Nielsen/NetRatings is a global leader in Internet media and market research. In a recent year, the firm reported on the "search" shares (i.e., percentage of all Internet searches) for the most
University of Louisville Professor Julia Karcher conducted an experiment to investigate the ethical behavior of accountants (Journal of Business Ethics, Vol. 15, 1996). She focused on auditor
An article in Sociological Methods & Research (May 2001) analyzed the data presented in the table. A sample of 262 Kansas pig farmers was classified according to their education level (college or
The table below gives a breakdown of the root causes of a sample of 83 incidents. Are there significant differences in the percentage of incidents in the four cause categories? Test using
A multinomial experiment with k = 4 cells and n = 205 produced the data shown in the one-way table below.a. Do these data provide sufficient evidence to conclude that the multinomial probabilities
Data on the number of firms sampled and number that announced one or more acquisitions during the year from 1980 to 2000 are saved in the accompanying file. Suppose you want to determine if the
Westinghouse Electric Company has experimented with different means of evaluating the performance of solder-joint inspectors. One approach involves comparing an individual inspector's classifications
Interferons are proteins produced naturally by the human body that help fight infections and regulate the immune system. A drug developed from interferons, called Avonex, is now available for
Offshore oil drilling near an Alaskan estuary has led to increased air traffic-mostly large helicopters-in the area. The U.S. Fish and Wildlife Service commissioned a study to investigate the impact
Product or service quality is often defined as fitness for use. This means the product or service meets the customer's needs. Generally speaking, fitness for use is based on five quality
A statistical analysis is to be done on a set of data consisting of 1,000 monthly salaries. The analysis requires the assumption that the sample was drawn from a normal distribution. A preliminary
The PROMISE Software Engineering Repository at the University of Ottawa provides researchers with data sets for building predictive software models. Data on 498 modules of software code written in
Chance (Spring 2004) presented data from a recent election held to determine the board of directors of a local community. There were 27 candidates for the board, and each of 5,553 voters was allowed
Recall that a social (or service) robot is designed to entertain, educate, and care for human users. In a random sample of 106 social robots obtained through a Web search, the researchers found that
Recall that each of 30 business schools was rated according to student exposure to social and environmental issues in the classroom. Ratings ranged from 1 star (lowest-rated group) to 5 stars
The National Tax Journal (Dec. 2001) published a study of charitable givers based on data collected from the Independent Sector Survey on Giving and Volunteering. A total of 1,072 charitable givers
In each case, graph the line that passes through the given points. a. (1, 1) and (5, 5) b. (0, 3) and (3, 0) c. (-1, 1) and (4, 2) d. (-6, -3) and (2, 6)
The following table is similar to Table 11.2. It is used for making the preliminary computations for finding the least squares line for the given pairs of x and y values.a. Complete the table. b.
Sales and Marketing Management determined the "effective buying income" (EBI) of the average household in a state. Can the EBI be used to predict retail sales per household in the store-group
Refer to the Journal of Statistics Education study of 308 diamonds sold on the open market, Exercise 2.158. Recall that you related the size of the diamond (number of carats) to the asking price
The Sports Journal (Winter 2004) published the results of a study conducted to assess the factors that impact the time allotted to sports news on local television news broadcasts. Information on
H. Mintzberg's classic book The Nature of Managerial Work (1973) identified the roles found in all managerial jobs. An observational study of 19 managers from a medium-sized manufacturing plant
Recall that the medical researchers measured the length of time in practice (i.e., years of experience) and the amount of exposure to ethics in medical school (number of hours) for a sample of 118
Financial institutions have a legal and social responsibility to serve all communities. Do banks adequately serve both inner-city and suburban neighborhoods, both poor and wealthy communities? In New
The table listing the current value (without deduction for debt, except stadium debt) and operating income for each team is reproduced shown below.a. Propose a straight-line model relating an NFL
The Minnesota Department of Transportation installed a state-of-the-art weigh-in-motion scale in the concrete surface of the eastbound lanes of Interstate 494 in Bloomington. Minnesota. After
Firms planning to build new plants or make additions to existing facilities have become very conscious of the energy efficiency of proposed new structures and are interested in the relation between
One of the most difficult tasks of developing and managing a global portfolio is assessing the risks of potential foreign investments. Duke University researcher C. R. Henry collaborated with two
Refer to Exercise 11.10. After the least squares line has been obtained, the table below (which is similar to Table 11.2) can be used for (1) comparing the observed and the predicted values of y and
Sometimes it is known from theoretical considerations that the straight-line relationship between two variables, x and y, passes through the origin of the xy-plane. Consider the relationship between
Managers are interested in modeling past cost behavior in order to make more accurate predictions of future costs. Models of past cost behavior are called cost functions. Factors that influence costs
A civil suit revolved around a five-building brick apartment complex located in the Bronx. New York, which began to suffer spoiling damage (i.e., a separation of some portion of the face of a brick
Construct a scatter plot for the data in the following table.a. Plot the following two lines on your scatter plot:y = 3 - x and y = 1 + xb. Which of these lines would you choose to characterize the
Recall that college students repeatedly played a version of the game "prisoner's dilemma," where competitors choose cooperation, defection, or costly punishment. (Cooperation meant paying 1 unit for
The first five observations and last two observations in SATMAT the file are reproduced in the next table. In Exercise 2.126, you examined the relationship between the 2001 Math SAT scores and the
Two variables measured for each of 15 teams from two fishing cooperatives were y = total catch of lobsters (in kilograms) during the season and x = average percentage of traps allocated per day to
Researchers at Dow Chemical Co. investigated the effect of tablet surface area and volume on the rate at which a drug is released in a controlled-release dosage (Drug Development and Industrial
An investigation of the properties of bricks used to line aluminum smelter pots was published in The American Ceramic Society Bulletin (Feb. 2005). Six different commercial bricks were evaluated. The
In Outliers: The Story of Success (Little, Brown, 2008), the author notes that a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth
Give the slope and y-intercept for each of the lines graphed in Exercise 11.1. Exercise 11.1 In each case, graph the line that passes through the given points. a. (1, 1) and (5, 5) b. (0, 3) and (3,
The Federal Emergency Management Agency (FEMA) provides disaster relief for states impacted by natural disasters (e.g., hurricanes, tornados, floods). Do these bad weather windfalls lead to public
Recall that the method computes a driving performance index based on a golfer's average driving distance (yards) and driving accuracy (percent of drives that land in the fairway). Data for the top 40
The quality of the orange juice produced by a manufacturer (e.g., Minute Maid, Tropicana) is constantly monitored. There are numerous sensory and chemical components that combine to make the
Marketers are keenly interested in how social media (e.g., Facebook, Twitter) may influence consumers who buy their products. Researchers at HP Labs (Palo Alto, CA) investigated whether the volume of
In the state of Florida, elementary school performance is based on the average score obtained by students on a standardized exam, called the Florida Comprehensive Assessment Test (FCAT). An analysis
Each year, the Wall Street Journal and Harris Interactive track the opinions and experiences of college recruiters for large corporations and summarize the results in the Business School Survey. One
Recall that a DuPont Corp. engineer calculated the mass (in pounds) of a 50-gallon methanol spill after a period of time ranging from 0 to 60 minutes. Do the data in the table below indicate that the
Calculate SSE and s2 for each of the following cases:a. n = 20, SSyy = 95, SSxy = 50, 1 = .75b. n = 40, ∑y2 = 860, ∑y = 50, SSxy = 2,700, 1 = .2c. n = 10, ∑(yi - )2 = 58, SSxy = 91, SSxx =
Suppose you fit a least squares line to 26 data points and the calculated value of SSE is 8.34. a. Find s2, the estimator of σ2 (the variance of the random error term ε). b. What is the largest
The equation for a straight line (deterministic model) isy = β0 + β1xIf the line passes through the point (-2, 4), then x = -2, y = 4 must satisfy the equation; that is,4 = β0 + β1(-2)Similarly,
Refer to Exercise 11.10. Calculate SSE, s2, and s for the least squares line. Use the value of s to determine where most of the errors of prediction lie.Exercise 11.10The following table is similar
Recall that college students repeatedly played a version of the game "prisoner's dilemma," where competitors choose cooperation, defection, or costly punishment. At the conclusion of the games, the
A portion of the SPSS printout of the analysis is shown below.a. Locate the values of SSE, s2, and s on the SPSS printout. b. Give a practical interpretation of the value of s. For Information: Refer
Refer to the simple linear regression relating the drug release rate (y) to surface area-to-volume ratio (x), Exercise 11.17.a. Find the value of s for the straight-line model fit in Exercise
The data on structurally deficient highway bridges compiled by the Federal Highway Administration (FHWA) into the National Bridge Inventory (NBI). For each state, the NBI lists the number of
The data are reproduced below.a. Find SSE, s2, and s for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of U.S. births. b.
You used the data in the file to fit a straight-line model relating a state's average annual number of public corruption convictions (y) to the state's average annual FEMA relief (x). a. Estimate
Several quantitative variables were recorded for each in a sample of 28 geography journals: cost of a 1-year subscription (dollars); Journal Impact Factor (JIF) - the average number of times articles
Refer to the Journal of Educational and Behavioral Statistics (Spring 2004) study of scores on the Florida Comprehensive Assessment Test (FCAT), Exercise 11.24.a. Consider the simple linear
Construct both a 95% and a 90% confidence interval for β1 for each of the following cases:a. 1 = 31, s = 3, SSxx = 35, n = 10b. 1 = 64, SSE = 1,960, SSxx = 30, n = 14c. 1 = -8.4, SSE = 146, SSxx
Consider the following pairs of observations:a. Construct a scatter plot for the data.b. Use the method of least squares to fit a straight line to the seven data points in the table.c. Plot the least
Refer to Exercise 11.42. Construct an 80% and a 98% confidence interval for Î²1.Exercise 11.42Consider the following pairs of observations:
Do the accompanying data provide sufficient evidence to conclude that a straight line is useful for characterizing the relationship between x and y?
a. Give the null and alternative hypotheses for determining whether a positive linear relationship exists between y and x.b. Locate the p-value of the test on the SPSS printout. Interpret the result
A simple linear regression model relating y = total catch of lobsters (in kilograms) and x = average percentage of traps allocated per day to exploring areas of unknown catch (called search
The American Economic Review (March 2008) published research on how the gender mix of a U.S. legislator's children can influence the legislator's votes in Congress. Specifically, the researcher
The current workforce is dominated by "Generation Y"-people born between 1982 and 1999. These workers have a reputation as having an entitlement mentality (e.g., they believe they have a right to a
Refer to the simple linear regression analysis relating y = drug release rate to x = surface-area-to-volume ratio, Exercise 11.17. Use the results of the regression to form a 90% confidence interval
Refer to the simple linear regression relating y = sweetness index of an orange juice sample with x = amount of water-soluble pectin, Exercise 11.22. Use the results of the regression to form a 95%
The study of whether birth decade can predict the number of software millionaires born in the decade. The data are reproduced in the table shown below.a. Construct a 95% confidence interval for the
Are good looks an advantage when running for political office? This was the question of interest in an article published in the Journal of Public Economics (Feb. 2010). The researchers focused on a
a. In Exercise 11.38a, you fit a straight-line model relating cost (y) to JIF (x). Find and interpret a 95% confidence interval for the slope of the line.b. In Exercise 11.38b, you fit a
Refer to the Wall Street Journal (Sep. 25, 2005) Business School Survey, Exercise 11.25. If you pay more in tuition to go to a top business school, will it necessarily result in a higher probability
Refer to the Journal of Law and Economics (Nov. 2008) study of the link between Federal Emergency Management Agency (FEMA) disaster relief and public corruption, Exercise 11.20. Evaluate the overall
Refer to the Chance (Winter 2006) investigation of the effects of elevation on slugging percentage in Major League Baseball, Exercise 2.125. Recall that data were compiled on players' composite
Explain what each of the following sample correlation coefficients tells you about the relationship between the x and y values in the sample: a. r = 1 b. r = -1 c. r = 0 d. r = -.90 e. r = .10 f. r =
Calculate r2 for the least squares line in each of the following exercises. Interpret their values.a. Exercise 11.10b. Exercise 11.13Exercise 11.10The following table is similar to Table 11.2. It is
Construct a scatter plot for each data set. Then calculate r and r2 for each data set. Interpret their values.a.b.c.d.
Each week coaches in the National Football League (NFL) face a decision during the game. On fourth-down, should the team punt the ball or go for a first-down? To aid in the decision-making process,
Recall that college students repeatedly played a version of the game "prisoner's dilemma," and the researchers recorded the average payoff and the number of times cooperation, defection, and
An empirical analysis of women in upper management positions at U.S. firms was published in the Journal of Organizational Culture, Communications and Conflict (July 2007). Monthly data (n = 252
Recall that the researchers theorized that consumers with last names that begin with letters later in the alphabet would tend to acquire items faster than those whose last names begin with letters
The study of the seemingly disproportionate number of software millionaires born around the year 1955. The data are reproduced in the table shown below.For Information: Refer to Exercise 11.19 a.
Why do we generally prefer a probabilistic model to a deterministic model? Give examples for when the two types of models might be appropriate.
The role of child laborers on Africa's colonial-era diamond mines was the subject of research published in the Journal of Family History (Vol. 35, 2010). One particular mining company lured children
Refer to the simple linear regression relating y = sweetness index of an orange juice sample with x = amount of water-soluble pectin, Exercise 11.22 and the data saved in the file. Find and interpret
The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. Refer to Public Manager (Summer 2008) listing of
Refer to the Wall Street Journal (Sep. 25, 2005) Business School Survey, Exercise 11.25 and the data saved in the file. Find and interpret r and r2 for the simple linear regression relating y =
Refer to the Chemical Engineering Progress (Jan. 2005) study of the rate at which a spilled volatile liquid will spread across a surface, Exercise 11.26 and the data saved in the file. Find and
Are short people short-changed when it comes to salary? According to Business Professors T. A. Judge (University of Florida) and D. M. Cable (University of North Carolina), tall people tend to earn
Consider the pairs of measurements shown in the table. For these data, SSxx = 38.9, SSyy = 33.6, SSxy = 32.8, and = -.414 + .843x.a. Construct a scatter plot for these data.b. Plot the least squares
Refer to Exercise 11.77.a. Using no information about x, estimate and calculate a 95% confidence interval for the mean value of y.b. Plot the estimated mean value and the confidence interval as
In fitting a least squares line to n = 10 data points, the following quantities were computed:a. Find the least squares line.b. Graph the least squares line.c. Calculate SSE.d. Calculate s2.e. Find a
Recall that simple linear regression was used to model a player's average payoff (y) as a straight-line function of the number of times punishment was used (x) by the player. a. If the researchers
Recall that simple linear regression was used to model y = total catch of lobsters (in kilograms) during the season as a function of x = average percentage of traps allocated per day to exploring
Recall that data for six drug tablets were used to fit the simple linear model, E(y) = Î²0 + Î²1x, where y = drug release rate and x = surface-area-to-volume ratio. An
A 90% confidence interval for the mean sweetness index, E(y), for each of the first 12 runs is shown on the SPSS spreadsheet below. Select an observation and interpret this interval.For Information:
You determined that the p-value for testing the adequacy of the straight-line model relating a state's average annual number of public corruption convictions (y) to the state's average annual FEMA
The data are reproduced shown below. Recall that simple linear regression was used to model number (y) of software millionaire birthdays in a decade as a straight-line function of number (x) of CEO
Refer to The Sport Journal (Winter 2007) study of a new method for ranking the total driving performance of golfers on the PGA tour. Exercise 11.21. You fit a straight-line model relating driving

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