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theory of statistics

Basic Statistics For Business And Economics 6th Edition Douglas Lind, William Marchal, Samuel Wathen - Solutions

The Times-Observer is a daily newspaper in Metro City. Like many city newspapers, the Times-Observer is suffering through difficult financial times. The circulation manager is studying other papers in similar cities in the United States and Canada. She is particularly interested in what variables
Great Plains Roofing and Siding Company, Inc., sells roofing and siding products to home repair retailers, such as Lowe’s and Home Depot, and commercial contractors. The owner is interested in studying the effects of several variables on the value of shingles sold($000). The marketing manager is
Fran’s Convenience Marts are located throughout metropolitan Erie, Pennsylvania. Fran, the owner, would like to expand into other communities in northwestern Pennsylvania and southwestern New York, such as Jamestown, Corry, Meadville, and Warren. To prepare her presentation to the local bank, she
The district sales manager for a major automobile manufacturer is studying car sales. Specifically, he would like to determine what factors affect the number of cars sold at a dealership. To investigate, he randomly selects 12 dealers. From these dealers he obtains the number of cars sold last
Mike Wilde is president of the teachers’ union for Otsego School District. In preparing for upcoming negotiations, he would like to investigate the salary structure of classroom teachers in the district.He believes there are three factors that affect a teacher’s salary: years of experience, a
The administrator of a new paralegal program at Seagate Technical College wants to estimate the grade point average in the new program. He thought that high school GPA, the verbal score on the Scholastic Aptitude Test (SAT), and the mathematics score on the SAT would be good predictors of paralegal
Suppose that the sales manager of a large automotive parts distributor wants to estimate as early as April the total annual sales of a region. On the basis of regional sales, the total sales for the company can also be estimated. If, based on past experience, it is found that the April estimates of
The district manager of Jasons, a large discount electronics chain, is investigating why certain stores in her region are performing better than others. She believes that three factors are related to total sales:the number of competitors in the region, the population in the surrounding area, and
In a multiple regression equation k = 5 and n the MSE value is 5.10, and SS total is 519.68. At the .05 significance level, can we conclude that any of the regression coefficients are not equal to 0?
The following output was obtained.a. What is the sample size?b. Compute the value of R2.c. Compute the multiple standard error of estimate.d. Conduct a global test of hypothesis to determine whether any of the regression coefficients are significant. Use the .05 significance level.e. Test the
In a multiple regression equation two independent variables are considered, and the sample size is 25. The regression coefficients and the standard errors are as follows.Conduct a test of hypothesis to determine whether either independent variable has a coefficient equal to zero. Would you consider
A multiple regression equation yields the following partial results.a. What is the total sample size?b. How many independent variables are being considered?c. Compute the coefficient of determination.d. Compute the standard error of estimate.e. Test the hypothesis that none of the regression
A study by the American Realtors Association investigated the relationship between the commissions earned by sales associates last year and the number of months since the associates earned their real estate licenses. Also of interest in the study is the gender of the sales associate. A portion of
Refer to the data in Table 14–1, which relates the heating cost to the independent variables outside temperature, amount of insulation, and age of furnace. Develop a correlation matrix for all the independent variables. Does it appear there is a problem with multicollinearity? Find and interpret
Given the following regression output,answer the following questions:a. Write the regression equation.b. If X1 is 4 and X2 is 11, what is the value of the dependent variable?c. How large is the sample? How many independent variables are there?d. Conduct a global test of hypothesis to see if any of
The regression output about eating places in Myrtle Beach is repeated below (see earlier self-reviews).(a) Perform a global test of hypothesis to check if any of the regression coefficients are different from 0. What do you decide? Use the .05 significance level.(b) Do an individual test of each
Consider the ANOVA table that follows.a. Determine the standard error of estimate. About 95 percent of the residuals will be between what two values?b. Determine the coefficient of multiple determination. Interpret this value.c. Determine the coefficient of multiple determination, adjusted for the
Consider the ANOVA table that follows.a. Determine the standard error of estimate. About 95 percent of the residuals will be between what two values?b. Determine the coefficient of multiple determination. Interpret this value.c. Determine the coefficient of multiple determination, adjusted for the
Refer to Self-Review 14–1 on the subject of restaurants in Myrtle Beach. The ANOVA portion of the regression output is presented below.(a) How large was the sample?(b) How many independent variables are there?(c) How many dependent variables are there?(d) Compute the standard error of estimate.
4. Cellulon, a manufacturer of home insulation, wants to develop guidelines for builders and consumers on how the thickness of the insulation in the attic of a home and the outdoor temperature affect natural gas consumption. In the laboratory it varied the insulation thickness and temperature. A
A sample of General Mills employees was studied to determine their degree of satisfaction with their present life. A special index, called the index of satisfaction, was used to measure satisfaction. Six factors were studied, namely, age at the time of first marriage (X1) annual income (X2) number
Thompson Photo Works purchased several new, highly sophisticated processing machines. The production department needed some guidance with respect to qualifications needed by an operator. Is age a factor? Is the length of service as an operator (in years) important? In order to explore further the
The director of marketing at Reeves Wholesale Products is studying monthly sales. Three independent variables were selected as estimators of sales: regional population, per capita income, and regional unemployment rate. The regression equation was computed to be (in dollars):a. What is the full
There are many restaurants in northeastern South Carolina. They serve beach vacationers in the summer, golfers in the fall and spring, and snowbirds in the winter. Bill and Joyce Tuneall manage several restaurants in the North Jersey area and are considering moving to Myrtle Beach, SC, to open a
Salsberry Realty sells homes along the east coast of the United States. One of the questions most frequently asked by prospective buyers is: If we purchase this home, how much can we expect to pay to heat it during the winter? The research department at Salsberry has been asked to develop some
Describe the relationship between several independent variables and a dependent variable using multiple regression analysis.
Refer to the CIA data, which report demographic and economic information on 46 countries.a. You wish to use the labor force variable as the independent variable to predict the unemployment rate. Interpret the slope value. Use the appropriate linear regression equation to predict unemployment in the
Refer to the Wage data, which report information on annual wages for a sample of 100 workers. Also included are variables relating to industry, years of education, and gender for each worker.a. Determine the correlation between the annual wage and the years of education. At the .05 significance
Refer to the Baseball 2006 data, which report information on the 2006 Major League Baseball season.a. Let the games won be the dependent variable and total team salary, in millions of dollars, be the independent variable. Can you conclude that there is a positive association between the two
Refer to the Real Estate data, which report information on homes sold in Denver, Colorado, last year.a. Let selling price be the dependent variable and size of the home the independent variable. Determine the regression equation. Estimate the selling price for a home with an area of 2,200 square
Many real estate companies and rental agencies now publish their listings on the Web. One example is Dunes Realty Company, located in Garden City and Surfside Beaches in South Carolina. Go to the website http://www.dunes.com and select Vacation Rentals, then Beach Home Search. The indicate 5
Suppose you want to study the association between the literacy rate in a country, the population, and the country’s Gross Domestic Product (GDP). Go to the website of Information Please Almanac(http://www.infoplease.com). Select the category World & News, and then select Countries. A list of 195
Listed below are the movies with the largest world box office sales and their budget (total amount available to spend making the picture).Find the correlation between the world box office budget and world box office sales. Comment on the association between the two variables. Can we conclude that
Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of
A dog trainer is exploring the relationship between the size of the dog (weight in pounds) and its daily food consumption (measured in standard cups). Below is the result of a sample of 18 observations.a. Compute the correlation coefficient. Is it reasonable to conclude that the correlation in the
A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results.a. Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship?b. Conduct a test of hypothesis to
The following data show the retail price for 12 randomly selected laptop computers along with their corresponding processor speeds in gigahertz.a. Develop a linear equation that can be used to describe how the price depends on the processor speed.b. Based on your regression equation, is there one
The following table shows the mean annual percent return on capital (profitability) and the mean annual percentage sales growth for eight aerospace and defense companiesa. Compute the coefficient of correlation. Conduct a test of hypothesis to determine if it is reasonable to conclude that the
A regression analysis relating the current market value in dollars to the size in square feet of homes in Greene County, Tennesse follows.The regression equation is: Value = -37,186 + 65.0 Size.a. How many homes were in the sample?b. Compute the standard error of estimate.c. Compute the coefficient
PDOT (Pennsylvania Department of Transportation) performed an analysis on the relationship between the number of construction work-zone fatalities and the number of unemployed people in a state.The regression equation is (Unemp). Some additional output is:a. How many states were in the sample?b.
Below is information on the price per share and the dividend for a sample of 30 companies. The sample data are available on the data disk supplied with the text.a. Calculate the regression equation using selling price based on the annual dividend. Interpret the slope value.b. Determine the
Super Markets, Inc., is considering expanding into the Scottsdale, Arizona, area. You as director of planning, must present an analysis of the proposed expansion to the operating committee of the board of directors. As a part of your proposal, you need to include information on the amount people in
The National Highway Association is studying the relationship between the number of bidders on a highway project and the winning(lowest) bid for the project. Of particular interest is whether the number of bidders increases or decreases the amount of the winning bid.a. Determine the regression
An ANOVA table is:a. Complete the ANOVA table.b. How large was the sample?c. Determine the standard error of estimate.d. Determine the coefficient of determination. SOURCE Regression Error Total DF SS MS F 1 50 24 500
Following is a regression equation.Ŷ = 17.08 + 0.16X This information is also available: Sy.x = 4.05, and n = 5.a. Estimate the value of Ŷ when X = 50.b. Develop a 95 percent prediction interval for an individual value of Y for X= 50. - 2 = 1,030
The following regression equation was computed from a sample of 20 observations:SSE was found to be 100 and SS total 400.a. Determine the standard error of estimate.b. Determine the coefficient of determination.c. Determine the coefficient of correlation. (Caution: Watch the sign!) Y 15 - 5X
The manufacturer of Cardio Glide exercise equipment wants to study the relationship between the number of months since the glide was purchased and the length of time the equipment was used last week.a. Plot the information on a scatter diagram. Let hours of exercise be the dependent variable.
A sample of 12 homes sold last week in St. Paul, Minnesota, is selected. Can we conclude that, as the size of the home (reported below in thousands of square feet) increases, the selling price(reported in $ thousands) also increases?a. Compute the coefficient of correlation.b. Determine the
What is the relationship between the amount spent per week on recreation and the size of the family? Do larger families spend more on recreation? A sample of 10 families in the Chicago area revealed the following figures for family size and the amount spent on recreation per week.a. Compute the
For a sample of 32 large U.S. cities, the correlation between the mean number of square feet per office worker and the mean monthly rental rate in the central business district is -.363. At the .05 significance level, can we conclude that there is a negative association in the population between
The table below shows the number of cars (in millions) sold in the United States for the period from 1995 to 2005 and the percent of those cars manufactured by GM. Use a statistical software package to answer the following questions.a. Is the number of cars sold directly or indirectly related to
A suburban hotel derives its gross income from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days(Monday through Thursday) from last year
An Environmental Protection Agency study of 12 automobiles revealed a correlation of 0.47 between engine size and emissions. At the .01 significance level, can we conclude that there is a positive association between these variables? What is the p-value? Interpret.
A sociologist claims that the success of students in college(measured by their GPA) is related to their family’s income. For a sample of 20 students, the coefficient of correlation is 0.40. Using the 0.01 significance level, can we conclude that there is a positive correlation between the
A regional commuter airline selected a random sample of 25 flights and found that the correlation between the number of passengers and the total weight, in pounds, of luggage stored in the luggage compartment is 0.94. Using the .05 significance level, can we conclude that there is a positive
On the first statistics exam the coefficient of determination between the hours studied and the grade earned was 80 percent. The standard error of estimate was 10. There were 20 students in the class.Develop an ANOVA table.
Given the following ANOVA table:a. Determine the coefficient of determination.b. Assuming a direct relationship between the variables, what is the coefficient of correlation?c. Determine the standard error of estimate. SOURCE Regression Error Total DF SS 1 1000.0 13 500.0 14 1500.0 MS F 1000.00
In the Copier Sales of America example we studied the relationship between the number of sales calls made and the number of copiers sold. Use a computer software package to determine the least squares regression equation and the ANOVA table. Identify the regression equation, the standard error of
The number of shares of Icom, Inc., turned over during a month, and the price at the end of the month, are listed in the following table.Also given are the Ŷ values.a. Draw a scatter diagram. Plot a line through the dots.b. Compute the coefficient of determination using formula (13–9).c.
Using the preceding problem, involving years on the job and weekly production, verify that the coefficient of determination is in fact .80.
Refer to Exercise 16.a. Determine the .95 confidence interval, in thousands of dollars, for the mean of all sales personnel who make 40 contacts.b. Determine the .95 prediction interval, in thousands of dollars, for a particular salesperson who makes 40 contacts.
Refer to Exercise 15.a. Determine the .95 confidence interval, in thousands of kilowatthours, for the mean of all six-room homes.b. Determine the .95 prediction interval, in thousands of kilowatt-hours, for a particular six-room home.
Refer to the sample data in Self-Reviews 13–1, 13–3, and 13–4, where the owner of Haverty’s Furniture was studying the relationship between sales and the amount spent on advertising. The sales information for the last four months is repeated below.The regression equation was computed to be
We return to the Copier Sales of America illustration.Determine a 95 percent confidence interval for all sales representatives who make 25 calls and a prediction interval for Sheila Baker, a West Coast sales representative who made 25 calls.
Refer to Exercise 16.a. Determine the standard error of estimate.b. Suppose a large sample is selected (instead of just 10). About 95 percent of the predictions regarding sales would occur between what two values?
Refer to Exercise 15.a. Determine the standard error of estimate.b. Suppose a large sample is selected (instead of just 10). About 95 percent of the predictions regarding kilowatt-hours would occur between what two values?
Refer to Exercise 14.a. Determine the standard error of estimate.b. Suppose a large sample is selected (instead of just eight). About 95 percent of the predictions would be between what two values?
Refer to Exercise 13.a. Determine the standard error of estimate.b. Suppose a large sample is selected (instead of just five). About 68 percent of the predictions would be between what two values?
Refer to Self-Reviews 13–1 and 13–3, where the owner of Haverty’s Furniture was studying the relationship between sales and the amount spent on advertising. Determine the standard error of estimate.
Recall the example involving Copier Sales of America. The sales manager determined the least squares regression equation to be Ŷ= 18.9476 + 1.1842 X, where Ŷ refers to the predicted number of copiers sold and X the number of sales calls made. Determine the standard error of estimate as a measure
Refer to Exercise 5.a. Determine the regression equation.b. Estimate the number of crimes for a city with 20 police.c. Interpret the regression equation.
We are studying mutual bond funds for the purpose of investing in several funds. For this particular study, we want to focus on the assets of a fund and its five-year performance. The question is: Can the five-year rate of return be estimated based on the assets of the fund? Nine mutual funds were
A recent article in BusinessWeek listed the “Best Small Companies.”We are interested in the current results of the companies’ sales and earnings. A random sample of 12 companies was selected and the sales and earnings, in millions of dollars, are reported below.Let sales be the independent
Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client
Bradford Electric Illuminating Company is studying the relationship between kilowatt-hours (thousands) used and the number of rooms in a private single-family residence. A random sample of 10 homes yielded the following.a. Determine the regression equation.b. Determine the number of kilowatt-hours,
The following sample observations were randomly selected.a. Determine the regression equation.b. Determine the value of Ŷ when X is 7. X 5 3 6 3 4 4 6 8 Y: 13 15 7 12 13 11 9 5
The following sample observations were randomly selected.a. Determine the regression equation.b. Determine the value of Ŷ when X is 7. 56 4 * 4 35 6 7 17
Refer to Self-Review 13–1, where the owner of Haverty’s Furniture Company was studying the relationship between sales and the amount spent on advertising. The sales information for the last four months is repeated below.(a) Determine the regression equation.(b) Interpret the values of a and
The Student Government Association at Middle Carolina University wanted to demonstrate the relationship between the number of beers a student drinks and their blood alcohol content (BAC). A random sample of 18 students participated in a study in which each participating student was randomly
The Airline Passenger Association studied the relationship between the number of passengers on a particular flight and the cost of the flight. It seems logical that more passengers on the flight will result in more weight and more luggage, which in turn will result in higher fuel costs. For a
A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be .86. At the .05 significance level, can we conclude that there is positive correlation in the population?
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the correlation was .78. At the .01 significance level, is the correlation in the population greater than zero?
The following hypotheses are given.A random sample of 15 paired observations have a correlation of -.46. Can we conclude that the correlation in the population is less than zero? Use the .05 significance level. H: p
The following hypotheses are given.A random sample of 12 paired observations indicated a correlation of .32.Can we conclude that the correlation in the population is greater than zero?Use the .05 significance level. 0 H: p>0
The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last yeara. If we want to estimate selling price on the basis of the age of the car, which
A sample of 25 mayoral campaigns in cities with populations between 50,000 and 250,000 showed that the correlation between the percent of the vote received and the amount spent on the campaign by the candidate was .43. At the .05 significance level, is there a positive association between the
The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asks the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of
The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then
Bi-lo Appliance Super-Store has outlets in several large metropolitan areas in New England. The general sales manager plans to air a commercial for a digital camera on selected local TV stations prior to a sale starting on Saturday and ending Sunday. She plans to get the information for
Haverty’s Furniture is a family business that has been selling to retail customers in the Chicago area for many years. The company advertises extensively on radio, TV, and the Internet, emphasizing low prices and easy credit terms. The owner would like to review the relationship between sales and
Refer to the Wage data, which report information on annual wages for a sample of 100 workers. Also included are variables relating to industry, years of education, and gender for each worker.a. Conduct a test of hypothesis to determine if there is a difference in the mean annual wages for workers
Copier Sales of America sells copiers to businesses of all sizes throughout the United States and Canada. Ms. Marcy Bancer was recently promoted to the position of national sales manager. At the upcoming sales meeting, the sales representatives from all over the country will be in attendance. She
Refer to the Real Estate data, which report information on the homes sold in the Denver, Colorado, area last year.a. At the .02 significance level, is there a difference in the variability of the selling prices of the homes that have a pool versus those that do not have a pool?b. At the .02
Refer to the Baseball 2006 data, which report information on the 30 Major League Baseball teams for the 2006 season.a. At the .10 significance level, is there a difference in the variation in team salary among the American and National league teams?b. Create a variable that classifies a team’s
The percentages of quarterly changes in the Gross Domestic Product for 20 countries are available at the following site:http://www.oecd.org. Select Statistics, National Accounts, Quarterly National Accounts and select Quarterly Growth Rates of GDP at Constant Price for OECD Countries. Copy the data
Many real estate companies and rental agencies now publish their listings on the Web. One example is Dunes Realty Company, located in Garden City Beach, South Carolina. Go to its website, http://www.dunes.com, select Vacation Rentals, then Beach Home w/Pool Search, then indicate 5 bedrooms,
There are four radio stations in Midland. The stations have different formats (hard rock, classical, country/western, and easy listening), but each is concerned with the number of minutes of music played per hour. From a sample of 10 hours from each station, the following sample means were
One reads that a business school graduate with an undergraduate degree earns more than a high school graduate with no additional education, and a person with a master’s degree or a doctorate earns even more. To investigate we select a sample of 25 mid-level managers of companies in southeast
A grocery store wants to monitor the amount of withdrawals that its customers make from automatic teller machines (ATMs) located within its stores. It samples 10 withdrawals from each location and the output from a statistical software package is:a. Use a .01 level of significance to test if there
Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of six hourly periods is chosen for each assembly line and the number of components produced during these periods for each line is recorded.The output from a statistical

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