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mathematics
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Business Statistics For Contemporary Decision Making 8th Edition Black Ken - Solutions

The €œEconomic Report to the President of the United States€ included data on the amounts of manufacturers€™ new and unfilled orders in millions of dollars. Shown here are the figures for new orders over a 21-year period. Use a computer to develop a regression model
The following data on the number of union members in the United States for the years 1984 through 2012 are provided by the U.S. Bureau of Labor Statistics. Using regression techniques discussed in this section, analyze the data for trend. Develop a scatter plot of the data and fit the trend line
Shown below are dollar figures for commercial and industrial loans at all commercial banks in the United States as recorded for the month of April during a recent 9-year period and published by the Federal Reserve Bank of St. Louis. Plot the data, fit a trend line, and discuss the strength of the
The U.S. Department of Agriculture publishes statistics on the production of various types of food commodities by month. Shown here are the production figures on broccoli for January of a recent year through December of the next year.Use these data to compute 12-month centered moving averages (T.
The U.S. Department of Commerce publishes census information on manufacturing. Included in these figures are monthly shipment data for the paperboard container and box industry shown below for 6 years. The shipment figures are given in millions of dollars. Use the data to analyze the effects of
The U.S. Department of Labor publishes consumer price indexes (CPIs) on many commodities. Following are the percentage changes in the CPIs for food and for shelter for the years 1994 through 2011.Use these data to develop a linear regression model to forecast the percentage change in food CPIs by
Use the data from Problem 15.15 to create a regression forecasting model using the first-differences data transformation. How do the results from this model differ from those obtained in Problem15.15?
The Federal Deposit Insurance Corporation (FDIC) releases data on bank failures. Following are data on the number of U.S. bank failures in a given year and the total amount of bank deposits (in $ millions) involved in such failures for a given year. Use these data to develop a simple regression
Use the data in Problem 15.17 to compute a regression model after recoding the data by the first-differences approach. Compute a Durbin-Watson statistic to determine whether significant autocorrelation is present in this first-differences model. Compare this model with the model determined in
Current Construction Reports from the U.S. Census Bureau contain data on new privately owned housing units. Data on new privately owned housing units (1000s) built in the West between 1980 and 2010 follow. Use these time-series data to develop an auto-regression model with a one-period lag. Now try
The U.S. Department of Agriculture publishes data on the production, utilization, and value of fruits in the United States. Shown here are the amounts of non-citrus fruit processed into juice (in kilotons) for a 25-year period. Use these data to develop an auto-regression forecasting model with a
Suppose the following data represent the price of 20 reams of office paper over a 60-year time frame. Find the simple index numbers for the data.a. Let 1950 be the base year.b. Let 1980 be the baseyear.
The U.S. Patent and Trademark Office reports fiscal year figures for patents issued in the United States. Following are the numbers of patents issued for the years 1980 through 2012.Using these data and a base year of 1990, determine the simple index numbers for eachyear.
Using the data that follow, compute the aggregate index numbers for the four types of meat. Let 1995 be the base year for this market basket ofgoods.
Suppose the following data are prices of market goods involved in household transportation for the years 2006 through 2013.Using 2008 as a base year, compute aggregate transportation price indexes for thisdata.
Calculate Laspeyres price indexes for 2011€“2013 from the following data. Use 2005 as the baseyear.
Calculate Paasche price indexes for 2012 and 2013 using the following data and 2005 as the baseyear.
Following are the average yields of long-term new corporate bonds over a several-month period published by the Office of Market Finance of the U.S. Department of the Treasury..:.a. Explore trends in these data by using regression trend analysis. How strong are the models? Is the quadratic model
Compute index numbers for the following data using 1997 as the baseyear.
Compute un-weighted aggregate price index numbers for each of the given years using 2009 as the baseyear.
Using the following data and 2010 as the base year, compute the Laspeyres price index for 2013 and the Paasche price index for2012.
The following data contain the quantity (million pounds) of U.S. domestic fish caught annually over a 25-year period as published by the National Oceanic and Atmospheric Administration.a. Use a 3-year moving average to forecast the quantity of fish for the years 1989 through 2010 for these
The U.S. Department of Commerce publishes a series of census documents referred to as Current Industrial Reports. Included in these documents are the manufacturers€™ shipments, Inventories, and orders over a 5-year period. Displayed here is a portion of these data representing the
Use the seasonal indexes computed to de-seasonalize the data in Problem15.32.
Determine the trend for the data in Problem 15.32 using the de-seasonalized data from Problem 15.33. Explore both a linear and a quadratic model in an attempt to develop the better trendmodel.
Shown here are retail price figures and quantity estimates for five different food commodities over 3 years. Use these data and a base year of 2011 to compute Un-weighted aggregate price indexes for this market basket of food. Using a base year of 2011, calculate Laspeyres price indexes and Paasche
Given below are data on the number of business establishments (millions) and the self-employment rate (%) released by the Small Business Administration, Office of Advocacy, for a 21-year period of U.S. business activity. Develop a regression model to predict the self-employment rate by the number
Shown here are the consumer price indexes (CPIs) for housing for the years 1990 through 2011 from the Bureau of Labor Statistics Data Web site. Use the data to answer the following questions.a. Compute the 4-year moving average to forecast the CPIs from 1994 through 2011.b. Compute the 4-year
In the Survey of Current Business, the U.S. Department of Commerce publishes data on farm commodity prices. Given are the cotton prices from November of year 1 through February of year 4.The prices are indexes with a base of 100 from the period of 1910 through 1914.Use these data to develop
The U.S. Department of Commerce publishes data on industrial machinery and equipment. Shown here are the shipments (in $ billions) of industrial machinery and equipment from the first quarter of year 1 through the fourth quarter of year 6. Use these data to determine the seasonal indexes for the
Use the seasonal indexes computed to de-seasonalize the data in Problem 15.39.Industrial Machinery andTime Period ........ Equipment Shipments1st quarter (year 1) ...... 54.0192nd quarter ....... 56.4953rd quarter ....... 50.1694th quarter ........ 52.8911st quarter (year 2) .... 51.9152nd
Use both a linear and quadratic model to explore trends in the de-seasonalized data from Problem 15.40. Which model seems to produce a better fit of the data?Industrial Machinery andTime Period ........ Equipment Shipments1st quarter (year 1) ...... 54.0192nd quarter ....... 56.4953rd quarter
Shown here are data from the Investment Company Institute on Total Net Assets and Total Number of Shareholder Accounts of money market funds over a period of 27 years. Use these data to develop a regression model to forecast Total Net Assets by the Total Number of Shareholder Accounts. Total Net
The purchasing-power value figures for the minimum wage in dollars for the years 1 through 18 are shown here. Use these data and exponential smoothing to develop forecasts for the years 2 through 18. Try Î± = .1, .5, and .8, and compare the results using MAD. Discuss your findings.
Shown below is the Excel output for a regression analysis to predict the number of business bankruptcy filings over a 16-year period by the number of consumer bankruptcy filings. How strong is the model? Note the residuals. Compute a Durbin-Watson statistic from the data and discuss the presence of
The Board of Governors of the Federal Reserve System publishes data on mortgage debt outstanding by type of property and holder. The following data give the amounts of residential nonfarm debt (in $ billions) held by savings institutions in the United States over a 10-year period. Use these data to
The DeBourgh Manufacturing Company was founded in 1909 as a metal-fabricating company in Minnesota by the four Berg brothers. In the 1980s, the company ran into hard times, as did the rest of the metal-fabricating industry. Among the problems that DeBourgh faced were declining sales, deteriorating
Use a chi-square goodness-of-fit test to determine whether the observed frequencies are distributed the same as the expected frequencies (Î± =.05).
Use the following data and α = .01 to determine whether the observed frequencies represent a uniform distribution.Category .... fo1 ........ 192 ........ 173 ........ 144 ....... 185 ...... 196 ........ 217 ........ 188 ........ 18
Are the following data Poisson distributed? Use α = .05 and the chi-square goodness-of-fit test to answer this question. What is your estimated lambda?Number of Arrivals ... fo0 .......... 281 ......... 172 .......... 113 .......... 5
Use the chi-square goodness-of-fit to test to determine if the following observed data are normally distributed. Let α = .05.What are your estimated mean and standard deviation?Category .... Observed10–under 20 ... 620–under 30 ... 1430–under 40 .... 2940–under 50 ... 3850–under 60
In one survey, successful female entrepreneurs were asked to state their personal definition of success in terms of several categories from which they could select. Thirty-nine percent responded that happiness was their definition of success, 12% said that sales/profit was their definition, 18%
The following percentages come from a national survey of the ages of prerecorded-music shoppers. A local survey produced the observed values. Does the evidence in the observed data indicate that we should reject the national survey distribution for local prerecorded-music shoppers? Use
The general manager of a major league baseball team believes the ages of purchasers of game tickets are normally distributed. The following data represent the distribution of ages for a sample of observed purchasers of major league baseball game tickets. Use the chi-square goodness-of-fit test to
The Springfield Emergency Medical Service keeps records of emergency telephone calls. A study of 150 five-minute time intervals resulted in the distribution of number of calls that follows. For example, during 18 of the 5-minute intervals, no calls occurred. Use the chi-square goodness-of-fit test
According to a report by the U.S. Environmental Protection Agency (EPA), containers and packaging generated about 30.3% of all municipal solid waste (MSW) in the country in a recent year. This was the largest category of such waste. The next highest group was nondurable goods, which accounted for
Use the following contingency table to test whether variable 1 is independent of variable 2.Let a Î± =.01.
Use the following contingency table to determine whether variable 1 is independent of variable 2. Let Î± =.01.
Use the following contingency table and the chi-square test of independence to determine whether social class is independent of number of children in a family. Let Î± =.05.
A group of 30-year-olds is interviewed to determine whether the type of music most listened to by people in their age category is independent of the geographic location of their residence. Use the chi-square test of independence, Î± = .01, and the following contingency table to
Is the transportation mode used to ship goods independent of type of industry? Suppose the following contingency table represents frequency counts of types of transportation used by the publishing and the computer hardware industries. Analyze the data by using the chi-square test of independence to
According to data released by the U.S. Department of Housing and Urban Development about new homes built in the United States, there is an almost 50€“50 split between one-story and two-story homes. In addition, more than half of all new homes have three bedrooms. Suppose a study is done
A study was conducted to determine the impact of major Mexican peso devaluation on U.S. border retailers. As a part of the study, data were gathered on the magnitude of business that U.S. border retailers were doing with Mexican citizens. Forty-one shoppers of border city department stores were
Use a chi-square goodness-of-fit test to determine whether the following observed frequencies are distributed the same as the expected frequencies. Let Î± =.01.
Use the chi-square contingency analysis to test to determine whether variable 1 is independent of variable 2. Use 5% level ofsignificance.
Is a manufacturer€™s geographic location independent of type of customer? Use the following data for companies with primarily industrial customers and companies with primarily retail customers to test this question. Let Î± =.10.
A national youth organization sells six different kinds of cookies during its annual cookie campaign. A local leader is curious about whether national sales of the six kinds of cookies are uniformly distributed. He randomly selects the amounts of each kind of cookies sold by five youths and
A researcher interviewed 2067 people and asked whether they were the primary decision makers in the household when buying a new car last year. Two hundred seven were men and had bought a new car last year. Sixty-five were women and had bought a new car last year. Eight hundred eleven of the
Are random arrivals at a shoe store at the local mall Poisson distributed? Suppose a mall employee researches this question by gathering data for arrivals during one-minute intervals on a weekday between 6:30 P.M. and 8:00 P.M. The data obtained follow. Use α = .05 to determine whether the
According to Beverage Digest and Accu Val, the distribution of market share for the top seven soft drinks in the United States is Coke Classic 26%,Diet Coke 15%, Pepsi Cola 15%, Mountain Dew 10%, Dr. Pepper 9%, Sprite 8%, Diet Pepsi 8%, and Others 9%. Suppose a marketing analyst wants to determine
Are the types of professional jobs held in the computing industry independent of the number of years a person has worked in the industry? Suppose 246 workers are interviewed. Use the results obtained to determine whether type of professional job held in the computer industry is independent of years
Is the number of children that a college student currently has independent of the type of college or university being attended? Suppose students were randomly selected from three types of colleges and universities and the data shown represent the results of a survey of those students. Use a
A survey by Ipsos-Reid reported in American Demographics showed that if a person was given a $1,000 windfall, 36% would spend the money on home improvement, 24% on leisure travel/vacation, 15% on clothing, 15% on home entertainment or electronic products, and 10% on local entertainment including
Do men and women prefer the same colors of cars? That is, is sex independent of color preference for cars? Suppose a study is undertaken to address this question. A random sample of men and women are asked which of five colors (silver, white, and black, green, blue) they prefer in a car. The
Foot Locker Inc. is the world€™s number one retailer of athletic footwear and apparel. Headquartered in New York City, the company has over 44,000 employees and 3369 retail stores in 23 countries across North America, Europe, Australia, and New Zealand operating under such brand names as
Test the following sequence of observations by using the runs test and Î± = .05 to determine whether the process produced randomresults.
Test the following sequence of observations by using the runs test and Î± = .05 to determine whether the process produced randomresults.
A process produced good parts and defective parts. A sample of 60 parts was taken and inspected. Eight defective parts were found. The sequence of good and defective parts was analyzed by using Minitab. The output is given herewith a two-tailed test and Î± = .05, what conclusions can
A Watson Wyatt Worldwide survey showed that 58% of all Hispanic Americans are satisfied with their salary. Suppose a researcher randomly samples 27 Hispanic American workers and asks whether they are satisfied with their salary with the result that 15 say yes. The sequence of Yes and No responses
A Virginia Slims Opinion Poll by Roper Starch found that more than 70% of the women interviewed believe they have had more opportunity to succeed than their parents. Suppose a researcher in your state conducts a similar poll and asks the same question with the result that of 64 women interviewed,
A survey conducted by the Ethics Resource Center discovered that 35% of all workers say that coworkers have committed some kind of office theft. Suppose a survey is conducted in your large company to ask the same question of 13 randomly selected employees. The results are that five of the sample
Use the Mann-Whitney U test and the following data to determine whether there is a significant difference between the values of group 1 and group 2.Let α = .05.Group 1 .. Group 215 ..... 2317 ...... 1426 ...... 2411 .... 1318 ..... 2221 ..... 2313 .... 1829 ..... 21
The data shown represent two random samples gathered from two populations. Is there sufficient evidence in the data to determine whether the values of population 1 are significantly larger than the values of population 2? Use the Mann-Whitney U test and α = .01.Sample 1 .. Sample 2224
Results of a survey by the National Center for Health Statistics indicated that people between 65 and 74 years of age contact a physician an average of 9.8 times per year. People 75 and older contact doctors an average of 12.9 times per year. Suppose you want to validate these results by taking
Suppose 12 urban households and 12 rural households are selected randomly and each family is asked to report the amount spent on food at home annually. The results follow. Use a Mann-Whitney U test to determine whether there is a significant difference between urban and rural households in the
Does the male stock market investor earn significantly more than the female stock market investor? One study by the New York Stock Exchange showed that the male investor has an income of $46,400 and that the female investor has an income of $39,400.Suppose an analyst wanted to “prove” that the
The National Association of Realtors reports that the median price of an existing single-family home in Denver, Colorado, is $225,100 and the median price of an existing single-family home in Hartford, Connecticut, is $233,700.Suppose a survey of 13 randomly selected single-family homes is taken in
Use the Wilcoxon matched-pairs signed rank test to determine whether there is a significant difference between the two groups of related data given. Use Î± = .10. Assume the underlying distributions aresymmetrical.
Use the Wilcoxon matched-pairs signed rank test and α = .05 to analyze the before-and-after measurements given. Assume the underlying distributions are symmetrical.Before ... After49 .... 4341 .... 2947 .... 3039 .... 3853 .... 4051 .... 4351 .... 4649 .... 4038 .... 4254 .... 5046 .... 4750
A corporation owns a chain of several hundred gasoline stations on the eastern seaboard. The marketing director wants to test a proposed marketing campaign by running ads on some local television stations and determining whether gasoline sales at a sample of the company€™s stations
Most supermarkets across the United States have invested heavily in optical scanner systems to expedite customer checkout, increase checkout productivity, and improve product accountability. These systems are not 100% effective, and items often have to be scanned several times. Sometimes items are
American attitudes toward big business change over time and probably are cyclical. Suppose the following data represent a survey of 20 American adults taken in 1990 and again in 2013 in which each adult was asked to rate American big business overall on a scale from 1 to 100 in terms of positive
Suppose 16 people in various industries are contacted in 2012 and asked to rate business conditions on several factors. The ratings of each person are tallied into a €œbusiness optimism€ score. The same people are contacted in 2013 and asked to do the same thing. The higher the
Use the Kruskal-Wallis test to determine whether groups 1 through 5 come from different populations. Let Î± =.01.
Use the Kruskal-Wallis test to determine whether there is a significant difference in the following groups. Use Î± =.05.
Is there a difference in the amount of customers€™ initial deposits when they open savings accounts according to geographic region of the United States? To test this question, an analyst selects savings and loan offices of equal size from four regions of the United States. The offices
Does the asking price of a new car vary according to whether the dealership is in a small town, a city, or a suburban area? To test this question, a researcher randomly selects dealerships selling Buicks in the state of Illinois. The researcher goes to these dealerships posing as a prospective
A survey by the U.S. Travel Data Center showed that a higher percentage of Americans travel to the ocean/beach for vacation than to any other destination. Much further behind in the survey, and virtually tied for second place, were the mountains and small/rural towns. How long do people stay at
Do workers on different shifts get different amounts of sleep per week? Some people believe that shift workers who regularly work the graveyard shift (12:00 A.M.to 8:00 A.M.) or swing shift (4:00 P.M.to 12:00 A.M.) are unable to get the same amount of sleep as day workers because of family
Use the following data to test to determine whether there are any differences between treatment levels. Let Î± =.05.
Use the Friedman test and Î± = .05 to test the following data to determine whether there is a significant difference between treatmentlevels.
An experiment is undertaken to study the effects of four different medical treatments on the recovery time for a medical disorder. Six physicians are involved in the study. One patient with the disorder is sampled for each physician under each treatment, resulting in 24 patients in the study.
Does the configuration of the workweek have any impact on productivity? This question is raised by a researcher who wants to compare the traditional 5-day workweek with a 4-day workweek and a workweek with three 12-hour days and one 4-hour day. The researcher conducts the experiment in a factory
Shown here is Minitab output for a Friedman test. Discuss the experimental design and the outcome of theexperiment.
Compute a Spearman’s rank correlation for the following variables to determine the degree of association between the two variables.x .... y23 .... 20141 .... 25937 .... 23429 .... 24025 .... 23117 .... 20933 .... 22941 .... 24640 .... 24828 .... 22719 .... 200
The following data are the ranks for values of the two variables, x and y. Compute a Spearman€™s rank correlation to determine the degree of relation between the twovariables.
Compute a Spearman€™s rank correlation for the followingdata.
Over a period of a few months, is there a strong correlation between the value of the U.S. dollar and the prime interest rate? The following data represent a sample of these quantities over a period of time. Compute a Spearman€™s rank correlation to determine the strength of the
Shown here are the percentages of consumer loans with payments that are 30 days or more overdue for both bank credit cards and home equity loans over a 14-year period, according to the American Bankers Association. Compute a Spearman€™s rank correlation to determine the degree of
Shown here are the net tonnage figures for total pig iron and raw steel output in the United States as reported by the American Iron and Steel Institute over a 12-year period. Use these data to calculate a Spearman€™s rank correlation to determine the degree of association between

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