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Business Statistics A Decision Making Approach 8th Edition David F. Groebner, Patrick W. Shannon, Phillip C. Fry, Kent D. Smith - Solutions
As an example of how the sampling distribution for the Mann–Whitney Test is derived, consider two samples with sample sizes n1 2 and n2 3. The distribution is obtained under the assumption that the two variables, say x and y, are identically distributed. Under this assumption, each
In the library, locate two journal articles that use one of the nonparametric tests discussed in this chapter. Prepare a brief outline of the articles, paying particular attention to the reasons given for using the particular test.
Find an organization you think would be interested in data that would violate the measurement scale or known distribution assumptions necessary to use the statistical tools found in Chapters 10–12 (retail stores are a good candidate). Determine to what extent this organization considers these
Suppose as part of your job you are responsible for installing emergency lighting in a series of state office buildings. Bids have been received from four manufacturers of battery-operated emergency lights.The costs are about equal, so the decision will be based on the length of time the lights
Referring to Exercise 17-41, suppose that there were 40 ties at eight different salary levels. The following shows how many scores were ties at each salary level:a. Given the results in the previous exercise, is it necessary to use the H-value adjusted for ties?b. If your answer to part a is yes,
The American Beef Growers Association is trying to promote the consumption of beef products. The organization performs numerous studies, the results of which are often used in advertising campaigns. One such study involved a quality perception test. Three grades of beef were involved: choice,
A study was conducted in which samples were selected independently from four populations. The sample size from each population was 20. The data were converted to ranks. The sum of the ranks for the data from each sample is as follows:Sample 1 Sample 2 Sample 3 Sample 4 Sum of ranks 640 780 460
Given the following data:Group 1 Group 2 Group 3 Group 4 20 28 17 21 27 26 15 23 26 21 18 19 22 29 20 17 25 30 14 20 30 25 23a. State the appropriate null and alternative hypotheses for determining whether a difference exists in the median value for the four populations.b. Based on the sample data,
Given the following sample data:Group 1 Group 2 Group 3 10 8 13 9 6 12 11 8 12 12 9 11 13 10 13 12 10 15a. State the appropriate null and alternative hypotheses for determining whether a difference exists in the median value for the three populations.b. Based on the sample data, use the
Given the following sample data:Group 1 Group 2 Group 3 21 17 29 25 15 38 36 34 28 35 22 27 33 16 14 23 19 26 31 30 39 32 20 36a. State the appropriate null and alternative hypotheses to test whether there is a difference in the medians of the three populations.b. Based on the sample data and a
The Montgomery Athletic Shoe Company has developed a new shoe-sole material it thinks provides superior wear compared with the old material the company has been using for its running shoes. The company selected 10 cross-country runners and supplied each runner with a pair of shoes. Each pair had
Radio advertisements have been stressing the virtues of an audiotape program to help children learn to read.To test whether this tape program can cause a quick improvement in reading ability, 10 children were given a nationally recognized reading test that measures reading ability. The same 10
The Kansas Tax Commission recently conducted a study to determine whether there is a difference in median deductions taken for charitable contributions depending on whether a tax return is filed as a single or a joint return. A random sample from each category was selected, with the following
Property taxes are based on assessed values of property. In most states, the law requires that assessed values be “at or near” market value of the property.In one Washington county, a tax protest group has claimed that assessed values are higher than market values. To address this claim, the
The makers of the Plus 20 Hardcard, a plug-in hard disk unit on a PC board, have recently done a marketing research study in which they asked two independently selected groups to rate the Hardcard on a scale of 1 to 100, with 100 being perfect satisfaction. The first group consisted of professional
Consider the following data for two paired samples:Case # Sample 1 Sample 2 1 258 304 2 197 190 3 400 500 4 350 340 5 237 250 6 400 358 7 370 390 8 130 100a. Test the following null and alternative hypotheses at an a 0.05 level:H0: There is no difference between the two population
You are given two paired samples with the following information:Item Sample 1 Sample 2 1 234 245 2 221 224 3 196 194 4 245 267 5 234 230 6 204 198 Based on these paired samples, test at the a 0.05 level whether the true median paired difference is 0.
You are given two paired samples with the following information:Item Sample 1 Sample 2 1 19.6 21.3 2 22.1 17.4 3 19.5 19.0 4 20.0 21.2 5 21.5 20.1 6 20.2 23.5 7 17.9 18.9 8 23.0 22.4 9 12.5 14.3 10 19.0 17.8 Based on these paired samples, test at the a 0.05 level whether the true median paired
For each of the following tests, determine which of the two sums of absolute ranks (negative or positive) you would choose, the appropriate test statistic, and the rejection region for the Wilcoxon matched-pairs signed rank test: a. Ha=0.025, n=15 b. H, = 0.01, n = 12 C. HAM,a=0.05, n=9 d.
The following sample data have been collected from independent samples from two populations.Do the populations have different medians? Test at a significance level of 0.05. Use the Mann–Whitney U-test.Sample 1 Sample 2 550 489 594 538 483 480 542 505 379 433 447 486 438 436 466 425 398 540 560
Determine the rejection region for the Mann–Whitney U-test in each of the following cases: a. H, a=0.05, n=3, and n = 15 b. H, a=0.10, n=5, and n = 20 c. H, a=0.025, n=9, and n=12 d. H, a=0.10, n=124, and n = 25 #
For each of the following tests, determine which of the two U statistics (U1 or U2) you would choose, the appropriate test statistic, and the rejection region for the Mann–Whitney test: A a. HM, a=0.05, n=5, and n = 10 b. H,a=0.05, n = 15, and n = 12 c. H,a=0.10, n=12, and n =17 d. Ha=0.05, n
The Wilson Company uses a great deal of water in the process of making industrial milling equipment. To comply with federal clean-water laws, it has a water purification system that all wastewater goes through before being discharged into a settling pond on the company’s property. To determine
The Penn Oil Company wished to verify the viscosity of its premium 30-weight oil. A simple random sample of specimens taken from automobiles running at normal temperatures was obtained. The viscosities observed were as follows:25 24 21 35 25 25 35 38 32 36 35 29 30 27 28 27 31 32 30 30 Determine if
Sylvania’s quality control division is constantly monitoring various parameters related to its products.One investigation addressed the life of incandescent light bulbs (in hours). Initially, they were satisfied with examining the average length of life. However, a recent sample taken from the
At Hershey’s, the chocolate maker, a particular candy bar is supposed to weigh 11 ounces. However, the company has received complaints that the bars are under weight. To assess this situation, the company has conducted a statistical study that concluded that the average weight of the candy is
A recent trade newsletter reported that during the initial 6-month period of employment, new sales personnel in an insurance company spent a median of 119 hours per month in the field. A random sample of 20 new salespersons was selected. The numbers of hours spent in the field by members in a
A cable television customer call center has a goal that states that the median time for each completed call should not exceed four minutes. If calls take too long, productivity is reduced and other customers have to wait too long on hold. The operations manager does not want to incorrectly conclude
Sigman Corporation makes batteries that are used in highway signals in rural areas. The company managers claim that the median life of a battery exceeds 4,000 hours. To test this claim, they have selected a random sample of n 12 batteries and have traced their life spans between installation and
Consider the following set of observations:3.1 4.8 2.3 5.6 2.8 2.9 4.4 You should not assume these data come from a normal distribution. Test the hypothesis that these data come from a distribution with a median equal to 4. Use a 0.10.
Continuing with the DataNet forecasting problems, develop a double exponential smoothing model using smoothing constants a 0.20 and b 0.20.
Referring to Problem 16-58, the managers of DataNet, the Internet company where users can purchase products like airline tickets, need to forecast monthly call volumes in order to have sufficient capacity.Develop a single exponential smoothing model using a 0.30. Use as a starting value the
DataNet is an Internet service where clients can find information and purchase various items such as airline tickets, stereo equipment, and listed stocks. DataNet has been in operation for four years. Data on monthly calls for service for the time that the company has been in business are in the
College tuition has risen at a pace faster than inflation for more than two decades, according to an article in USA Today. The following data indicate the average college tuition (in 2003 dollars) for public colleges:Period 1983–1984 1988–1989 1993–1994 1998–1999 2003–2004 2008–2009
Amazon.com has become one of the most successful online merchants. Two measures of its success are sales and net income/loss figures. They are given here.Year Net Income/Loss Sales 1995 -0.3 0.5 1996 -5.7 15.7 1997 -27.5 147.7 1998 -124.5 609.8 1999 -719.9 1,639.8 2000 -1,411.2 2,761.9 2001 -567.3
Using whatever diagnostic tools you are familiar with, determine which of the three forecasting methods utilized to forecast sales for Malcar Autoparts Company in the previous three problems provides superior forecasts. Explain the reasons for your choice.
Develop a double exponential smoothing model using smoothing constants a 0.20 and b 0.40. As starting values, use the least squares trend line slope and intercept values.a. Compute the MAD for this model.b. Plot the forecast values against the actual data.c. Use the same starting values but try
Develop a single exponential smoothing model using a 0.20. Use as a starting value the average of the first 6 years’ data. Determine the forecasted value for year 2010.a. Compute the MAD for this model.b. Plot the forecast values against the actual data.c. Use the same starting value but try
As a start in analyzing these data,a. Graph these data and indicate whether they appear to have a linear trend.b. Develop a simple linear regression model with time as the independent variable. Using this regression model, describe the trend and the strength of the linear trend over the 16 years.
Identify the businesses in your community that might be expected to have sales that exhibit a seasonal component. Discuss.
A time series exhibits the pattern stated below. Indicate the type of time-series component described.a. The pattern is “wavelike” with a recurrence period of nine months.b. The time series is steadily increasing.c. The pattern is “wavelike” with a recurrence period of two years.d. The
Referring to Problem 16-44, in which the sales manager for Grossmieller Imports of New York City needs to forecast monthly sales,a. Discuss why a double exponential smoothing model might be preferred over a single exponential smoothing model.b. (1) Develop a double exponential smoothing model using
The human resources manager for a medium-sized business is interested in predicting the dollar value of medical expenditures filed by employees of her company for the year 2011. From her company’s database she has collected the following information showing the dollar value of medical
“The average college senior graduated this year with more than $19,000 in debt” was the beginning sentence of a recent article in USA Today. The majority of students have loans that are not due until the student leaves school. This can result in the student ignoring the size of debt that piles
With tax revenues declining in many states, school districts have been searching for methods of cutting costs without affecting classroom academics. One district has been looking at the cost of extracurricular activities ranging from band trips to athletics. The district business manager has
The following data represent the average number of employees in outlets of a large consumer electronics retailer:Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Number 20.6 17.3 18.6 21.5 23.2 19.9 18.7 15.6 19.7 20.4a. Construct a time-series plot of this time series. Does it appear that a
The federal funds rate is the interest rate charged by banks when banks borrow “overnight” from each other. The funds rate fluctuates according to supply and demand and is not under the direct control of the Federal Reserve Board, but is strongly influenced by the Fed’s actions. The file
Refer to Problem 16-30.a. Use the linear trend model (without transformation) for the first 15 months and provide a cash balance forecast for month 16. Then make the t2 transformation and develop a new linear trend forecasting model based on months 1–15.Forecast the cash balance for month 16. Now
A major brokerage company has an office in Miami, Florida. The manager of the office is evaluated based on the number of new clients generated each quarter.The following data reflect the number of new customers added during each quarter between 2006 and 2009.2006 2007 1st quarter 218 1st quarter
Manuel Gutierrez correctly predicted the increasing need for home health care services due to the country’s aging population. Five years ago, he started a company offering meal delivery, physical therapy, and minor housekeeping services in the Galveston area. Since that time he has opened offices
The average monthly price of regular gasoline in Southern California is monitored by the Automobile Club of Southern California’s monthly Fuel Gauge Report. The prices of the time period July 2004 to June 2006 are given here.Month Price ($) Month Price ($) Month Price ($)7/04 2.247 5/05 2.532
“The average college senior graduated this year with more than $19,000 in debt” was the beginning sentence of a recent article in USA Today. The majority of students have loans that are not due until the student leaves school. This can result in the student ignoring the size of debt that piles
Examine the following quarterly data:t 1 2 3 4 5 6 7 8 9 10 11 12 yt 2 12 23 20 18 32 48 41 35 52 79 63a. Compute the four-period moving averages for this set of data.b. Compute the centered moving averages from the moving averages of part a.c. Compute the ratio-to-moving-averages values.d.
Examine the following time series:t 1 2 3 4 5 6 7 8 9 10 yt 52 72 58 66 68 60 46 43 17 3a. Produce a scatter plot of this time series. Indicate the appropriate forecasting model for this time series.b. Construct the equation for the forecasting model identified in part a.c. Produce forecasts for
Based on your work in the previous three problems,a. Determine a seasonally adjusted linear trend forecasting model. Compare this model with an unadjusted linear trend model. Use both models to forecast Tran’s sales for period 49.b. Which of the two models developed has the lower MAD and lower
Retail Forward, Inc., is a global management consulting and market research firm specializing in retail intelligence and strategies. One of its press releases (June Consumer Outlook: Spending Plans Show Resilience, June 1, 2006) divulged the result of the Retail Forward ShopperScape™ survey
Construct a Laspeyres index using the data, assuming that in 1999, 40% of the cost of a townhouse was labor.
Construct a Paasche index for 2004 using the data. Use 1999 as the base year and assume that in 2004 60% of the cost of a townhouse was in materials.
Plot both series of data and comment on the trend you see in both plots.
Using 1999 as the base year, construct a separate index for each component in the construction of a house.
The following values represent advertising rates paid by a regional catalog retailer that advertises either on radio or in newspapers:Year Radio Rates ($) Newspaper Rates ($)1 300 400 2 310 420 3 330 460 4 346 520 5 362 580 6 380 640 7 496 660a. Determine a relative index for each type of
Analyze the stepwise regression model. Write a report to the marketing manager pointing out the strengths and weaknesses of the model. Be sure to comment on the department’s goal of being able to use the model to predict which customers will purchase high volumes from McCracken.
Referring to Problem 15-75, suppose the manager of McCracken’s marketing department questions the appropriateness of adding a second variable. How would you respond to her question?
Describe the regression model at Step 2 of the analysis.In your discussion, be sure to discuss the effect of adding a new variable on the standard error of the estimate and on R2.
Use forward selection stepwise regression to develop the multiple regression model. The variable x2, family income, was brought into the model. Discuss why this happened.
A first step in regression analysis often involves developing a scatter plot of the data. Develop the scatter plots of all the possible pairs of variables, and with a brief statement indicate what each plot says about the relationship between the two variables.
The publishing company recently came up with some additional data for the 15 books in the original sample.Two new variables, production expenditures (x5) and number of prepublication reviewers (x6), have been added. These additional data are as follows:Book x5 ($) x6 1 38,000 5 2 86,000 8 3 59,000
Amazon.com has become one of the most successful online merchants. Two measures of its success are sales and net income/loss figures. They are given here.Year Net Income/Loss Sales 1995 0.3 0.5 1996 5.7 15.7 1997 27.5 147.7 1998 124.5 609.8 1999 719.9 1,639.8 2000 1,411.2 2,761.9 2001 567.3
Consider the following model:y = 5 3x1 5x2a. Provide an interpretation of the coefficient of x1.b. Is the interpretation provided in part a true regardless of the value of x2? Explain.c. Now consider the model 5 3x1 5x2 yˆ 4x1x2. Let x2 1. Give an interpretation of the coefficient of
Go to the library or use the Internet to locate three articles using a regression model with more than one independent variable. For each article write a short summary covering the following points:Purpose for using the model How the variables in the model were selected How the data in the model
Refer to Exercise 15-9, which referenced an article in BusinessWeek that presented a list of the 100 companies perceived as having “hot growth” characteristics. The file entitled Logrowth contains sales ($million), sales increase (%), return on capital, market value ($million), and recent stock
Examine the following data set:y x1 x2 25 5 25 35 5 5 14 5 5 45 25 40 52 25 5 41 25 25 65 30 30 63 30 30 68 30 25 75 40 30a. Determine the estimated regression equation for this data set.b. Calculate the residuals and the standardized residuals for this regression equation.c. Produce the
The consumer price index (CPI) is a measure of the average change in prices over time in a fixed market basket of goods and services typically purchased by consumers. One of the items in this market basket that affects the CPI is the price of oil and its derivatives.The file entitled Consumer
A variety of sources suggest that individuals assess their health, at least in part, by estimating their percentage of body fat. A widely accepted measure of body fat uses an underwater weighing technique. There are, however, more convenient methods using only a scale and a measuring tape. An
An investment analyst collected data of 20 randomly chosen companies. The data consisted of the 52-weekhigh stock prices, PE ratios, and the market values of the companies. These data are in the file entitled Investment. The analyst wishes to produce a regression equation to predict the market
Which model would you choose? Explain your answer.
Refer to Problem 15-45.a. Develop the correlation matrix that includes all independent variables and the dependent variable.Predict the order that the variables will be selected into the model if forward selection stepwise regression is used.b. Use forward selection stepwise regression to develop a
The U.S. Energy Information Administration publishes summary statistics concerning the energy sector of the U.S. economy. The electric power industry continues to grow. Electricity generation and sales rose to record levels. The file entitled Energy presents the revenue from retail sales ($million)
Consider the following set of data:y x1 x2 x3 x4 61 37 18 2 13 37 25 5 4 10 22 23 12 7 4 48 12 6 2 15 66 34 14 3 25 y x1 x2 x3 x4 69 35 21 2 20 24 23 7 6 9 68 35 15 3 14 65 37 19 2 19 45 30 12 3 12a. Use standard stepwise regression to produce an estimate of a multiple regression model to predict
The following data represent a dependent variable and four independent variables:y x1 x2 x3 x4 61 37 13 10 21 37 25 7 11 32 22 23 6 7 18 48 12 8 8 30 66 34 15 2 33 y x1 x2 x3 x4 69 35 19 9 23 24 23 14 7 31 68 35 17 3 33 65 37 11 17 19 45 30 9 24 31a. Use the standard stepwise regression to produce
You are given the following set of data:y x1 x2 x3 45 40 41 39 41 31 41 35 43 45 49 39 38 43 41 41 50 42 42 51 39 48 40 42 50 44 44 41 y x1 x2 x3 45 42 39 37 43 37 52 41 34 40 47 40 49 35 44 44 45 39 40 45 40 43 30 42 43 53 34 34a. Determine the appropriate correlation matrix and use it to predict
You are given the following set of data:y x1 x2 x3 33 9 192 40 44 11 397 47 34 10 235 37 60 13 345 61 20 11 245 23 30 7 235 35 y x1 x2 x3 45 12 296 52 25 9 235 27 53 10 295 57 45 13 335 50 37 11 243 41 44 13 413 51a. Determine the appropriate correlation matrix and use it to predict which variable
The National Association of Realtors Existing-Home Sales Series provides a measurement of the residential real estate market. One of the measurements it produces is the Housing Affordability Index (HAI). It is a measure of the financial ability of U.S. families to buy a house. A value of 100 means
A regression equation to be used to predict a dependent variable with four independent variables is developed from a sample of size 10. The resulting equation is 32.8 0.470x1 0.554x2 4.77x3 0.929x4 Two other equations are developed from the sample:The respective sum of squares errors for the
Consider the following values for the dependent and independent variables:x y x y 6 5 18 30 9 20 22 33 14 28 27 35a. Develop a scatter plot of the data. Does the plot suggest a linear or nonlinear relationship between the dependent and independent variables?b. Develop an estimated linear regression
Consider the following values for the dependent and independent variables:x y x y 5 10 50 44 15 15 60 79 40 25 80 112a. Develop a scatter plot of the data. Does the plot suggest a linear or nonlinear relationship between the dependent and independent variables?b. Develop an estimated linear
The Energy Information Administration (EIA), created by Congress in 1977, is a statistical agency of the U.S.Department of Energy. It provides data, forecasts, and analyses to promote sound policymaking and public understanding regarding energy and its interaction with the economy and the
Refer to Exercise 15-8, which referenced a list of the 100 companies perceived as having “hot growth” characteristics.The file entitled Logrowth contains sales($million), sales increase (%), return on capital, market value ($million), and recent stock price of the companies ranked from 81 to
An investment analyst collected data about 20 randomly chosen companies. The data consisted of the 52-week-high stock prices, price-to-earnings (PE)ratio, and the market value of the company. These data are in the file entitled Investment.a. Produce a regression equation to predict the market value
Consider the following set of data:x2 10 8 11 7 10 11 6 x1 50 45 37 32 44 51 42 y 103 85 115 73 97 102 65a. Obtain the estimated regression equation.b. Examine the coefficient of determination and the adjusted coefficient of determination. Does it seem that either of the independent
The following correlation matrix is associated with the same data used to build the regression model in Problem 15-1:y x1 x2 x3 y 1 x1 0.406 1 x2 0.459 0.051 1 x3 0.244 0.504 0.272 1 Does this output indicate any potential multicollinearity problems with the analysis?
In working for a local retail store you have developed the following estimated regression equation:yˆ 22,167 412x1 818x2 93x3 71x4 where:y Weekly sales x1 Local unemployment rate x2 Weekly average high temperature x3 Number of activities in the local community x4 Average gasoline
Refer to the Grinfield Service Company discussed in Problem14-64.a. Develop the least squares regression equation for these variables. Plot the regression line on the scatter plot.b. Develop a 95% confidence interval estimate for the increase in sales resulting from increasing the advertising
One of the advances that have helped to diminish carpal tunnel syndrome is ergonomic keyboards. The ergonomic keyboards may also increase typing speed.Ten administrative assistants were chosen to type on both standard and ergonomic keyboards. The resulting typing speeds follow:Ergonomic: 69 80 60
The Farmington City Council recently commissioned a study of park users in their community. Data were collected on the age of the person surveyed and the amount of hours he or she spent in the park in the past month. The data collected were as follows:Time in Park Age Time in Park Age 7.2 16 4.4 48
A previous exercise discussed the relationship between the average college tuition (in 2003 dollars) for private and public colleges. The data indicated in the article follow:Period 1983–1984 1988–1989 1993–1994 Private 9,202 12,146 13,844 Public 2,074 2,395 3,188 Period 1998–1999
Go to the library and locate an article in a journal related to your major (Journal of Marketing, Journal of Finance, etc.) that uses linear regression. Discuss the following:a. How the author chose the dependent and independent variablesb. How the data were gatheredc. What statistical tests the
The National Highway Transportation Safety Administration’s National Center for Statistics and Analysis released its Vehicle Survivability Travel Mileage Schedules in January 2006. One item investigated was the relationship between the annual vehicle miles traveled (VMT) as a function of vehicle
Gym Outfitters sells and services exercise equipment such as treadmills, ellipticals, and stair climbers to gymnasiums and recreational centers. The company’s management would like to determine if there is a relationship between the number of minutes required to complete a routine service call
During the recession that began in 2008, not only did some people stop making house payments, they also stopped making payments for local government services such as trash collection and water and sewer services. The following data have been collected by an accountant who is performing an audit of
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