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Business Statistics 10th Global Edition David Groebner, Patrick Shannon, Phillip Fry - Solutions
J.A. Hersh and Company provides court transcription services. The company is considering two keyboard styles for its staff to use in court. One factor that will influence its decision is the ease of use. Suppose that to test the keyboards, nine court transcribers were selected and asked to
When a new home-use digital blood pressure monitor is developed it needs to be tested for accuracy. One such test is to have a physician first determine the blood pressure of a randomly sampled group of participants. Then each participant is measured using the home test monitor. If the mean blood
An intern for the California Transportation Department conducted a study on a stretch of interstate highway south of San Francisco to determine whether the mean speed for California vehicles exceeded the mean speed for out-of-state vehicles. A total of 140 California cars were included in the
There has been a debate over whether children who are placed in child-care facilities while their parents work suffer as a result. A New York Times article suggests that this might not be the case and, in fact, children might actually do better when their mothers work (source: Claire Cain Miller,
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 online audio program to help children learn to read.To test whether this program can cause a quick improvement in reading ability, suppose 10 children were given a nationally recognized reading test that measures reading ability. The same
A cattle feedlot operator has collected data for 40 matched pairs of cattle showing weight gain on two different feed supplements. His purpose in collecting the data is to determine whether there is a difference in the median weight gains for the two supplements. He has no preconceived idea about
Suppose a state tax commission 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
Steven just registered to an undergraduate business program and he managed to get the first-year booklist for his study program. For the purpose of saving money, he plans to find out whether online purchase is cheaper than purchasing in brick-and-mortar bookstore. To answer his question, the median
The makers of a new mobile theater system that is vision correctable so there is no need to wear glasses while using the device have done a marketing research study in which they asked two independently selected groups to rate the mobile theater system on a scale of 1 to 100, with 100 being perfect
National Reading Academy claims that graduates of its program have a higher median reading speed per minute than people who do not take the course.Suppose an independent agency conducted a study to determine whether this claim was justified. Researchers from the agency selected a random sample of
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 distributions.HA:
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.
From a recent study we have collected the following data from two independent random samples:Sample 1 Sample 2 405 300 450 340 290 400 370 250 345 270 460 410 425 435 275 390 380 225 330 210 500 395 215 315 Suppose we do not wish to assume normal distributions.Use the appropriate nonparametric test
You are given two paired samples with the following information:Item Sample 1 Sample 2 1 1,004 1,045 2 1,245 1,145 3 1,360 1,400 4 1,150 1,000 5 1,300 1,350 6 1,450 1,350 7 900 1,140 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 Item Sample 1 Sample 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
You are given two paired samples with the following information:Item Sample 1 Sample 2 1 3.4 2.8 2 2.5 3.0 3 7.0 5.5 4 5.9 6.7 5 4.0 3.5 6 5.0 5.0 7 6.2 7.5 8 5.3 4.2a. Based on these paired samples, test at the a = 0.05 level whether the true median paired difference is 0.b. Answer part a assuming
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: m 1 6 m 2, a = 0.025, n = 15b. HA: m 1 7 m 2, a = 0.01,
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 Sample 1 Sample 2 438 436 466
Determine the rejection region for the Mann–Whitney U-test in each of the following cases:a. HA: m 1 6 m 2, a = 0.05, n1 = 3, and n2 = 15b. HA: m 1 m 2, a = 0.10, n1 = 5, and n2 = 20c. HA: m 1 6 m 2, a = 0.025, n1 = 9, and n2 = 12d. HA: m 1 m 2, a = 0.10, n1 = 124, and n2 = 25
The following sample data have been collected from two independent random samples from two populations. Test the claim that the first population median will exceed the median of the second population.Sample 1 Sample 2 50 43 38 31 47 46 44 38 44 72 38 39 48 40 37 54 40 55 43 41 36 38 44 40a. State
The following sample data have been collected from independent samples from two populations. The claim is that the first population median will be larger than the median of the second population.Sample 1 Sample 2 4.4 2.6 3.7 4.2 2.7 2.4 3.5 5.2 1.0 2.0 4.0 4.4 3.5 2.8 4.9 4.3 2.8 3.1a. State the
The following sample data have been collected from two independent samples from two populations. Test the claim that the second population median will exceed the median of the first population.Sample 1 Sample 2 12 11 9 20 21 14 18 7 15 12 16 12 10 8 17 19a. State the appropriate null and
For each of the following tests, determine which of the two U statistics 1U1 or U22 you would choose, the appropriate test statistic, and the rejection region for the Mann–Whitney test:a. HA: m 1 6 m 2, a = 0.05, n1 = 5, and n2 = 10b. HA: m 1 7 m 2, a = 0.05, n1 = 15, and n2 = 12c. HA: m
The Wilson Company uses a great deal of water in the process of making industrial milling equipment. To determine whether the company is complying with federal clean water laws, sample measures are taken every so often. One requirement is that the median pH level must be lower than 7.4. A sample of
The marketing manager of a cell phone company is working on an advertising plan that is to be directed toward a young audience. In conjunction with the plan, the manager states that the median age of the company’s customers is younger than 40. Before actually completing the advertising plan, the
Suppose an engine oil manufacturer wants 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
Fillmore, Inc.’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, the division was satisfied with examining the average length of life.However, a recent sample taken
A company that packages salted peanuts has stated that each package weighs 11 ounces. However, the company has received complaints that the packages are underweight. To assess this situation, suppose the company has conducted a statistical study that concluded the average weight of packages is
The human resources manager at an insurance company has stated that during their initial 6-month period of employment, new sales personnel spent a median of 119 hours per month in training. A random sample of 20 new salespersons was selected. The numbers of hours they spent in training in a
A cable television customer call center has a goal that the median time for each completed call should not exceed four minutes. The operations manager does not want to incorrectly conclude that the goal isn’t being satisfied unless sample data justify that conclusion. A sample of 12 calls was
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.Business Applications
Consider the following set of observations:10.21 13.65 12.30 9.51 11.32 12.77 6.16 8.55 11.78 12.32 You should not assume these data come from a normal distribution. Test the hypothesis that these data come from a distribution with a median less than or equal to 10.
Consider the following set of observations:9.0 15.6 21.1 11.1 13.5 9.2 13.6 15.8 12.5 18.7 18.9 You should not assume these data come from a normal distribution. Test the hypothesis that the median of these data is greater than or equal to 14.
The file Quarterly Shipments lists the number of units shipped each quarter for the years 2011–2015 by Bourff Manufacturing.a. Produce a time-series graph of the data. Are there noticeable trend and seasonal components?b. Using the Excel 2016 Forecast Sheet option, produce a forecast for each
The file Phone Expenses contains the monthly telephone expenses for a small business.a. Produce a time-series graph of the data. Can you identify a trend or seasonal component?b. Using the Excel 2016 Forecast Sheet option, produce a forecast for January 2016.c. Report the smoothing parameter and
Referring to Exercise 16-61, the managers at Armstead & Associates 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 average of the first six months’ data.a. Compute the MAD for this
The data file Armstead contains the monthly number of calls received by Armstead & Associates, a company that was formed to help individuals locate long-term health care assistance for elderly individuals.a. Plot these data in a time-series graph. Based on the graph, what time-series components are
Freddie Mac is an organization that was formed by the U.S. Congress in 1970 to help maintain mortgage interest rates at a fairly stable level. The data in the file Mortgage Rates show the 30-year fixed mortgage interest rates on a monthly basis from January 2002 through December 2015 (source:
Suppose the median weekly earnings for recent college graduates in a large city by quarter for the years 2008 to 2015 are as follows:Quarter Median Weekly Earnings Quarter Median Weekly Earnings Qtr 1 2008 816 Qtr 1 2012 947.2 Qtr 2 2008 816 Qtr 2 2012 961.6 Qtr 3 2008 835.2 Qtr 3 2012 963.2 Qtr 4
Tom and Hank’s is a regional convenience store with locations in several small towns along the Mississippi River. The quarterly revenues for the store beginning with the first quarter of 2005 and ending with the second quarter of 2011 are listed here.Period Sales Period Sales 1Q05 $ 304,072 2Q08
Loans and leases data for the years 2005 through 2015 for Glen Lake Bank are shown below:Year Loans & Leases ($ millions)2005 511 2006 616 2007 718 2008 909 2009 1,135 2010 1,371 2011 1,677 2012 1,871 2013 2,021 2014 1,904 2015 2,354a. Produce a time-series plot of these data.b. Fit a linear trend
A pizza outlet has tracked the total number of super deluxe pizzas sold in each of the past six years. The data are as follows:Year 2011 2012 2013 2014 2015 2016 Sales 2,074 2,395 3,138 3,632 4,694 5,652a. Produce a time-series plot of these data. Indicate the time-series components in the data.b.
Below are income and sales data for a company for the years 2003 through 2015.Year Net Income/Loss Sales 2003 - 0.3 0.5 2004 - 5.7 15.7 2005 - 27.5 147.7 2006 - 124.5 609.8 2007 - 719.9 1,639.8 2008 - 1,411.2 2,761.9 2009 -567.3 3,122.9 2010 -149.1 3,933 2011 35.3 5,263.7 2012 588.5 6,921 2013 359
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 exercises 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 2016.a. Compute the MAD for this model.b. Plot the forecast values against the actual data.c. Use the same starting value but try
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. Is the trend line statistically
Identify the businesses in your community that you expect to have sales that exhibit a seasonal component.Discuss.
Go to the library or use the Internet to find data showing your state’s population for the past 20 years. Plot these data and indicate which of the time-series components are present.
Discuss which model is preferred.d. Referring to partb, try different alpha and beta values in an attempt to determine an improved forecast model for monthly sales. For each model, show the forecast for period 17 and the MAD. Write a short report that compares the different models.e. Referring to
The sales manager at Grossmieller Importers in New York City needs to determine a monthly forecast for the number of men’s golf shirts that will be sold so that he can order an appropriate number of packing boxes.Grossmieller ships shirts to retail stores throughout the United States and Canada.
The file Museum Visitors contains the number of visitors to a city museum each day during the period January 3 to March 20, 2015.a. Use the data and the Excel 2016 Forecast Sheet option to develop a forecast for the number of museum visitors on March 21, 2015.b. Report the forecast value and its
Harrison Avenue Burgers is a fast-food business that has been open since 1992. Suppose that the owner has monitored the average price he has paid for a pound of hamburger on an annual basis since 1992. The data are in a file called Hamburger.a. Produce a time-series plot for these data. Specify the
An electrical utility in a city in a South American country needs to forecast the highest temperature in the city on any day during a month. The following data reflect the highest recorded temperature (in degrees Fahrenheit) on any day during each month between June 2015 and June 2016:Year Month
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 2017. From her company’s database, she has collected the following information for the previous seven years:Year Medical
A May 2015 Wall Street Journal article indicated that 2015 college graduates had the highest average student debt ever, at slightly more than $35,000 per student.The following data show the average student debt for the years 1993 through 2015 (source: Jeffrey Sparshott,“Congratulations, class of
With tax revenues declining in many states, school districts have been searching for ways to cut costs without affecting classroom academics. Suppose 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 enrollment in a major at your university for the past six semesters. (Note:Semester 1 is the oldest data; semester 6 is the most recent data.)Semester Enrollment 1 87 2 110 3 123 4 127 5 145 6 160a. Prepare a graph of enrollment for the six semesters.b. Based on the
The following table represents two years of data:Year 1 Year 2 1st quarter 242 1st quarter 272 2nd quarter 252 2nd quarter 267 3rd quarter 257 3rd quarter 276 4th quarter 267 4th quarter 281a. Prepare a single exponential smoothing forecast for the first quarter of year 3 using an alpha value of
The United States Census Bureau collects and maintains data on a wide range of statistics associated with the U.S. economy. For example, the file Retail Sales contains the total retail sales in January for the years 2001 through 2016 (source: www.census.gov/retail).a. Produce a time-series plot of
The federal funds rate is the interest rate charged by banks when banks borrow “overnight” from each other.The file titled The Fed contains the federal funds rates for the period 1955 through 2015 (source: “Effective federal funds rate,” Economic Research, Federal Reserve Bank of St. Louis,
Refer to Exercise 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 through 15. Forecast the cash balance for month
Logan Pickens is a plan/build construction company specializing in resort area construction projects.Suppose that plan/build companies typically have a cash flow problem, since they tend to be paid in lump sums when projects are completed or hit milestones.The data file Logan-Pickens contains
The manager of a financial investment 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 from 2012 to 2015.2012 2013 1st quarter 218 1st quarter 250 2nd quarter 190 2nd quarter 220 3rd
Suppose that a company was formed five years ago to provide meal delivery, physical therapy, and minor housekeeping services to senior citizens. The revenue data for the first five years of operation are shown here.Revenue ($10,000s)2011 2012 2013 2014 2015 January 23 67 72 76 81 February 34 63 64
Suppose the owner of a convenience store has tracked the average price of a gallon of milk for the months between July 2013 and June 2015. The data are shown in the table.Month Price ($) Month Price ($) Month Price ($)7/13 2.247 3/14 2.344 11/14 2.637 8/13 2.108 4/14 2.642 12/14 2.289 9/13 2.111
A May 2015 Wall Street Journal article indicated that 2015 college graduates had the highest average student debt ever, at slightly more than $35,000 per student.The following data show the average student debt for the years 1993 through 2015 (source: Jeffrey Sparshott, “Congratulations, class of
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.16.2 EXERCISESc. Compute the ratio-to-moving-averages
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 and 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 time periods 11,
Refer to the sales data for the years 2013 through 2016 shown in Exercise 16-20 and provide a seasonally adjusted forecast using the linear trend model for each quarter of the year 2017. Also use the seasonal index values computed in Exercise 16-21 to provide seasonally adjusted forecasts for the
Refer to the sales data for the years 2013 through 2016 shown in Exercise 16-20 and fit the linear trend model to the data. Determine the MAD and MSE values.Comment on the adequacy of the linear model based on these measures of forecast error.
Refer to the sales data for the years 2013 through 2016 shown in Exercise 16-20 and determine the seasonal indexes for the 1st, 2nd, 3rd, and 4th quarters.
Consider the following sales data, in millions of dollars:2013 2015 1st quarter 152 1st quarter 217 2nd quarter 162 2nd quarter 209 3rd quarter 157 3rd quarter 202 4th quarter 167 4th quarter 221 2014 2016 1st quarter 182 1st quarter 236 2nd quarter 192 2nd quarter 242 3rd quarter 191 3rd quarter
Refer back to your work in the previous three exercises.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
Extract the irregular component by taking the normalized average of the ratio-to-moving-averages.Make a table that shows the normalized seasonal indexes. Interpret what the index for January means relative to the index for July.
Estimate the S * I portion of the multiplicative model by finding the ratio-to-moving-averages for the timeseries data. Determine whether these ratio-to-movingaverages are stable from year to year.
Using the multiplicative model, estimate the T * C portion by computing a 12-month moving average and then the centered 12-month moving average.
Based on the Durbin-Watson statistic, is there evidence of autocorrelation in these data? Use a linear trend model.
Refer back to Exercises 16-12 and 16-13 involving the federal funds rate and the data in the file called The Fed. Indicate the recurrence period for any cyclical or seasonal component in the data.
Refer back to Exercise 16-12 involving the federal funds rate and the data in the file called The Fed.Describe the time-series components that are present in the data.
The federal funds rate is the interest rate charged by banks when banks borrow “overnight” from each other. The file titled The Fed contains the federal funds rates for the period 1955–2015 (source: “Effective federal funds rate,” Economic Research, Federal Reserve Bank of St.Louis,
Plot both series of data and comment on the trend you see in both plots.Computer Software Exercises
Using 2005 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 7 496 660 Determine a relative index for each type of
A Greek entrepreneur followed the olive harvests. He noted that olives ripen in September. Each March he tried to determine if the upcoming olive harvest would be especially bountiful. If his analysis indicated it would, he entered into agreements with the owners of all the olive oil presses in the
Provide an example of a business decision that requires(1) a short-term forecast, (2) a medium-term forecast, and (3) a long-term forecast.
Badeaux Brothers Louisiana Treats ships packages of Louisiana coffee, cakes, and Cajun spices to customers around the United States. The cost to ship these products depends primarily on the weight of the package.Badeaux charges the customers for shipping and then ships the product itself. As a part
An investment analyst collected data from publicly available sources on 20 randomly chosen companies.The data consisted of the 52-week-high stock prices, PE ratios, and market values of the companies. These data are in the file titled Investment. The analyst wishes to produce a regression equation
Plot the residuals against the predicted value of y and comment on what this plot means relative to the aptness of the model.a. Compute the standardized residuals and form these in a frequency histogram. What does this indicate about the normality assumption?b. Comment on the overall aptness 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 make a high volume of purchases from McCracken.
Looking carefully at the stepwise regression model, you can see that the value of the slope coefficient for variable x2, family income, changes as a new variable is added to the regression model. Discuss why this change takes place.
Referring to Exercise 15-74, 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.Be sure to discuss the effect of adding a new variable on the standard error of the estimate and on R2.
Develop a 95% confidence level for the slope coefficient for the family income variable at Step 1 of the model.Be sure to interpret this confidence interval.
Test the significance of the regression model at Step 1 of the process. Justify the significance level you have selected.
Use forward selection stepwise regression to develop the multiple regression model. The variable x2, family income, was brought into the model. Discuss the reason for this.
Compute the correlation matrix for these data. Develop the decision rule for testing the significance of each coefficient. Which, if any, correlations are not significant?Use a = 0.05.
A first step in regression analysis often involves developing a scatter plot of the data. Make 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.
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