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The following table shows Googles annual revenue for 2009 to 2014 (The Wall Street Journal, August 2014). Year Period (t) Revenue ( billions) 2009 1 23.7 2010 2 29.3 2011 3 37.9 2012 4 50.2 2013 5 59.8 2014 6 66.7 a. Construct a time series plot. What type of pattern exists in the data? b. Develop a linear trend equation for this time series. c. What is the average revenue increase per year that Google has been realizing? d. Compute an estimate of Googles revenue for 2015.FRED (Federal Reserve Economic Data), a database of more than 3000 U.S. economic time series, contains historical data on foreign exchange rates. The following data show the foreign exchange rate for the United States and China (Federal Reserve Bank of St.Louis website). The units for Rate are the number of Chinese yuan to one U.S. dollar. Year Month Rate 2007 October 7.5019 2007 November 7.4210 2007 December 7.3682 2008 January 7.2405 2008 February 7.1644 2008 March 7.0722 2008 April 6.9997 2008 May 6.9725 2008 June 6.8993 2008 July 6.8355 a. Construct a time series plot. Does a linear trend appear to be present? b. Using Minitab or Excel, develop the linear trend equation for this time series. c. Use the trend equation to forecast the exchange rate for August 2008. d. Would you feel comfortable using the trend equation to forecast the exchange rate for December 2008?Quarterly revenue ( millions) for Twitter for the first quarter of 2012 through the first quarter of 2014 are shown below (adexchange.com, April, 2015): Quarter Revenue ( millions) 1 54 2 68 3 82 4 112 5 114 6 139 7 169 8 243 9 250 a. Construct a time series plot. What type of pattern exists in the data? b. Using Excel or Minitab, develop a linear trend equation for this time series. c. Using Excel or Minitab, develop a quadratic trend equation for this time series. d. Compare the MSE for each model. Which model appears better according to MSE? e. Use the models developed in parts (b) and (c) to forecast revenue for the tenth quarter. f. Which of the two forecasts in part (e) would you use? Explain.Giovanni Food Products produces and sells frozen pizzas to public schools throughout the eastern United States. Using a very aggressive marketing strategy they have been able to increase their annual revenue by approximately 10 million over the past 10 years. But increased competition has slowed their growth rate in the past few years. The annual revenue, in millions of dollars, for the previous 10 years is shown. Year Revenue 1 8.53 2 10.84 3 12.98 4 14.11 5 16.31 6 17.21 7 18.37 8 18.45 9 18.40 10 18.43 a. Construct a time series plot. Comment on the appropriateness of a linear trend. b. Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue. c. Using the trend equation developed in part (b), forecast revenue in year 11.27EConsider the following time series. a. Construct a time series plot. What type of pattern exists in the data? b. Use the following dummy variables to develop an estimated regression equation to account for seasonal effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2,0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. c. Compute the quarterly forecasts for next year.Consider the following time series data. a. Construct a time series plot. What type of pattern exists in the data? b. Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2,0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. c. Compute the quarterly forecasts for next year.The quarterly sales data (number of copies sold) for a college textbook over the past three years follow. a. Construct a time series plot. What type of pattern exists in the data? b. Use the following dummy variables to develop an estimated regression equation to account for any seasonal effects in the data: Qtr1 = 1 if Quarter 1,0 otherwise; Qtr2 = 1 if Quarter 2,0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. c. Compute the quarterly forecasts for next year. d. Let t = 1 to refer to the observation in quarter 1 of year 1; t = 2 to refer to the observation in quarter 2 of year 1; ... and t = 12 to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (b) and t, develop an estimated regression equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for next year.Air pollution control specialists in southern California monitor the amount of ozone, carbon dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data exhibit seasonality, with the levels of pollutants showing patterns that vary over the hours in the day. On July 15, 16, and 17, the following levels of nitrogen dioxide were observed for the 12 hours from 6:00 a.m. to 6:00 p.m. July 15: 25 28 35 50 60 60 40 35 30 25 25 20 July 16: 28 30 35 48 60 65 50 40 35 25 20 20 July 17: 35 42 45 70 72 75 60 45 40 25 25 25 a.Construct a time series plot. What type of pattern exists in the data? b.Use the following dummy variables to develop an estimated regression equation to account for the seasonal effects in the data. Hour1 = 1 if the reading was made between 6:00 A.M. and 7:00 A.M.; 0 otherwise Hour2 = 1 if if the reading was made between 7:00 A.M. and 8:00 A.M.; 0 otherwise . . . Hour11 = 1 if the reading was made between 4:00 P.M. and 5:00 P.M., 0 otherwise. Note that when the values of the 11 dummy variables are equal to 0, the observation corresponds to the 5:00 p.m. to 6:00 p.m. hour. c.Using the estimated regression equation developed in part (a), compute estimates of the levels of nitrogen dioxide for July 18. d.Let t = 1 to refer to the observation in hour 1 on July 15; t = 2 to refer to the observation in hour 2 of July 15; and t = 36 to refer to the observation in hour 12 of July 17. Using the dummy variables defined in part (b) and t, develop an estimated regression equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute estimates of the levels of nitrogen dioxide for July 18.South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from 308,000 in the first year of operation to 1,084,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. a. Construct a time series plot. What type of pattern exists in the data? b. Use the following dummy variables to develop an estimated regression equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1,0 otherwise; Qtr2 = 1 if Quarter 2,0 otherwise; Qtr3 = 1 if Quarter 3,0 otherwise. Based only on the seasonal effects in the data, compute estimates of quarterly sales for year 6. c. Let Period = 1 to refer to the observation in quarter 1 of year 1; Period = 2 to refer to the observation in quarter 2 of year 1; . .. and Period = 20 to refer to the observation in quarter 4 of year 5. Using the dummy variables defined in part (b) and Period, develop an estimated regression equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute estimates of quarterly sales for year 6.33EThree years of monthly lawn-maintenance expenses () for a six-unit apartment house in southern Florida follow. a. Construct a time series plot. What type of pattern exists in the data? b. Develop an estimated regression equation that can be used to account for any seasonal and linear trend effects in the data. Use the following dummy variables to account for the seasonal effects in the data: Jan = 1 if January, 0 otherwise; Feb = 1 if February, 0 otherwise; Mar = 1 if March, 0 otherwise; Nov = 1 if November, 0 otherwise. Note that using this coding method, when all the 11 dummy variables are 0, the observation corresponds to an expense in December. c. Compute the monthly forecasts for next year based upon both trend and seasonal effects.Consider the following time series data. a. Construct a time series plot. What type of pattern exists in the data? b. Show the four-quarter and centered moving average values for this time series. c. Compute seasonal indexes and adjusted seasonal indexes for the four quarters.Refer to exercise 35. a. Deseasonalize the time series using the adjusted seasonal indexes computed in part (c) of exercise 35. b. Using Minitab or Excel, compute the linear trend regression equation for the deseasonalized data. c. Compute the deseasonalized quarterly trend forecast for year 4. d. Use the seasonal indexes to adjust the deseasonalized trend forecasts computed in part (c). 35. Consider the following time series data. a. Construct a time series plot. What type of pattern exists in the data? b. Show the four-quarter and centered moving average values for this time series. c. Compute seasonal indexes and adjusted seasonal indexes for the four quarters.The quarterly sales data (number of copies sold) for a college textbook over the past three years follow. a. Construct a time series plot. What type of pattern exists in the data? b. Show the four-quarter and centered moving average values for this time series. c. Compute the seasonal and adjusted seasonal indexes for the four quarters. d. When does the publisher have the largest seasonal index? Does this result appear reasonable? Explain. e. Deseasonalize the time series. f. Compute the linear trend equation for the deseasonalized data and forecast sales using the linear trend equation. g. Adjust the linear trend forecasts using the adjusted seasonal indexes computed in part (c).Three years of monthly lawn-maintenance expenses () for a six-unit apartment house in southern Florida follow. a. Construct a time series plot. What type of pattern exists in the data? b. Identify the monthly seasonal indexes for the three years of lawn-maintenance expenses for the apartment house in southern Florida as given here. Use a 12-month moving average calculation. c. Deseasonalize the time series. d. Compute the linear trend equation for the deseasonalized data. e. Compute the deseasonalized trend forecasts and then adjust the trend forecasts using the seasonal indexes to provide a forecast for monthly expenses in year 4.Air pollution control specialists in southern California monitor the amount of ozone, carbon dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data exhibit seasonality, with the levels of pollutants showing patterns over the hours in the day. On July 15, 16, and 17, the following levels of nitrogen dioxide were observed in the downtown area for the 12 hours from 6:00 a.m. to 6:00 p.m. July 15: 25 28 35 50 60 60 40 35 30 25 25 20 July 16: 28 30 35 48 60 65 50 40 35 25 20 20 July 17: 35 42 45 70 72 75 60 45 40 25 25 25 a. Construct a time series plot. What type of pattern exists in the data? b. Identify the hourly seasonal indexes for the 12 readings each day. c. Deseasonalize the time series. d. Using Minitab or Excel, compute the linear trend equation for the deseasonalized data. e. Compute the deseasonalized trend forecasts for the 12 hours for July 18 and then adjust the trend forecasts using the seasonal indexes computed in part (b).Electric power consumption is measured in kilowatt-hours (kWh). The local utility company offers an interrupt program whereby commercial customers that participate receive favorable rates but must agree to cut back consumption if the utility requests them to do so. Timko Products cut back consumption at 12:00 noon Thursday. To assess the savings, the utility must estimate Timkos usage without the interrupt. The period of interrupted service was from noon to 8:00 p.m. Data on electric power consumption for the previous 72 hours are available. a. Is there a seasonal effect over the 24-hour period? b. Compute seasonal indexes for the six 4-hour periods. c. Use trend adjusted for seasonal indexes to estimate Timkos normal usage over the period of interrupted service.The weekly demand (in cases) for a particular brand of automatic dishwasher detergent for a chain of grocery stores located in Columbus, Ohio, follows. Week Demand Week Demand 1 22 6 24 2 18 7 20 3 23 8 19 4 21 9 18 5 17 10 21 a. Construct a time series plot. What type of pattern exists in the data? b. Use a three-week moving average to develop a forecast for week 11. c. Use exponential smoothing with a smoothing constant of = .2 to develop a forecast for week 11. d. Which of the two methods do you prefer? Why?The following table reports the percentage of stocks in a portfolio for nine quarters from 2010 to 2012. Quarter Stock % 1st2010 29.8 2nd2010 31.0 3rd2010 29.9 4th2010 30.1 1st2011 32.2 2nd2011 31.5 3rd2011 32.0 4th2011 31.9 1st2012 30.0 a. Construct a time series plot. What type of pattern exists in the data? b. Use exponential smoothing to forecast this time series. Consider smoothing constants of = .2, .3, and .4. What value of the smoothing constant provides the most accurate forecasts? c. What is the forecast of the percentage of stocks in a typical portfolio for the second quarter of 2009?United Dairies. Inc., supplies milk to several independent grocers throughout Dade County, Florida. Managers at United Dairies want to develop a forecast of the number of half-gallons of milk sold per week. Sales data for the past 12 weeks follow. a. Construct a time series plot. What type of pattern exists in the data? b. Use exponential smoothing withf = .4 to develop a forecast of demand for week 13.The data contained in the DATAfile named CrudeCost shows the U.S. refiner acquisition cost of crude oil in dollars per barrel (Energy Information Administration website, February 3. 2014). a. Construct a time series plot. What type of pattern exists in the data? b. Compute the linear trend equation for the time series. Use the linear trend equation to forecast the crude cost for January 2014. c. Compute the quadratic trend equation for the time series. Use the quadratic trend equation to forecast the crude cost for January 2014. d. Using MSE. which approach provides the most accuratre forecasts for the historical data?Annual retail store revenue for Apple from 2007 to 2014 are shown below (source: ifoapple.com). Year Period Retail Store Revenue ( billions) 2007 1 4,115 2008 2 6,310 2009 3 6,577 2010 4 9,080 2011 5 14,127 2012 6 18,828 2013 7 20,228 2014 8 21,462 a. Construct a time series plot. What type of pattern exists in the data? b. Using Mini tab or Excel, develop a linear trend equation for this time series. c. Use the trend equation developed in part (b) to forecast retail store revenue for 2015.The Mayfair Department Store in Davenport, Iowa, is trying to determine the amount of sales lost while it was shut down during July and August because of damage caused by the Mississippi River flood. Sales data for January through June follow. Month Sales (1000s) January 185.72 February 167.84 March 205.11 April 210.36 May 255.57 June 261.19 a. Use exponential smoothing, with = .4, to develop a forecast for July and August. (Hint: Use the forecast for July as the actual sales in July in developing the August forecast.) Comment on the use of exponential smoothing for forecasts more than one period into the future. b. Use trend projection to forecast sales for July and August. c. Mayfairs insurance company proposed a settlement based on lost sales of 240,000 in July and August. Is this amount fair? If not, what amount would you recommend as a counteroffer?47SEThe Costello Music Company has been in business for five years. During that time, sales of pianos increased from 12 units in the first year to 76 units in the most recent year. Fred Costello, the firm's owner, wants to develop a forecast of piano sales for the coming year. The historical data follow. Year 1 2 3 4 5 Sales 12 28 34 50 76 a. Construct a time series plot. What type of pattern exists in the data? b. Develop the linear trend equation for the time series. What is the average increase in sales that the firm has been realizing per year? c. Forecast sales for years 6 and 7.Consider the Costello Music Company problem in exercise 48. The quarterly sales data follow. Year Quarter I Quarter 2 Quarter 3 Quarter 4 Total Yearly Sales 1 4 2 1 5 12 2 6 4 4 14 28 3 10 3 5 16 34 4 12 9 7 22 50 5 18 10 13 35 76 a. Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; and Qtr3 = 1 if Quarter 3, 0 otherwise. b. Compute the quarterly forecasts for next year.Refer to the Costello Music Company problem in exercise 49. a. Using time series decomposition, compute the seasonal indexes for the four quarters. b. When does Costello Music experience the largest seasonal effect? Does this result appear reasonable? Explain. 49. Consider the Costello Music Company problem in exercise 48. The quarterly sales data follow. Year Quarter I Quarter 2 Quarter 3 Quarter 4 Total Yearly Sales 1 4 2 1 5 12 2 6 4 4 14 28 3 10 3 5 16 34 4 12 9 7 22 50 5 18 10 13 35 76 a. Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; and Qtr3 = 1 if Quarter 3, 0 otherwise. b. Compute the quarterly forecasts for next year.Refer to the Costello Music Company time series in exercise 49. a. Deseasonalize the data and use the deseasonalized time series to identify the trend. b. Use the results of part (a) to develop a quarterly forecast for next year based on trend. c. Use the seasonal indexes developed in exercise 50 to adjust the forecasts developed in part (b) to account for the effect of season. 50. Refer to the Costello Music Company problem in exercise 49. a. Using time series decomposition, compute the seasonal indexes for the four quarters. b. When does Costello Music experience the largest seasonal effect? Does this result appear reasonable? Explain. 49. Consider the Costello Music Company problem in exercise 48. The quarterly sales data follow. Year Quarter I Quarter 2 Quarter 3 Quarter 4 Total Yearly Sales 1 4 2 1 5 12 2 6 4 4 14 28 3 10 3 5 16 34 4 12 9 7 22 50 5 18 10 13 35 76 a. Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; and Qtr3 = 1 if Quarter 3, 0 otherwise. b. Compute the quarterly forecasts for next year.Hudson Marine has been an authorized dealer for CD marine radios for the past seven years. The following table reports the number of radios sold each year. Year 1 2 3 4 5 6 7 Number Sold 35 50 75 90 105 110 130 a. Construct a time series plot. Does a linear trend appear to be present? b. Using Minitab or Excel, develop a linear trend equation for this time series. c. Use the linear trend equation developed in part (b) to develop a forecast for annual sales in year 8.Refer to the Hudson Marine problem in exercise 52. Suppose the quarterly sales values for the seven years of historical data are as follows. Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total Yearly Sales 1 6 15 10 4 35 2 10 18 15 7 50 3 14 26 23 12 75 4 19 28 25 18 90 5 22 34 28 21 105 6 24 36 30 20 110 7 28 40 35 27 130 a. Use the following dummy variables to develop an estimated regression equation to account for any season and linear trend effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; and Qtr3 = 1 if Quarter 3, 0 otherwise. b. Compute the quarterly forecasts for next year.Refer to the Hudson Marine problem in exercise 53. a. Compute the centered moving average values for this time series. b. Construct a time series plot that also shows the centered moving average and original time series on the same graph. Discuss the differences between the original time series plot and the centered moving average time series. c. Compute the seasonal indexes for the four quarters. d. When does Hudson Marine experience the largest seasonal effect? Does this result seem reasonable? Explain. 53. Refer to the Hudson Marine problem in exercise 52. Suppose the quarterly sales values for the seven years of historical data are as follows. Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total Yearly Sales 1 6 15 10 4 35 2 10 18 15 7 50 3 14 26 23 12 75 4 19 28 25 18 90 5 22 34 28 21 105 6 24 36 30 20 110 7 28 40 35 27 130 a. Use the following dummy variables to develop an estimated regression equation to account for any season and linear trend effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; and Qtr3 = 1 if Quarter 3, 0 otherwise. b. Compute the quarterly forecasts for next year.Refer to the Hudson Marine data in exercise 53. a. Deseasonalize the data and use the deseasonalized time series to identify the trend. b. Use the results of part (a) to develop a quarterly forecast for next year based on trend. c. Use the seasonal indexes developed in exercise 54 to adjust the forecasts developed in part (b) to account for the effect of season. 53. Refer to the Hudson Marine problem in exercise 52. Suppose the quarterly sales values for the seven years of historical data are as follows. Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total Yearly Sales 1 6 15 10 4 35 2 10 18 15 7 50 3 14 26 23 12 75 4 19 28 25 18 90 5 22 34 28 21 105 6 24 36 30 20 110 7 28 40 35 27 130 a. Use the following dummy variables to develop an estimated regression equation to account for any season and linear trend effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; and Qtr3 = 1 if Quarter 3, 0 otherwise. b. Compute the quarterly forecasts for next year.Forecasting Food and Beverage Sales The Vintage Restaurant, on Captiva Island near Fort Myers, Florida, is owned and operated by Karen Payne. The restaurant just completed its third year of operation. Since opening her restaurant, Karen has sought to establish a reputation for the Vintage as a high-quality dining establishment that specializes in fresh seafood. Through the efforts of Karen and her staff, her restaurant has become one of the best and fastest growing restaurants on the island. To better plan for future growth of the restaurant, Karen needs to develop a system that will enable her to forecast food and beverage sales by month for up to one year in advance. Table 17.25 shows the value of food and beverage sales ( 1000s) for the first three years of operation. Managerial Report Perform an analysis of the sales data for the Vintage Restaurant. Prepare a report for Karen that summarizes your findings, forecasts, and recommendations. Include the following: 1. A time series plot. Comment on the underlying pattern in the time series. 2. An analysis of the seasonality of the data. Indicate the seasonal indexes for each month, and comment on the high and low seasonal sales months. Do the seasonal indexes make intuitive sense? Discuss. TABLE 17.25 FOOD AND BEVERAGE SALES FOR THE VINTAGE RESTAURANT (1000s) 1. Deseasonalize the time series. Does there appear to be any trend in the deseasonalized time series? 2. Using the time series decomposition method, forecast sales for January through December of the fourth year. 3. Using the dummy variable regression approach, forecast sales for January through December of the fourth year. 4. Provide summary tables of your calculations and any graphs in the appendix of your report. Assume that January sales for the fourth year turn out to be 295,000. What was your forecast error? If this error is large. Karen may be puzzled about the difference between your forecast and the actual sales value. What can you do to resolve her uncertainty in the forecasting procedure?Forecasting Lost Sales The Carlson Department Store suffered heavy damage when a hurricane struck on August 31. The store was closed for four months (September through December), and Carlson is now- involved in a dispute with its insurance company about the amount of lost sales during the time the store was closed. Two key issues must be resolved: (1) the amount of sales Carlson would have made if the hurricane had not struck and (2) whether Carlson is entitled to any compensation for excess sales due to increased business activity after the storm. More than 8 billion in federal disaster relief and insurance money came into the county, resulting in increased sales at department stores and numerous other businesses. Table 17.26 gives Carlsons sales data for the 48 months preceding the storm. Table 17.27 reports total sales for the 48 months preceding the storm for all department stores in the county, as well as the total sales in the county for the four months the Carlson Department Store was closed. Carlsons managers asked you to analyze these data and develop estimates of the lost sales at the Carlson Department Store for the months of September through December. They also asked you to determine whether a case can be made for excess storm-related sales during the same period. If such a case can be made, Carlson is entitled to compensation for excess sales it would have earned in addition to ordinary sales. TABLE 17.26 SALES FOR CARLSON DEPARTMENT STORE (SMILLIONS) TABLE 17.27 DEPARTMENT STORE SALES FOR THE COUNTY (S MILLIONS) Managerial Report Prepare a report for the managers of the Carlson Department Store that summarizes your findings, forecasts, and recommendations. Include the following: 1. An estimate of sales for Carlson Department Store had there been no hurricane. 2. An estimate of countywide department store sales had there been no hurricane. 3. An estimate of lost sales for the Carlson Department Store for September through December. In addition, use the countywide actual department stores sales for September through December and the estimate in part (2) to make a case for or against excess storm-related sales.The following hypothesis test is to be conducted. H0: Median 150 Ha: Median 150 A sample of 30 provided 22 observations greater than 150, 3 observations equal to 150, and 5 observations less than 150. Use = .01. What is your conclusion?Ten individuals participated in a taste test involving two brands of a product. Sample results show 7 preferred brand A, 2 preferred brand B, and 1 was unable to state a preference. With = .05, test for a significant difference in the preferences for the two brands. What is your conclusion?The median number of part-time employees at fast-food restaurants in a particular city was known to be 18 last year. City officials think the use of part-time employees may be increasing. A sample of nine fast-food restaurants showed that seven restaurants were employing more than 18 part-time employees, one restaurant was employing exactly 18 part-time employees, and one restaurant was employing fewer than 18 part-time employees. Can it be concluded that the median number of part-time employees has increased? Test using = .05.Net assets for the 50 largest stock mutual funds show a median of 15 billion. A sample of 10 of the 50 largest bond mutual funds follows. Using the median, can it be concluded that bond mutual funds are smaller and have fewer net assets than stock mutual funds? Use = .05. a. What are the hypotheses for this test? b. What is the p-value? What is your conclusion?The median price of homes in Austin, Texas is 248,640 (AustinHomeSearch website, April 2015). A sample of 200 homes sold in the south Austin suburb of Westlake Hills found 111 homes with sales prices over 248,640 and 89 homes with sales prices under 248,640. Can you conclude that the median price of homes in Westlake Hills differs from the median price of homes in Austin? Use = .05.The median annual income for families living in the United States is 56,200. Annual incomes in thousands of dollars for a sample of 50 families living in Chicago, Illinois, are shown. Use the sample data to see if it can be concluded that the families living in Chicago have a median annual income greater than 56,200. Use = .05. What is your conclusion?7EA Pew Research Center survey asked adults if their ideal place to live would have a faster pace of life or a slower pace of life. A preliminary sample of 16 respondents showed 4 preferred a faster pace of life, 11 preferred a slower place of life, and 1 said it did not matter. a. Are these data sufficient to conclude there is a difference between the preferences for a faster pace of life or a slower pace of life? Use = .05. What is your conclusion? b. Considering the entire sample of 16 respondents, what is the percentage who would like a faster pace of life? What is the percentage who would like a slower pace of life? What recommendation do you have for the study?In a recent poll six hundred adults were asked a series of questions about the state of the economy and their childrens future. One question was, Do you expect your children to have a better life than you have had, a worse life, or a life about the same as yours? The responses showed 242 better, 310 worse, and 48 about the same. Use the sign test and =.05 to determine whether there is a difference between the number of adults who feel their children will have a better life compared to a worse life. What is your conclusion?Nielsen Media Research identified Empire and the Big Bang theory as the two top-rated prime-time television series. In a local television preference survey, 750 individuals were asked to indicate their favorite prime-time television series: Three hundred thirty selected Empire, 270 selected The Big Bang Theory, and 150 selected another television show. Use a .05 level of significance to test the hypothesis that there is no difference in the preference for Empire and The Big Bang Theory. What is your conclusion?Competition in the personal computer market is intense. A sample of 450 purchases showed 202 Brand A computers, 175 brand B computers, and 73 other computers. Use a .05 level of significance to test the null hypothesis that Brand A and Brand B have the same share of the personal computer market. What is your conclusion?Two fuel additives are tested to determine their effect on miles per gallon for passenger cars. Test results for 12 cars follow; each car was tested with both fuel additives. Use = .05 and the Wilcoxon signed-rank test to see whether there is a significant difference between the median miles per gallon for the additives.A sample of 10 men was used in a study to test the effects of a relaxant on the time required to fall asleep. Data for 10 subjects showing the number of minutes required to fall asleep with and without the relaxant follow. Use a .05 level of significance to determine whether the relaxant reduces the median time required to fall asleep. What is your conclusion?Percents of on-time arrivals for flights in the past two years were collected for 11 randomly selected airports. Data for these airports follow. Use = .05 to test the hypothesis that there is no difference between the median percent of on-time arrivals for the two years. What is your conclusion? Percent On Time Airport Two Years Ago Last Year Boston Logan 71.78 69.69 Chicago OHare 68.23 65.88 Chicago Midway 77.98 78.40 Denver 78.71 75.78 Fort Lauderdale 77.59 73.45 Houston 77.67 78.68 Los Angeles 76.67 76.38 Miami 76.29 70.98 New York (JFK) 69.39 62.84 Orlando 79.91 76.49 Washington (Dulles) 75.55 72.42A test was conducted for two overnight mail delivery services. Two samples of identical deliveries were set up so that both delivery services were notified of the need for a delivery at the same time. The hours required to make each delivery follow. Do the data shown suggest a difference in the median delivery times for the two services? Use a .05 level of significance for the test. Service Delivery 1 2 1 24.5 28.0 2 26.0 25.5 3 28.0 32.0 4 21.0 20.0 5 18.0 19.5 6 36.0 28.0 7 25.0 29.0 8 21.0 22.0 9 24.0 23.5 10 26.0 29.5 11 31.0 30.0The LPGA ANA Inspiration tournament was held in April 2015 at the Mission Hills Country Club in Rancho Mirage, California. Shown here are first-round and second-round scores for a random sample of 13 golfers. Use = .05 to determine whether the first- and second-round median scores for golfers in the LPGA ANA Inspiration tournament differed significantly. What is your conclusion? Golfer Round 1 Round 2 Brittany Lang 73 72 Amy Anderson 74 70 Meena Lee 71 73 Juli Inkster 69 75 Ha Na Jang 72 72 Haeji Kang 71 74 Ai Miyazato 68 74 Stephanie Meadow 76 68 Catriona Matthew 71 69 Sandra Gal 75 68 Caroline Masson 72 73 Suzann Pettersen 76 68 Mo Martin 74 72The Scholastic Aptitude Test (SAT) consists of three parts: critical reading, mathematics, and writing. Each part of the test is scored on a 200- to 800-point scale with a median of approximately 500. Scores for each part of the test can be assumed to be symmetric. Use the following data to test the hypothesis that the population median score for the students taking the writing portion of the SAT is 500. Using = .05, what is your conclusion?Two fuel additives are being tested to determine their effect on gasoline mileage. Seven cars were tested with additive 1 and nine cars were tested with additive 2. The following data show the miles per gallon obtained with the two additives. Use = .05 and the MWW test to see whether there is a significant difference between gasoline mileage for the two additives. Additive 1 Additive 2 17.3 18.7 18.4 17.8 19.1 21.3 16.7 21.0 18.2 22.1 18.6 18.7 17.5 19.8 20.7 20.2Samples of starting annual salaries for individuals entering the public accounting and financial planning professions follow. Annual salaries are shown in thousands of dollars. Public Accountant Financial Planner 50.2 49.0 58.8 49.2 56.3 53.1 58.2 55.9 54.2 51.9 55.0 53.6 50.9 49.7 59.5 53.9 57.0 51.8 51.9 48.9 a. Use a .05 level of significance and test the hypothesis that there is no difference between the starting annual salaries of public accountants and financial planners. What is your conclusion? b. What are the sample median annual salaries for the two professions?The gap between the earnings of men and women with equal education is narrowing but has not closed. Sample data for seven men and seven women with bachelors degrees are as follows. Data are shown in thousands of dollars. Men Women 35.6 49.5 80.5 40.4 50.2 32.9 67.2 45.5 43.2 30.8 54.9 52.5 60.3 29.8 a. What is the median salary for men? For women? b. Use = .05 and conduct the hypothesis test for identical population distributions. What is your conclusion?Are Southern and Western states equally prone to fatal lightning strikes? The National Weather Service maintains a database that provides information on lightning strike fatalities by state. The number of lightning strike fatalities from 2010 to 2014 for Southern and Western states are shown as follows. (National Weather Service website, April 2015) Use = .05 and test to determine whether the distribution of lightning fatalities is the same for these two regions. What is your conclusion?Each year Bloomberg Businessweek publishes statistics on the worlds 1000 largest companies. A companys price/earnings (P/E) ratio is the companys current stock price divided by the latest 12 months earnings per share. The following table shows the P/E ratios for a sample of 10 Japanese companies and 12 U.S. companies. Is the difference between the P/E ratios for the two countries significant? Use the MWW test and = .01 to support your conclusion.Police records show the following numbers of daily crime reports for a sample of days during the winter months and a sample of days during the summer months. Use a .05 level of significance to determine whether there is a significant difference between the winter and summer months in terms of the number of crime reports. What is your conclusion? Winter Summer 18 28 20 18 15 24 16 32 21 18 20 29 12 23 16 38 19 28 20 18A certain brand of microwave oven was priced at 10 stores in Dallas and 13 stores in San Antonio. The data follow. Use a .05 level of significance and test whether prices for the microwave oven are the same in the two cities. Dallas San Antonio 445 460 489 451 405 435 485 479 439 475 449 445 436 429 420 434 430 410 405 422 425 459 430Chicago Midway International Airport and Baltimore/Washington International Thurgood Marshall Airport are the U.S. airports with the worst percentage of delayed flights (Travel+Leisure website, April 2015). But when flights are delayed, do these two airports experience delays of the same length? The delay times in minutes for seven recent, randomly selected delayed flights departing from each of these airports are as follows. Chicago Midway International Airport Baltimore/Washington International Thurgood Marshall Airport 68 105 99 35 42 34 31 87 54 73 25 41 49 57 Use the MWW test to determine if there is a difference in length of flight delays for these two airports. Use = .05. What is the p-value? What is your conclusion?A sample of 15 consumers provided the following product ratings for three different products. Five consumers were randomly assigned to test and rate each product. Use the Kruskal-Wallis test and = .05 to determine whether there is a significant difference among the ratings for the products. Product A B C 50 80 60 62 95 45 75 98 30 48 87 58 65 90 57Three admission test preparation programs are being evaluated. The scores obtained by a sample of 20 people who used the programs provided the following data. Use the Kruskal-Wallis test to determine whether there is a significant difference among the three test preparation programs. Use = .05. Program A B C 540 450 600 400 540 630 490 400 580 530 410 490 490 480 590 610 370 620 550 570Forty-minute workouts of one of the following activities three days a week will lead to a loss of weight. The following sample data show the number of calories burned during 40-minute workouts for three different activities. Do these data indicate differences in the amount of calories burned for the three activities? Use a .05 level of significance. What is your conclusion? Swimming Tennis Cycling 408 415 385 380 485 250 425 450 295 400 420 402 427 530 268The National Football League (NFL) holds its annual draft of the nations best college football players in April each year. prior to the draft, various sporting news services project the players who will be drafted along with the order in which each will be selected in what are called mock drafts. Players who are considered to have superior potential as professional football players are selected earlier in the draft. The following table shows, for the 2015 NFL draft, projections by one mock draft service of what position in the first round players from the Atlantic Coast Conference, the big Ten Conference, the PAC-12 Conference, and the Southeastern Conference will be selected follow (DraftSite website, April 2015). Use the Kruskal-Wallis test to determine if there is any difference among NFL teams for players from these four conferences. Use = .05. What is the p-value? What is your conclusion?A large corporation sends many of its first-level managers to an off-site supervisory skills training course. Four different management development centers offer this course. The director of human resources would like to know whether there is a difference among the quality of training provided at the four centers. An independent random sample of five employees was chosen from each training center. The employees were then ranked 1 to 20 in terms of supervisory skills. A rank of 1 was assigned to the employee with the best supervisory skills. The ranks are shown. Use = .05 and test whether there is a significant difference among the quality of training provided by the four programs.The better-selling candies are often high in calories. Assume that the following data show the calorie content from samples of MMs, Kit Kat, and Milky Way II. Test for significant differences among the calorie content of these three candies. At a .05 level of significance, what is your conclusion? MMs Kit Kat Milky Way II 230 225 200 210 205 208 240 245 202 250 235 190 230 220 180Consider the following set of rankings for a sample of 10 elements. a. Compute the Spearman rank-correlation coefficient for the data. b. Use = .05 and test for significant rank correlation. What is your conclusion?33E34EA national study by Harris Interactive, Inc., evaluated the top technology companies and their reputations. The following shows how 10 technology companies ranked in reputation and how the companies ranked in percentage of respondents who said they would purchase the companys stock. A positive rank correlation is anticipated because it seems reasonable to expect that a company with a higher reputation would have the more desirable stock to purchase. Company Reputation Stock Purchase Microsoft 1 3 Intel 2 4 Dell 3 1 Lucent 4 2 Texas Instruments 5 9 Cisco Systems 6 5 Hewlett-Packard 7 10 IBM 8 6 Motorola 9 7 Yahoo 10 8 a. Compute the rank correlation between reputation and stock purchase. b. Test for a significant positive rank correlation. What is the p-value? c. At = .05, what is your conclusion?36EA student organization surveyed both current students and recent graduates to obtain information on the quality of teaching at a particular university. An analysis of the responses provided the following teaching-ability rankings. Do the rankings given by the current students agree with the rankings given by the recent graduates? Use = .10 and test for a significant rank correlation. Professor Current Students Recent Graduates 1 4 6 2 6 8 3 8 5 4 3 1 5 1 2 6 2 3 7 5 7 8 10 9 9 7 4 10 9 10A survey asked the following question: Do you favor or oppose providing tax-funded vouchers or tax deductions to parents who send their children to private schools? Of the 2010 individuals surveyed, 905 favored the proposal, 1045 opposed the proposal, and 60 offered no opinion. Do the data indicate a significant difference in the preferences for the financial support of parents who send their children to private schools? Use a .05 level of significance.Due to a recent decline in the housing market, the national median sales price for single-family homes is 180,000 (The National Association of Realtors, January 2009). Assume that the following data were obtained from samples of recent sales of single-family homes in St. Louis and Denver. a. Is the median sales price in St. Louis significantly lower than the national median of 180,000? Use a statistical test with = .05 to support your conclusion. b. Is the median sales price in Denver significantly higher than the national median of 180,000? Use a statistical test with = .05 to support your conclusion.Twelve homemakers were asked to estimate the retail selling price of two models of refrigerators. Their estimates of selling price are shown in the following table. Use these data and test at the .05 level of significance to determine whether there is a difference between the two models in terms of homemakers perceptions of selling price.41SEThe following data are product weights for the same items produced on two different production lines. Test for a difference between the product weights for the two lines. Use = .05. Line 1 Line 2 13.6 13.7 13.8 14.1 14.0 14.2 13.9 14.0 13.4 14.6 13.2 13.5 13.3 14.4 13.6 14.8 12.9 14.5 14.4 14.3 15.0 14.9A client wants to determine whether there is a significant difference in the time required to complete a program evaluation with the three different methods that are in common use. The times (in hours) required for each of 18 evaluators to conduct a program evaluation follow. Use = .05 and test to see whether there is a significant difference in the time required by the three methods. Method 1 Method 2 Method 3 68 62 58 74 73 67 65 75 69 76 68 57 77 72 59 72 70 6244SE45SE46SE47SEA process that is in control has a mean of = 12.5 and a standard deviation of = .8. a. Construct the x control chart for this process if samples of size 4 are to be used. b. Repeat part (a) for samples of size 8 and 16. c. What happens to the limits of the control chart as the sample size is increased? Discuss why this is reasonable.Twenty-five samples, each of size 5, were selected from a process that was in control. The sum of all the data collected was 677.5 pounds. a. What is an estimate of the process mean (in terms of pounds per unit) when the process is in control? b. Develop the x control chart for this process if samples of size 5 will be used. Assume that the process standard deviation is .5 when the process is in control, and that the mean of the process is the estimate developed in part (a).Twenty-five samples of 100 items each were inspected when a process was considered to be operating satisfactorily. In the 25 samples, a total of 135 items were found to be defective. a. What is an estimate of the proportion defective when the process is in control? b. What is the standard error of the proportion if samples of size 100 will be used for statistical process control? c. Compute the upper and lower control limits for the control chart.A process sampled 20 times with a sample of size 8 resulted in x = 28.5 and R = 1.6. Compute the upper and lower control limits for the x and R charts for this process.Temperature is used to measure the output of a production process. When the process is in control, the mean of the process is = 128.5 and the standard deviation is = .4. a. Construct the x chart for this process if samples of size 6 are to be used. b. Is the process in control for a sample providing the following data? 128.8 128.2 129.1 128.7 128.4 129.2 c. Is the process in control for a sample providing the following data? 129.3 128.7 128.6 129.2 129.5 129.0A quality control process monitors the weight per carton of laundry detergent. Control limits are set at UCL = 20.12 ounces and LCL = 19.90 ounces. Samples of size 5 are used for the sampling and inspection process. What are the process mean and process standard deviation for the manufacturing operation?The Goodman Tire and Rubber Company periodically tests its tires for tread wear under simulated road conditions. To study and control the manufacturing process, 20 samples, each containing three radial tires, were chosen from different shifts over several days of operation, with the following results. Assuming that these data were collected when the manufacturing process was believed to be operating in control, develop the R and x charts. Sample Tread Wear 1 31 42 28 2 26 18 35 3 25 30 34 4 17 25 21 5 38 29 35 6 41 42 36 7 21 17 29 8 32 26 28 9 41 34 33 10 29 17 30 11 26 31 40 12 23 19 25 13 17 24 32 14 43 35 17 15 18 25 29 16 30 42 31 17 28 36 32 18 40 29 31 19 18 29 28 20 22 34 26 Hundredths of an inchOver several weeks of normal, or in-control, operation, 20 samples of 150 packages each of synthetic-gut tennis strings were tested for breaking strength. A total of 141 packages of the 3000 tested failed to conform to the manufacturers specifications. a. What is an estimate of the process proportion defective when the system is in control? b. Compute the upper and lower control limits for a p chart. c. With the results of part (b), what conclusion should be made about the process if tests on a new sample of 150 packages find 12 defective? Do there appear to be assignable causes in this situation? d. Compute the upper and lower control limits for an np chart. e. Answer part (c) using the results of part (d). f. Which control chart would be preferred in this situation? Explain.An airline operates a call center to handle customer questions and complaints. The airline monitors a sample of calls to help ensure that the service being provided is of high quality. Ten random samples of 100 calls each were monitored under normal conditions. The center can be thought of as being in control when these 10 samples were taken. The number of calls in each sample not resulting in a satisfactory resolution for the customer is as follows: 4 5 3 2 3 3 4 6 4 7 a. What is an estimate of the proportion of calls not resulting in a satisfactory outcome for the customer when the center is in control? b. Construct the upper and lower limits for a p chart for the manufacturing process, assuming each sample has 100 calls. c. With the results of part (b), what conclusion should be made if a sample of 100 has 12 calls not resulting in a satisfactory resolution for the customer? d. Compute the upper and lower limits for the np chart. e. With the results of part (d), what conclusion should be made if a sample of 100 calls has 12 not resulting in a satisfactory conclusion for the customer?For an acceptance sampling plan with n = 25 and c = 0, find the probability of accepting a lot that has a defect rate of 2%. What is the probability of accepting the lot if the defect rate is 6%?Consider an acceptance sampling plan with n = 20 and c = 0. Compute the producers risk for each of the following cases. a. The lot has a defect rate of 2%. b. The lot has a defect rate of 6%.Repeat exercise 11 for the acceptance sampling plan with n = 20 and c = 1. What pens to the producers risk as the acceptance number c is increased? Explain.Refer to the KALI problem presented in this section. The quality control manager requested a producers risk of .10 when p0 was .03 and a consumers risk of .20 when p1 was .15. Consider the acceptance sampling plan based on a sample size of 20 and an acceptance number of 1. Answer the following questions. a. What is the producers risk for the n = 20, c = 1 sampling plan? b. What is the consumers risk for the n = 20, c = 1 sampling plan? c. Does the n = 20, c = 1 sampling plan satisfy the risks requested by the quality control manager? Discuss.To inspect incoming shipments of raw materials, a manufacturer is considering samples of sizes 10, 15, and 19. Use the binomial probabilities from Table 5 of Appendix B to select a sampling plan that provides a producers risk of = .03 when p0 is .05 and a consumers risk of = .12 when p1 is .30.Samples of size 5 provided the following 20 sample means for a production process that is believed to be in control. 95.72 95.24 95.18 95.44 95.46 95.32 95.40 95.44 95.08 95.50 95.80 95.22 95.56 95.22 95.04 95.72 94.82 95.46 95.60 95.78 a. Based on these data, what is an estimate of the mean when the process is in control? b. Assume that the process standard deviation is = .50. Develop the x control chart for this production process. Assume that the mean of the process is the estimate developed in part (a). c. Do any of the 20 sample means indicate that the process was out of control?Product filling weights are normally distributed with a mean of 350 grams and a standard deviation of 15 grams. a. Develop the control limits for the x chart for samples of size 10, 20, and 30. b. What happens to the control limits as the sample size is increased? c. What happens when a Type I error is made? d. What happens when a Type II error is made? e. What is the probability of a Type I error for samples of size 10, 20, and 30? f. What is the advantage of increasing the sample size for control chart purposes? What error probability is reduced as the sample size is increased?Twenty-five samples of size 5 resulted in x = 5.42 and R = 2.0. Compute control limits for the x and R charts, and estimate the standard deviation of the process.The following are quality control data for a manufacturing process at Kensport Chemical Company. The data show the temperature in degrees centigrade at five points in time during a manufacturing cycle. The company is interested in using control charts to monitor the temperature of its manufacturing process. Construct the x chart and R chart. What conclusions can be made about the quality of the process? Sample x R 1 95.72 1 2 95.24 0.9 3 95.18 0.8 4 95.44 0.4 5 95.46 0.5 6 95.32 1.1 7 95.40 0.9 8 95.44 0.3 9 95.08 0.2 10 95.50 0.6 11 95.80 0.6 12 95.22 0.2 13 95.56 1.3 14 95.22 0.5 15 95.04 0.8 16 95.72 1.1 17 94.82 0.6 18 95.46 0.5 19 95.60 0.4 20 95.74 0.6The following were collected for the Master Blend Coffee production process. The data show the filling weights based on samples of 3-pound cans of coffee. Use these data to construct the x and R charts. What conclusions can be made about the quality of the production process? Observations Sample 1 2 3 4 5 1 3.05 3.08 3.07 3.11 3.11 2 3.13 3.07 3.05 3.10 3.10 3 3.06 3.04 3.12 3.11 3.10 4 3.09 3.08 3.09 3.09 3.07 5 3.10 3.06 3.06 3.07 3.08 6 3.08 3.10 3.13 3.03 3.06 7 3.06 3.06 3.08 3.10 3.08 8 3.11 3.08 3.07 3.07 3.07 9 3.09 3.09 3.08 3.07 3.09 10 3.06 3.11 3.07 3.09 3.07An insurance company samples claim forms for errors created by its employees as well as the amount of time it takes to process a claim. a. When the process is in control, the proportion of claims with an error is .033. A p chart has LCL = 0 and UCL = .068. Plot the following seven sample results: .035, .062, .055, .049, .058, .066, and .055. Comment on whether there might be concern about the quality of the process. b. An x chart for the mean processing time has LCL = 22.2 and UCL = 24.5. The mean is = 23.35 when the claim process is in control. Plot the following seven sample results: 22.4, 22.6, 22.65, 23.2, 23.4, 23.85, and 24.1. Comment on whether there might be concern about the quality of the process.Managers of 1200 different retail outlets make twice-a-month restocking orders from a central warehouse. Past experience shows that 4% of the orders result in one or more errors such as wrong item shipped, wrong quantity shipped, and item requested but not shipped. Random samples of 200 orders are selected monthly and checked for accuracy. a. Construct a control chart for this situation. b. Six months of data show the following numbers of orders with one or more errors: 10, 15, 6, 13, 8, and 17. Plot the data on the control chart. What does your plot indicate about the order process?An n = 10, c = 2 acceptance sampling plan is being considered; assume that p0 = .05 and p] = .20. a. Compute both producers and consumers risk for this acceptance sampling plan. b. Would the producer, the consumer, or both be unhappy with the proposed sampling plan? c. What change in the sampling plan, if any, would you recommend?24SEThe following table reports prices and usage quantities for two items in 2009 and 2011. a. Compute price relatives for each item in 2011 using 2009 as the base period. b. Compute an unweighted aggregate price index for the two items in 2011 using 2009 as the base period. c. Compute a weighted aggregate price index for the two items using the Laspeyres method. d. Compute a weighted aggregate price index for the two items using the Paasche method.An item with a price relative of 132 cost 10.75 in 2011. Its base year was 1994. a. What was the percentage increase or decrease in cost of the item over the 17-year period? b. What did the item cost in 1994?A large manufacturer purchases an identical component from three independent suppliers that differ in unit price and quantity supplied. The relevant data for 2012 and 2014 are given here. a. Compute the price relatives for each of the component suppliers separately. Compare the price increases by the suppliers over the two-year period. b. Compute an unweighted aggregate price index for the component part in 2014. c. Compute a 2014 weighted aggregate price index for the component part. What is the interpretation of this index for the manufacturing firm?4EUnder the last-in, first-out (LIFO) inventory valuation method, a price index for inventory must be established for tax purposes. The quantity weights are based on year-ending inventory levels. Use the beginning-of-the-year price per unit as the base-period price and develop a weighted aggregate index for the total inventory value at the end of the year. What type of weighted aggregate price index must be developed for the LIFO inventory valuation?Price relatives for three items, along with base-period prices and usage are shown in the following table. Compute a weighted aggregate price index for the current period.The Mitchell Chemical Company produces a special industrial chemical that is a blend of three chemical ingredients. The beginning-year cost per pound, the ending-year cost per pound, and the blend proportions follow. a. Compute the price relatives for the three ingredients. b. Compute a weighted average of the price relatives to develop a one-year cost index for raw materials used in the product. What is your interpretation of this index value?8ECompute the price relatives for the RB Beverages products in exercise 4. Use a weighted average of price relatives to show that this method provides the same index as the weighted aggregate method. 4. RB Beverages, Inc., provides a complete line of beer, wine, and soft drink products for distribution through retail outlets in central Iowa. Unit price data for 2011 and 2014 and quantities sold in cases for 2011 follow. Compute a weighted aggregate index for the RB Beverage sales in 2014, with 2011 as the base period.Registered nurses in 2007 made an average hourly wage of 30.04. In 2011, their hourly wage had risen to 33.23. Given that the CPI for 2007 was 207.3 and the 2011 CPI was 224.9, answer the following. a. Give the real wages for registered nurses for 2007 and 2011 by deflating the hourly wage rates. b. What is the percentage change in the actual hourly wage for registered nurses from 2007 to 2011? c. For registered nurses, what was the percentage change in real wages from 2007 to 2011?The average hourly wage rate for construction laborers in 2001 was 13.36. In 2011 construction laborers made 16.43 per hour. The CPI for 2001 was 177.1 and for 2011, 224.9. Calculate the percentage increase or decrease in real hourly wages from 2001 to 2011.Shipments of product from manufacturer to the retailer are tracked by the U.S. Census Bureau. The value of shipments for computer and electronic products for three consecutive years are shown in the table below, along with the CPI and PPI for each of these months. a. Use the CPI to deflate the value of the shipped computer and electronics products. b. Use the PPI to deflate the value of the shipped computer and electronics products. c. Which index, the CPI or PPI, do you feel is more appropriate for deflating these shipment values? Why?The revenue for Google for the years 2010-2014 is shown in the following table (Wall Street Journal, August 2014). Deflate the revenue in dollars based on the CPI (19821984 base period). Comment on the companys revenue in deflated dollars.Data on quantities of three items sold in Year 1 and Year 5 are given here along with the sales prices of the items in Year 1. Compute a weighted aggregate quantity index for Year 5.15E16EMany factors influence the retail price of gasoline. The following table shows the average retail price for a gallon of regular grade gasoline for each year from 2011 through 2014 (U.S. Energy Information Administration website, April 2015). Year Average Price () 2011 3.521 2012 3.618 2013 3.505 2014 3.358 a. Use 2011 as the base year and develop a price index for the retail price of a gallon of regular grade gasoline over this four-year period. b. Use 2012 as the base year and develop a price index for the retail price of a gallon of regular grade gasoline over this four-year period.Nickerson Manufacturing Company has the following data on quantities shipped and unit costs for each of its four products: a. Compute the price relative for each product. b. Compute a weighted aggregate price index that reflects the shipping cost change over the four-year period.19E20E21E22ESeafood price and quantity data are reported by the U.S. Census Bureau. Data for the years 2000 and 2009 follow. a. Compute a price relative for each type of seafood. b. Compute a weighted aggregate price index for the U.S. domestic seafood catch. Comment on the change in seafood prices over the nine-year period.24E25E26E1EA decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table. The decision maker obtains information that enables the following probabilities assessments: P(s1) = .5, P(s2) = .2, P(s3) = .2, and P(s1) = .1. a. Use the expected value approach to determine the optimal solution. b. Now assume that the entries in the payoff table are costs. Use the expected value approach to determine the optimal decision.Hudson Corporation is considering three options for managing its data processing operation: continue with its own staff, hire an outside vendor to do the managing (referred to as outsourcing), or use a combination of its own staff and an outside vendor. The cost of the operation depends on future demand. The annual cost of each option (in thousands of dollars) depends on demand as follows: a. If the demand probabilities are .2, .5, and .3, which decision alternative will minimize the expected cost of the data processing operation? What is the expected annual cost associated with your recommendation? b. What is the expected value of perfect information?Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full price service using the companys new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars). Demand for Service Service Strong Weak Full price 960 490 Discount 670 320 a. What is the decision to be made, what is the chance event, and what is the consequence for this problem? How many decision alternatives are there? How many outcomes are there for the chance event? b. Suppose that management of Myrtle Air Express believes that the probability of strong demand is .7 and the probability of weak demand is .3. Use the expected value approach to determine an optimal decision. c. Suppose that the probability of strong demand is .8 and the probability of weak demand is .2. What is the optimal decision using the expected value approach?The distance from Potsdam to larger markets and limited air service have hindered the town in attracting new industry. Air Express, a major overnight delivery service, is considering establishing a regional distribution center in Potsdam. But Air Express will not establish the center unless the length of the runway at the local airport is increased. Another candidate for new development is Diagnostic Research, Inc. (DRI), a leading producer of medical testing equipment. DRI is considering building a new manufacturing plant. Increasing the length of the runway is not a requirement for DRI, but the planning commission feels that doing so will help convince DRI to locate its new plant in Potsdam. Assuming that the town lengthens the runway, the Potsdam planning commission believes that the probabilities shown in the following table are applicable. DRI Plant No DRI Plant Air Express Center .30 .10 No Air Express Center .40 .20 For instance, the probability that Air Express will establish a distribution center and DRI will build a plant is .30. The estimated annual revenue to the town, after deducting the cost of lengthening the runway, is as follows: DRI Plant No DRI Plant Air Express Center 600,000 150,000 No Air Express Center 250,000 200,000 If the runway expansion project is not conducted, the planning commission assesses the probability that DRI will locate its new plant in Potsdam at .6; in this case, the estimated annual revenue to the town will be 450,000. If the runway expansion project is not conducted and DRI does not locate in Potsdam, the annual revenue will be 0 since no cost will have been incurred and no revenues will be forthcoming. a. What is the decision to be made, what is the chance event, and what is the consequence? b. Compute the expected annual revenue associated with the decision alternative to lengthen the runway. c. Compute the expected annual revenue associated with the decision alternative to not lengthen the runway. d. Should the town elect to lengthen the runway? Explain. e. Suppose that the probabilities associated with lengthening the runway were as follows: DRI Plant No DRI Plant Air Express Center .40 .10 No Air Express Center .30 .20 What effect, if any, would this change in the probabilities have on the recommended decision?Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard. Management is considering two varieties of white grapes for the new vineyard: Chardonnay and Riesling. The Chardonnay grapes would be used to produce a dry Chardonnay wine, and the Riesling grapes would be used to produce a semi-dry Riesling wine. It takes approximately four years from the time of planting before new grapes can be harvested. This length of time creates a great deal of uncertainty concerning future demand and makes the decision concerning the type of grapes to plant difficult. Three possibilities are being considered: Chardonnay grapes only; Riesling grapes only; and both Chardonnay and Riesling grapes. Seneca management decided that for planning purposes it would be adequate to consider only two demand possibilities for each type of wine: strong or weak. With two possibilities for each type of wine it was necessary to assess four probabilities. With the help of some forecasts in industry publications management made the following probability assessments. Riesling Demand Chardonnay Demand Weak Strong Weak .05 .50 Strong .25 .20 Revenue projections show an annual contribution to profit of 20,000 if Seneca Hill only plants Chardonnay grapes and demand is weak for Chardonnay wine, and 70,000 if the company only plants Chardonnay grapes and demand is strong for Chardonnay wine. If the company only plants Riesling grapes, the annual profit projection is 25,000 if demand is weak for Riesling grapes and 45,000 if demand is strong for Riesling grapes. If Seneca plants both types of grapes, the annual profit projections are as shown in the following table. Riesling Demand Chardonnay Demand Weak Strong Weak 22,000 40,000 Strong 26,000 60,000 a. What is the decision to be made, what is the chance event, and what is the consequence? Identify the alternatives for the decisions and the possible outcomes for the chance events. b. Develop a decision tree. c. Use the expected value approach to recommend which alternative Seneca Hill Winery should follow in order to maximize expected annual profit. d. Suppose management is concerned about the probability assessments when demand for Chardonnay wine is strong. Some believe it is likely for Riesling demand to also be strong in this case. Suppose the probability of strong demand for Chardonnay and weak demand for Riesling is .05 and that the probability of strong demand for Chardonnay and strong demand for Riesling is .40. How does this change the recommended decision? Assume that the probabilities when Chardonnay demand is weak are still .05 and .50. e. Other members of the management team expect the Chardonnay market to become saturated at some point in the future, causing a fall in prices. Suppose that the annual profit projections fall to 50,000 when demand for Chardonnay is strong and Chardonnay grapes only are planted. Using the original probability assessments, determine how this change would affect the optimal decision.The Lake Placid Town Council has decided to build a new community center to be used for conventions, concerts, and other public events, but considerable controversy surrounds the appropriate size. Many influential citizens want a large center that would be a showcase for the area, but the mayor feels that if demand does not support such a center, the community will lose a large amount of money. To provide structure for the decision process, the council narrowed the building alternatives to three sizes: small, medium, and large. Everybody agreed that the critical factor in choosing the best size is the number of people who will want to use the new facility. A regional planning consultant provided demand estimates under three scenarios: worst case, base case, and best case. The worst-case scenario corresponds to a situation in which tourism drops significantly; the base-case scenario corresponds to a situation in which Lake Placid continues to attract visitors at current levels; and the best-case scenario corresponds to a significant increase in tourism. The consultant has provided probability assessments of .10, .60, and .30 for the worstcase, base-case, and best-case scenarios, respectively. The town council suggested using net cash flow over a five-year planning horizon as the criterion for deciding on the best size. A consultant developed the following projections of net cash flow (in thousands of dollars) for a five-year planning horizon. All costs, including the consultants fee, are included. a. What decision should Lake Placid make using the expected value approach? b. Compute the expected value of perfect information. Do you think it would be worth trying to obtain additional information concerning which scenario is likely to occur? c. Suppose the probability of the worst-case scenario increases to .2, the probability of the base-case scenario decreases to .5, and the probability of the best-case scenario remains at .3. What effect, if any, would these changes have on the decision recommendation? d. The consultant suggested that an expenditure of 150,000 on a promotional campaign over the planning horizon will effectively reduce the probability of the worst-case scenario to zero. If the campaign can be expected to also increase the probability of the best-case scenario to .4, is it a good investment?Consider a variation of the PDC decision tree shown in Figure 21.5. The company must first decide whether to undertake the market research study. If the market research study is conducted, the outcome will either be favorable (F) or unfavorable (U). Assume there are only two decision alternatives d1 and d2 and two states of nature s1 and s2. The payoff table showing profit is as follows: State of Nature Decision Alternative s1 s2 d1 100 300 d2 400 200 a. Show the decision tree. b. Use the following probabilities. What is the optimal decision strategy? P(F) = .56 P(s1 | F) = .57 P(s1 | U) = .18 P(s1) = .40 P(U) = .44 P(s2 | F) = .43 P(s2 | U) = .82 P(s2) = .60A real estate investor has the opportunity to purchase land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table. State of Nature Rezoning Approved Rezoning Not Approved Decision Alternative s1 s2 Purchase, d1 600 200 Do not purchase, d2 0 0 a. If the probability that the rezoning will be approved is .5, what decision is recommended? What is the expected profit? b. The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during the next three months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows. Let H = high resistance to rezoning L = low resistance to rezoning P(H) = .55 P(s1 | H) = .18 P(s2 | H) = .82 P(L) = .45 P(s1 | L) = .89 P(s2 | L) = .11Dante Development Corporation is considering bidding on a contract for a new office building complex. Figure 21.9 shows the decision tree prepared by one of Dantes analysts. At node 1, the company must decide whether to bid on the contract. The cost of preparing the bid is 200,000. The upper branch from node 2 shows that the company has a .8 probability of winning the contract if it submits a bid. If the company wins the bid, it will have to pay 2,000,000 to become a partner in the project. Node 3 shows that the company will then consider doing a market research study to forecast demand for the office units prior to beginning construction. The cost of this study is 150,000. Node 4 is a chance node showing the possible outcomes of the market research study. Nodes 5, 6, and 7 are similar in that they are the decision nodes for Dante to either build the office complex or sell the rights in the project to another developer. The decision to build the complex will result in an income of 5,000,000 if demand is high and 3,000,000 if demand is moderate. If Dante chooses to sell its rights in the project to another developer, income from the sale is estimated to be 3,500,000. The probabilities shown at nodes 4, 8, and 9 are based on the projected outcomes of the market research study. a. Verify Dantes profit projections shown at the ending branches of the decision tree by calculating the payoffs of 2,650,000 and 650,000 for first two outcomes. b. What is the optimal decision strategy for Dante, and what is the expected profit for this project? c. What would the cost of the market research study have to be before Dante would change its decision about conducting the study?Hales TV Productions is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. At this point in time, Hale may either produce the pilot and wait for the networks decision or transfer the rights for the pilot and series to a competitor for 100,000. Hales decision alternatives and profits (in thousands of dollars) are as follows: The probabilities for the states of nature are P(s1) = .2, P(s2) = .3, and P(s3) = .5. For a consulting fee of 5000, an agency will review the plans for the comedy series and indicate the overall chances of a favorable network reaction to the series. Assume that the agency review will result in a favorable (F) or an unfavorable (U) review and that the following probabilities are relevant. P(F) = .69 P(s1 | F) = .09 P(s1 | U) = .45 P(U) = .31 P(s2 | F) = .26 P(s2 | U) = .39 P(s3 | F) = .65 P(s3 | U) = .16 a. Construct a decision tree for this problem. b. What is the recommended decision if the agency opinion is not used? What is the expected value? c. W hat is the expected value of perfect information? d. What is Hales optimal decision strategy assuming the agencys information is used? e. What is the expected value of the agencys information? f. Is the agencys information worth the 5000 fee? What is the maximum that Hale should be willing to pay for the information? g. What is the recommended decision?Martins Service Station is considering entering the snowplowing business for the coming winter season. Martin can purchase either a snowplow blade attachment for the stations pick-up truck or a new heavy-duty snowplow truck. After analyzing the situation, Martin believes that either alternative would be a profitable investment if the snowfall is heavy. Smaller profits would result if the snowfall is moderate, and losses would result if the snowfall is light. The following profits/losses apply. The probabilities for the states of nature are P(s1) = .4, P(s2) = .3, and P(s3) = .3. Suppose that Martin decides to wait until September before making a final decision. Assessments of the probabilities associated with a normal (N) or unseasonably cold (U) September are as follows: P(N) = .8 P(s1 | N ) 5 .35 P(s1 | U ) 5 .62 P(U) = .2 P(s2 | N ) 5 .30 P(s2 | U ) 5 .31 P(s3 | N ) 5 .35 P(s3 | U ) 5 .07 a. Construct a decision tree for this problem. b. W hat is the recommended decision if Martin does not wait until September? What is the expected value? c. W hat is the expected value of perfect information? d. W hat is Martins optimal decision strategy if the decision is not made until the September weather is determined? What is the expected value of this decision strategy?Lawsons Department Store faces a buying decision for a seasonal product for which demand can be high, medium, or low. The purchaser for Lawsons can order 1, 2, or 3 lots of the product before the season begins but cannot reorder later. Profit projections (in thousands of dollars) are shown. a. If the prior probabilities for the three states of nature are .3, .3, and .4, respectively, what is the recommended order quantity? b. At each preseason sales meeting, the vice president of sales provides a personal opinion regarding potential demand for this product. Because of the vice presidents enthusiasm and optimistic nature, the predictions of market conditions have always been either excellent (E) or very good (V). Probabilities are as follows. What is the optimal decision strategy? P(E) = .7 P(s1 | E ) = .34 P(s1 | V ) = .20 P(V) = .3 P(s2 | E ) = .32 P(s2 | V) = .26 P(s3 | E) = .34 P(s3 | V) = .54 c. Compute EVPI and EVSI. Discuss whether the firm should consider a consulting expert who could provide independent forecasts of market conditions for the product.Suppose that you are given a decision situation with three possible states of nature: s1, s2, and s3. The prior probabilities are P(s1) = .2, P(s2) = .5, and P(s3) = .3. With sample information I, P(I | s1) = .1, P(I | s2) = .05, and P(I | s3) = .2. Compute the revised or posterior probabilities: P(s1 | I), P(s2 | I), and P(s3 | I).In the following profit payoff table for a decision problem with two states of nature and three decision alternatives, the prior probabilities for s1 and s2 are P(s1) = .8 and P(s2) = .2. State of Nature Decision Alternative s1 s2 d1 15 10 d2 10 12 d3 8 20 a. What is the optimal decision? b. Find the EVPI. c. Suppose that sample information I is obtained, with P(I | s1) = .20 and P(I | s2) = .75. Find the posterior probabilities P(s1 | I) and P(s2 | I). Recommend a decision alternative based on these probabilities.To save on expenses, Rona and Jerry agreed to form a carpool for traveling to and from work. Rona preferred to use the somewhat longer but more consistent Queen City Avenue. Although Jerry preferred the quicker expressway, he agreed with Rona that they should take Queen City Avenue if the expressway had a traffic jam. The following payoff table provides the one-way time estimate in minutes for traveling to and from work. State of Nature Expressway Open Expressway Jammed Decision Alternative s1 s2 Queen City Avenue, d1 30 30 Expressway, d2 25 45 Based on their experience with traffic problems, Rona and Jerry agreed on a .15 probability that the expressway would be jammed. In addition, they agreed that weather seemed to affect the traffic conditions on the expressway. Let C = clear O = overcast R = rain The following conditional probabilities apply. P(C | s1) 5= .8 P(O | s1) = .2 P(R | s1) = .0 P(C | s2) = .1 P(O | s2) = .3 P(R | s2) = .6 a. Use Bayes theorem for probability revision to compute the probability of each weather condition and the conditional probability of the expressway open, s1, or jammed, s2, given each weather condition. b. Show the decision tree for this problem. c. W hat is the optimal decision strategy, and what is the expected travel time?The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars). The state-of-nature probabilities are P(s1) = .35, P(s2) = .35, and P(s3) = .30. a. Use a decision tree to recommend a decision. b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand. c. A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows: P(F | s1) = .10 P(U | s1) = .90 P(F | s2) = .40 P(U | s2) = .60 P(F | s3) = .60 P(U | s3) = .40 What is the probability that the market research report will be favorable? d. What is Gormans optimal decision strategy? e. What is the expected value of the market research information?An investor wants to select one of seven mutual funds for the coming year. Data showing the percentage annual return for each fund during five typical one-year periods are shown here. The assumption is that one of these five-year periods will occur again during the coming year. Thus, years A, B, C, D, and E are the states of nature for the mutual fund decision. a. Suppose that an experienced financial analyst reviews the five states of nature and provides the following probabilities: .1, .3, .1, .1, and .4. Using the expected value approach, what is the recommended mutual fund? What is the expected annual return? Using this mutual fund, what are the minimum and maximum annual returns? b. A conservative investor notes that the Small-Cap mutual fund is the only fund that does not have the possibility of a loss. In fact, if the Small-Cap fund is chosen, the investor is guranteed a return of at least 6%. What is the expected annual return for this fund? c. Considering the mutual funds recommended in parts (a) and (b), which fund appears to have more risk? Why? Is the expected annual return greater for the mutual fund with more risk? d. What mutual fund would you recommend to the investor? Explain.Warren Lloyd is interested in leasing a new car and has contacted three automobile dealers for pricing information. Each dealer offered Warren a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The monthly lease cost, the mileage allowance, and the cost for additional miles follow: Warren decided to choose the lease option that will minimize his total 36-month cost. The difficulty is that Warren is not sure how many miles he will drive over the next three years. For purposes of this decision he believes it is reasonable to assume that he will drive 12,000 miles per year, 15,000 miles per year, or 18,000 miles per year. With this assumption Warren estimated his total costs for the three lease options. For example, he figures that the Forno Automotive lease will cost him 10,764 if he drives 12,000 miles per year, 12,114 if he drives 15,000 miles per year, or 13,464 if he drives 18,000 miles per year. a. What is the decision, and what is the chance event? b. Construct a payoff table. c. Suppose that the probabilities that Warren drives 12,000, 15,000, and 18,000 miles per year are 0.5, 0.4, and 0.1, respectively. What dealer should Warren choose? d. Suppose that after further consideration, Warren concludes that the probabilities that he will drive 12,000, 15,000 and 18,000 miles per year are 0.3, 0.4, and 0.3, respectively. What dealer should Warren select?Hemmingway, Inc. is considering a 50 million research and development (RD) project. Profit projections appear promising, but Hemmingways president is concerned because the probability that the RD project will be successful is only 0.50. Secondly, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of 20 million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized. Another option is that if the RD project is successful, the company could sell the rights to the product for an estimated 25 million. Under this option, the company would not build the 20 million production facility. The decision tree is shown in Figure 21.11. The profit projection for each outcome is shown at the end of the branches. For example, the revenue projection for the high-demand outcome is 59 million. However, the cost of the RD project (5 million) and the cost of the production facility (20 million) show the profit of this outcome to be 59 5 20 = 34 million. Branch probabilities are also shown for the chance events. a. Analyze the decision tree to determine whether the company should undertake the RD project. If it does, and if the RD project is successful, what should the company do? What is the expected value of your strategy? b. What must the selling price be for the company to consider selling the rights to the product?Embassy Publishing Company received a six-chapter manuscript for a new college textbook. The editor of the college division is familiar with the manuscript and estimated a 0.65 probability that the textbook will be successful. If successful, a profit of 750,000 will be realized. If the company decides to publish the textbook and it is unsuccessful, a loss of 250,000 will occur. Before making the decision to accept or reject the manuscript, the editor is considering sending the manuscript out for review. A review process provides either a favorable (F) or unfavorable (U) evaluation of the manuscript. Past experience with the review process suggests probabilities P(F) = 0.7 and P(U) = 0.3 apply. Let s1 = the textbook is successful, and s2 = the textbook is unsuccessful. The editors initial probabilities of s1 and s2 will be revised based on whether the review is favorable or unfavorable. The revised probabilities are as follows: P(s1 | F) = 0.75 P(s1 | U ) = 0.417 P(s2 | F) = 0.25 P(s2 | U) = 0.583 a. Construct a decision tree assuming that the company will first make the decision of whether to send the manuscript out for review and then make the decision to accept or reject the manuscript. b. Analyze the decision tree to determine the optimal decision strategy for the publishing company. c. If the manuscript review costs 5000, what is your recommendation? d. W hat is the expected value of perfect information? What does this EVPI suggest for the company?Lawsuit Defense Strategy John Campbell, an employee of Manhattan Construction Company, claims to have injured his back as a result of a fall while repairing the roof at one of the Eastview apartment buildings. In a lawsuit asking for damages of 1,500,000, filed against Doug Reynolds, the owner of Eastview Apartments, John claims that the roof had rotten sections and that his fall could have been prevented if Mr. Reynolds had told Manhattan Construction about the problem. Mr. Reynolds notified his insurance company, Allied Insurance, of the lawsuit. Allied must defend Mr. Reynolds and decide what action to take regarding the lawsuit. Following some depositions and a series of discussions between the two sides, John Campbell offered to accept a settlement of 750,000. Thus, one option is for Allied to pay John 750,000 to settle the claim. Allied is also considering making John a counteroffer of 400,000 in the hope that he will accept a lesser amount to avoid the time and cost of going to trial. Allieds preliminary investigation shows that John has a strong case; Allied is concerned that John may reject their counteroffer and request a jury trial. Allieds lawyers spent some time exploring Johns likely reaction if they make a counteroffer of 400,000. The lawyers concluded that it is adequate to consider three possible outcomes to represent Johns possible reaction to a counteroffer of 400,000: (1) John will accept the counteroffer and the case will be closed; (2) John will reject the counteroffer and elect to have a jury decide the settlement amount; or (3) John will make a counteroffer to Allied of 600,000. If John does make a counteroffer, Allied has decided that it will not make additional counteroffers. It will either accept Johns counteroffer of 600,000 or go to trial. If the case goes to a jury trial, Allied considers three outcomes possible: (1) The jury rejects Johns claim and Allied will not be required to pay any damages; (2) the jury finds in favor of John and awards him 750,000 in damages; or (3) the jury concludes that John has a strong case and awards him the full amount of 1,500,000. Key considerations as Allied develops its strategy for disposing of the case are the probabilities associated with Johns response to an Allied counteroffer of 400,000, and the probabilities associated with the three possible trial outcomes. Allieds lawyers believe the probability that John will accept a counteroffer of 400,000 is .10, the probability that John will reject a counteroffer of 400,000 is .40, and the probability that John will, himself, make a counteroffer to Allied of 600,000 is .50. If the case goes to court, they believe that the probability the jury will award John damages of 1,500,000 is .30, the probability that the jury will award John damages of 750,000 is .50, and the probability that the jury will award John nothing is .20. Managerial Report Perform an analysis of the problem facing Allied Insurance and prepare a report that summarizes your findings and recommendations. Be sure to include the following items: 1. A decision tree 2. A recommendation regarding whether Allied should accept Johns initial offer to settle the claim for 750,000 3. A decision strategy that Allied should follow if it decides to make John a counteroffer of 400,000 4. A risk profile for your recommended strategySimple random sampling was used to obtain a sample of n = 50 elements from a population of N = 800. The sample mean wasx=215, and the sample standard deviation was found to be s = 20. a. Estimate the population mean. b. Estimate the standard error of the mean. c. Develop an approximate 95% confidence interval for the population mean.2E3E4E5E6EA stratified simple random sample was taken with the following results. Stratum (h) xh Sh Ph Nh nh 1 138 30 .50 200 20 2 103 25 .78 250 30 3 210 50 .21 100 25 a. Develop an estimate of the population mean for each stratum. b. Develop an approximate 95% confidence interval for the population mean in each stratum. c. Develop an approximate 95% confidence interval for the overall population mean.8E9E10EA drug store chain has stores in four cities: 38 stores in Indianapolis. 45 in Louisville, 80 in St. Louis, and 70 in Memphis. Pharmacy sales in the four cities vary considerably because of the competition. The following sales data (in thousands of dollars) are available from a sample survey. Each of the cities was considered a separate stratum, and a stratified simple random sample was taken. Indianapolis Louisville St. Louts Memphis 50.3 48.7 16.7 14.7 41.2 59.8 38.4 88.3 15.7 28.9 51.6 94.2 22.5 36.5 42.7 76.8 26.7 89.8 45.0 35.1 20.8 96.0 59.7 48.2 77.2 80.0 57.9 81.3 27.6 18.8 22.0 74.3 a. Estimate the mean pharmacy sales for each city (stratum). b. Develop an approximate 95% confidence interval for the mean pharmacy sales in each city. c. Estimate the proportion of stores with sales of 50,000 or more. d. Develop an approximate 95% confidence interval for the proportion of stores with sales of 50,000 or more.12E13EA sample of four clusters is to be taken from a population with N = 25 clusters and M = 300 elements. The values of Mi, xi, and ai for each cluster in the sample follow. Cluster (i) Mi xi ai 1 7 95 1 2 18 325 6 3 15 190 6 4 10 140 2 Totals 50 750 15 a. Develop point estimates of the population mean, total, and proportion. b. Estimate the standard error for the estimates in part (a). c. Develop an approximate 95% confidence interval for the population mean. d. Develop an approximate 95% confidence interval for the population total. e. Develop an approximate 95% confidence interval for the population proportion.A sample of six clusters is to be taken from a population with N = 30 clusters and M = 600 elements. The following table shows values of Mi, xi, and ai for each cluster in the sample. Cluster (i) Mi xi ai 1 35 3500 3 2 15 965 0 3 12 960 1 4 23 2070 4 5 20 1100 3 6 25 1805 2 Totals 130 10,400 13 a. Develop point estimates of the population mean, total, and proportion. b. Develop an approximate 95% confidence interval for the population mean. c. Develop an approximate 95% confidence interval for the population total. d. Develop an approximate 95% confidence interval for the population proportion.16E17ETo assess consumer acceptance of a new series of ads for Miller Lite Beer. Louis Harris conducted a nationwide poll of 363 adults who had seen the Miller Lite ads. The following responses are based on that survey. (Note: Because the survey sampled only a small fraction of all adults, assume (N n)/N = 1 in any formulas involving the standard error.) a. Nineteen percent of all respondents indicated they liked the ads a lot. Develop a 95% confidence interval for the population proportion. b. Thirty-one percent of the respondents disliked the new ads. Develop a 95% confidence interval for the population proportion. c. Seventeen percent of the respondents felt the ads are very effective. Develop a 95% confidence interval for the proportion of adults who think the ads are very effective. d. Louis Harris reported that the margin of error is five percentage points. What does this statement mean and how do you think they arrived at this number? e. How might nonsampling error bias the results of such a survey?19SEA quality of life survey was conducted with employees of a manufacturing firm. Of the firms 3000 employees, a sample of 300 were sent questionnaires. Two hundred usable questionnaires were obtained for a response rate of 67%. a. The mean annual salary for the sample was x=23,200 with s = 3000. Develop an approximate 95% confidence interval for the mean annual salary of the population. b. Use the information in part (a) to develop an approximate 95% confidence interval for the total salary of all 3000 employees. c. Seventy-three percent of respondents reported that they were generally satisfied with their job. Develop an approximate 95% confidence interval for the population proportion. d. Comment on whether you think the results in part (c) might be biased. Would your opinion change if you knew the respondents were guaranteed anonymity?A U.S. Senate Judiciary Committee report showed the number of homicides in each state. In Indiana. Ohio, and Kentucky, the number of homicides was. respectively. 380,760, and 260. Suppose a stratified random sample with the following results was taken to learn more about the victims and the cause of death. Stratum Sample Size Shootings Beatings Urban Victims Indiana 30 10 9 21 Ohio 45 19 12 34 Kentucky 25 7 11 15 a. Develop an approximate 95% confidence interval for the proportion of shooting deaths in Indiana. b. Develop an estimate for the total number of shooting deaths in Ohio. c. Develop an approximate 95% confidence interval for the proportion of shooting deaths in Ohio. d. Develop an approximate 95% confidence interval for the proportion of shooting deaths across all three states.Refer again to the data in exercise 21. a. Develop an estimate of the total number of deaths (in the three states) due to beatings. b. Develop an approximate 95% confidence interval for the proportion of deaths across all three states due to beatings. c. Develop an approximate 95% confidence interval for the proportion of victims who are urban. d. Develop an estimate of the total number of urban victims. 21. A U.S. Senate Judiciary Committee report showed the number of homicides in each state. In Indiana. Ohio, and Kentucky, the number of homicides was. respectively. 380,760, and 260. Suppose a stratified random sample with the following results was taken to learn more about the victims and the cause of death. Stratum Sample Size Shootings Beatings Urban Victims Indiana 30 10 9 21 Ohio 45 19 12 34 Kentucky 25 7 11 1523SE24SE