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The Practice Of Statistics For Business And Economics 4th Edition Layth C. Alwan, Bruce A. Craig - Solutions

U.S. poverty rate, continued. Refer to Exercises 13.47, 13.48, and 13.49 (page 694) for explanation of the forecast accuracy measures MAD, MSE, and MAPE. POVERTY(a) Based on the forecasts calculated in part (a) of the previous exercise, calculate MAD, MSE, and MAPE.(b) Based on the forecasts
U.S. poverty rate, continued. Continue the analysis of the annual U.S. poverty rate. POVERTY(a) Set up an Excel spreadsheet to calculate forecasts for the time series using an exponential smoothing model with w 5 0.2. Provide a forecast for the poverty rate for 2013.(b) Set up an Excel spreadsheet
U.S. poverty rate. Consider a time series on the annual poverty rate of U.S. residents aged 18 to 64 from 1980 through 2012.39 POVERTY(a) Make a time plot. Describe the movement of the data over time.(b) Obtain the first differences for the series and test them for randomness. What do you
Facebook annual net income. Consider a time series on the annual net income of Facebook (in millions of dollars) from 2007 through 2013.38 FB(a) Using Excel’s line plot option, make a time plot.Describe the movement of the data over time. Would a linear trend model be appropriate? Explain.(b)
Mexican population density. Continue the analysis of the annual population density in Mexico. MEXICO(a) Fit a trend model based on a linear term t and a quadratic term t2. Report the estimated model.(b) Obtain the residuals for the quadratic trend model fit and calculate MAD, MSE, and MAPE (see
Mexican population density. Consider a time series on the annual population density (number of people per square kilometer) in Mexico from 2001 through 2013.37 MEXICO(a) Make a time plot. Describe the movement of the data over time.(b) Fit a linear trend model to the data series and report the
NFL offense. In the National Football League(NFL), many argue that rules changes over the years are favoring offenses. Consider a time series of the average number of offensive yards in the NFL per regular season from 1990 through 2013.36 NFLOFF(a) Make a time plot. Is there evidence that the
Annual precipitation. Continue the analysis of the annual precipitation time series. PRECIP(a) Make a histogram and Normal quantile plot of the precipitation data. What do you conclude from these plots?(b) What is a 90% prediction interval for the annual precipitation for 2014?
Annual precipitation. Global temperatures are increasing. Great Lakes water levels meander up and down (see Figure 13.41, page 687). Do all environmental processes exhibit time series patterns? Consider a time series of the annual precipitation (inches) in New Jersey from 1895 through 2013.35
Egg shipments. Continue the analysis of the weekly egg shipments to Chicago. EGGS(a) Make a histogram and Normal quantile plot of the egg data. What do you conclude from these plots?(b) What is a 95% prediction interval for the weekly egg shipments?
Egg shipments. The U.S. Department of Agriculture tracks prices, sales, and movement of numerous food commodities. Consider the weekly number of eggs shipped in the Chicago retail market for the 52 weeks of 2012. Units are 30 dozen eggs in thousands.34 EGGS(a) Make a time plot of the egg shipment
Just use last month’s figures! Working with the financial analysts at your company, you discover that, when it comes to forecasting various time series, they often just use last period’s value as the forecast for the current period. As noted in the chapter, this is known as a naive forecast
Exponential smoothing forecast equation. We have learned that the exponential smoothing forecast equation is written as y⁄t 5 wyt21 1 s1 2 wdy⁄t21(a) Show that the equation can be written as y⁄t 5y⁄t21 1 wet21 where et21 is the residual, or prediction error, for period t 2 1.(b) Explain in
Exponential smoothing for information services hires rate. Continue the analysis of monthly information services sector hires rate time series. HIRES(a) Use statistical software to determine the optimal smoothing constant w.(b) The series ended with the hires rate of June 2014.Based on the reported
Exponential smoothing for information services hires rate. Consider the monthly information services sector hires rate time series from Exercise 13.46(pages 693–694). HIRES(a) Calculate and plot (on a single time plot) exponential smoothing models using smoothing constants of w 5 0.1, 0.5, and
CTA commuters. The Chicago rapid transit rail system is well known as the “L” (abbreviation for“elevated”). It is the third busiest system after the New York City Subway and the Washington Metro. Consider the daily count of commuters going through a particular station. The count is based on
Moving averages and linear trend. The moving-average model provides reasonable predictions only under certain scenarios. Consider monthly seasonally adjusted Consumer Price Index (CPI)data, starting with January 1990 and ending in July 2014.32 CPI(a) Make a time plot of the CPI series. Describe its
H&R Block quarterly tax services revenue.H&R Block is the world’s largest consumer tax services provider. Consider a time series of its quarterly tax services revenues (in thousands of $) starting with the first quarter of fiscal year 2010 and ending on the second quarter of fiscal year 2014.31
Number of iPhones sold globally. Consider data on the quarterly global sales (in millions of dollars) of iPhones from the first quarter of 2012 to the third quarter of 2014. In Exercise 13.22 (page 677), you were asked to fit a trend-and-season model using regression.IPHONE(a) Use the
It’s exponential. In the previous exercise, you explored the behavior of the exponential smoothing model weights when the smoothing constant is between 0 and 1. We noted in the section that software can actually report an optimal smoothing constant greater than 1. Suppose software reports an
It’s exponential. Exponential smoothing models are so named because the weights w, s1 2 wdw, s1 2 wd2w, Á , s1 2 wdn22w decrease in value exponentially. For this exercise, take n 5 11. Use software to do the calculations.(a) Calculate the weights for a smoothing constant of w 5 0.1.(b) Calculate
Domestic average airfare. Refer to Exercises 13.47, 13.48, and 13.49(page 694) for explanation of the forecast accuracy measures MAD, MSE, and MAPE.(a) Based on the forecasts calculated in part (a) of Exercise 13.51, calculate MAD, MSE, and MAPE.(b) Based on the forecasts calculated in part (b) of
Domestic average air fare. The Bureau of Transportation Statistics conducts a quarterly survey to monitor domestic and international airfares.30 Here are the average airfares (inflation adjusted) for U.S. domestic flights for 2000 through 2013:Year Airfare Year Airfare Year Airfare 2000 $463.56
Seasonality ratios for Amazon sales data. In Example 13.18(pages 675–676), the seasonal component was estimated with the use of indicator variables. As an alternative, the seasonality can be captured with seasonal ratios computed by means of moving averages.(a) Use the moving-average approach to
Comparing models for hires rate with MAPE. MAD (Exercise 13.47)measures the average magnitude of the prediction errors, and MSE (Exercise 13.48)measures the average squared magnitude of the prediction errors. To put the prediction errors in perspective, it can be useful to measure the errors in
Comparing models for hires rate with MSE. In Exercise 13.47, the mean absolute deviation was introduced as a measure of forecasting accuracy.Another measure is mean squared error (MSE), which is a measure of the average size of the prediction errors in squared units:where et is the residual for
Comparing models for hires rate with MAD. When comparing competing forecast methods, a primary concern is the relative accuracy of the methods. Ultimately, how well a forecasting method does is reflected in the residuals (“prediction errors”).(a) One measure of forecasting accuracy is mean
Information services hires rate. The U.S. Department of Labor tracks hiring activity in various industry sectors. Consider monthly data on the hires rate (%)in the information services sector from January 2009 through June 2014.27 “Hires rate” is defined as the number of hires during the month
Warehouse club and superstore sales. Consider the warehouse club and superstore sales series discussed in Examples 13.15 and 13.16 (pages 671–674).(a) Make scatterplot of sales yt versus yt212 (a lag of 12 periods). What does the scatterplot suggest?(b) What is the correlation between yt and
OPEC basket prices. Continue the previous exercise. OPEC(a) Obtain a PACF for the OPEC price series. How many lags does the PACF suggest should be considered in building a lag-based model?(b) Based on your results from part (a), fit an appropriate lag model and report it.(c) Obtain the residuals
OPEC basket prices. In 2005, OPEC introduced a basket price which is the average price of seven blends from different OPEC countries. OPEC uses the basket price to monitor world oil market conditions. Consider data on the daily basket price from the beginning of January 2012 to the middle of August
MLB batting average. Continue the analysis of MLB batting averages from Exercise 13.40. MLB(a) Use software to fit a simple linear regression model, using yt as the response variable and yt21 as the explanatory variable. Record the estimated regression equation.(b) Obtain the residuals from the
Amazon sales. In Example 13.25, the one-step ahead forecast was calculated. Using the model of Example 13.25, determine the two-step ahead forecast in original dollar units.
MLB batting average. Consider data on the annual average batting average of all Major League Baseball (MLB) teams of a given year.The data series begins with 1960 and ends with 2013.24 MLB(a) Make a time plot of the batting average series.Describe any important features of the time series.(b)
Unemployment rate. Let yt denote the unemployment rate for time period t.(a) Use software to fit a simple linear regression model, using yt as the response variable and yt21 as the explanatory variable. Record the estimated regression equation.(b) Test the residuals for randomness. Does it appear
Unemployment rate. The Bureau of Labor Statistics tracks national unemployment rates on a monthly and annual basis. Use statistical software to analyze annual unemployment rates from 1947 through 2013.23(a) Make a time plot of the unemployment rate time series.(b) How would you best describe the
A more compact model. Suppose you fit a trend-and-seasonal model to a time series of quarterly sales and you find the following:y⁄t 5 300 1 20t 2 15Q1 2 15Q2 2 15Q3 Reexpress this fitted model in a more compact form using only one indicator variable.
Monthly warehouse club and superstore sales. Consider the monthly warehouse club and superstore sales series discussed in Examples 13.15 and 13.16 (pages 671–674). CLUB(a) Fit the trend-seasonal model shown in Example 13.16 and obtain the residuals from the fitted model. Plot the residuals as a
Runs test and autocorrelation. Suppose you have three different time series S1, S2, and S3. The observed number of runs for series S1 is significantly less than the expected number of runs. The observed number of runs for series S2 is significantly greater than the expected number of runs. The
AT&T wireline business. Continue the previous exercise. ATT(a) Based on the estimated linear trend model from part(c) of Exercise 13.33, obtain the residuals and plot them as a time series. Describe the pattern in the residuals.(b) Now consider a quadratic trend model. Fit a regression model based
AT&T wireline business. With the continuing growth of the wireless phone market, it is interesting to study the impact on the wireline (landline) phone market. Consider a time series of the quarterly number of AT&T customers (in thousands) who have wireline voice connections.20 The series begins
Visitors to Canada. Continue the previous exercise. VISITCA(a) Make indicator variables for the months of the year, and fit a linear trend along with 11 indicators to each of the two data series. Report your estimated models.(b) Based on these fits, make forecasts for the number of visitors from
Visitors to Canada. Given the economic implications of tourism on regions, governments and many businesses are keenly interested in tourism at local and national levels. To promote and monitor tourism to Canada, the Canadian national government established the Canadian Travel Commission (CTC).19
Hourly earnings. Continue the previous exercise. EARN(a) Make indicator variables for the months of the year, and fit a linear trend along with 11 indicators to the data series. Report your estimated model.(b) Does the regression output suggest the presence of seasonality? Explain how you reach
Hourly earnings. Consider monthly data on the hourly earnings of production and nonsupervisory employees in private U.S. industry, beginning in January 2010 and ending in July 2014.18 EARN(a) Make a time plot of these data. Describe the overall movement of the data series.(b) Does this time series
Hotel occupancy rate. Continue the previous exercise. HOTEL(a) Make indicator variables for the months of the year, and fit a linear trend along with 11 indicators to the data series. Report your estimated model.(b) Does the regression output suggest the presence of a trend? Explain how you reach
Hotel occupancy rate. A fundamental measure of the well-being of the hotel industry is the occupancy rate. Consider monthly data on the average hotal occupancy rate in the United States, beginning in January 2011 and ending in June 2014.17 HOTEL(a) Use statistical software to make a time plot of
Existing home sales. Continue the previous exercise. HSALES(a) Make indicator variables for the months of the year, and fit a linear trend along with 11 indicators to the data series. Report your estimated model.(b) Based on the fit, make a forecast for the number of existing homes sold for July
Existing home sales. Each month, the National Association of Realtors releases a report on the number of existing home sales. The number of existing home sales measures the strength of the housing market and is an key leading indicator of future consumer purchases such as home furnishings and
Chinese car ownership. In Example 13.14 (pages 669–670), an exponential trend-only model was fitted to the yearly time series of the number of passenger cars owned in China. In Exercise 13.23 (page 677), you were asked to determine the fitted model for the number of passenger cars in logged
Chinese car ownership. In Example 13.14 (pages 669–670), we found that an exponential trend model was a reasonable fit to the time series of the number of passenger cars owned in China. Based on the fitted model provided in the example, what is the fitted model for the number of passenger cars
Number of iPhones sold globally. Consider data on the quarterly global sales (in millions of dollars) of iPhones from the first quarter of 2012 to the third quarter of 2014. Create indicator variables for the first, second, and third quarters along with a trend index. Call these indicator variables
Monthly warehouse club and superstore sales. Consider the monthly warehouse club and superstore sales series discussed in Examples 13.15 and 13.16 (pages 671–674). Using the trend-and-season fitted model shown in Example 13.16, provide forecasts for the seven remaining months of 2014.
LinkedIn members. Refer to the quadratic fit shown in Figure 13.24(page 668) for the number of LinkedIn members by quarter. The series ended on the second quarter of 2014. Provide a forecast for the number of members for the third and fourth quarters of 2014.
Monthly cable sales. Refer to the computer output for the linear trend fit of Example 13.12 (pages 665–666).(a) Test the null hypothesis that the regression coefficient for the trend term is zero. Give the test statistic, P-value, and your conclusion.(b) The series ended at t 5 36. Provide
Percent of Canadian Internet users. Below are data on the time series of the percent of Canadians using the Internet for eight consecutive years ending in 2013.13 Year 2006 2007 2008 2009 2010 2011 2012 2013 Percent (%) 72.4 73.2 76.7 80.3 80.3 83.0 83.0 85.8 We usually want a time series longer
U.S.-Canadian exchange rates. Refer to Exercise 13.15. CANRATE(a) Obtain a histogram and Normal quantile plot of the daily changes in exchange rates. What do you conclude?(b) Test the daily changes against the null hypothesis that the underlying mean change is 0. What do you conclude?What is the
Honda returns. Consider the approximated returns plot in Figure 13.18 from Example 13.11.HONDA2(a) Obtain a histogram and Normal quantile plot of the returns data. What do you conclude about the distribution of the returns?(b) In the previous chapter on control charts, limits were placed plus and
U.S.-Canadian exchange rates. Consider the daily U.S.-Canadian exchange rates (Canadian dollars to one U.S. dollar) from the beginning of 2013 through the first week of August (bank holidays excluded).9 CANRATE(a) Test the randomness of the exchange rate series. What do you conclude?(b) Obtain the
Gold prices. Continue the previous exercise.GPRICE(a) Using the Normal distribution, provide an approximate 95% prediction interval for future monthly returns on gold prices.(b) Use the prediction interval on monthly returns found in part (a) to obtain an approximate 95% prediction interval for the
Gold prices. Consider the monthly data on the price of gold ($ per troy ounce) from January 2000 to July 2014.8 GPRICE(a) Test the randomness of the index series. What do you conclude?(b) Obtain the first differences for the series and plot these differences over time. What do you observe?(c) Take
Consumer sentiment index. Each month, the University of Michigan and Thomson Reuters conduct a survey of consumer attitudes concerning both the present situation as well as expectations regarding economic conditions. The results of the survey are used to construct a Consumer Sentiment Index. The
Computing returns. On August 7, 2014, the S&P 500 closed at 1909.57.On August 8, 2014, the S&P closed at 1931.51.(a) Compute the percentage change in the S&P from August 7 to August 8—that is, the daily return as a percentage.(b) Approximate the daily return using logs. Compare your answer with
Cleveland financial stress index. Several of the banks in the Federal Reserve system have developed indices to serve as barometers of the health of the U.S. financial system. For example, the Federal Reserve Bank of Cleveland constructed an index known as the Cleveland Financial Stress Index
Honda prices. Consider the Honda price series of Example 13.9.(a) What is the forecast for the closing price one week into the future?(b) What is the forecast for the closing price two weeks into the future?
Randomness versus distribution. In this section, we defined a Normal random process as being a process that generates independent observations that are well described by the Normal distribution. Consider daily data on the average waiting time (minutes) for patients at a health clinic over the
Runs test output. Here is the runs test output for a time series labeled X:Runs test for X Runs above and below K = 200.742 The observed number of runs = 53 The expected number of runs = 44.9091 46 observations above K, 42 below P-value = ???(a) How many observations are in the data series?(b)
Annual inflation rate. Here are the annual inflation rates for the United States for the years 2000 through 2013:Year 2000 2001 2002 2003 2004 2005 2006 Percent (%) 3.4 2.8 1.6 2.3 2.7 3.4 3.2 Year 2007 2008 2009 2010 2011 2012 2013 Percent (%) 2.8 3.8 20.4 1.6 3.2 2.1 1.5(a) Determine the values
Lag 0. The ACF shown in Figure 13.10 (page 654)starts with lag 1. However, some software will report and plot the autocorrelation for lag 0. Regardless of the series involved, what is the value of the lag 0 autocorrelation?
Disney prices. Continue with the study of the Disney price series.(a) Obtain the ACF for the price series. How many autocorrelations are beyond the ACF significance limits?(b) Aside from autocorrelations falling beyond significance limits, what else do you see in the ACF that gives evidence against
Disney prices. Continue the study of Disney closing prices from Exercise 13.1(page 651).(a) Using software, create a lag one variable for prices. Make a scatterplot of prices plotted against the lag one variable. Describe what you see.(b) Find the correlation between prices and their first lag.
Spam process. Most email servers keep inboxes clean by automatically moving incoming mail that is determined to be spam to a “Junk” folder. Here are the weekly counts of the number of emails moved to a Junk folder for 10 consecutive weeks:194 227 201 152 202 178 229 202 247 155 Answer the
Disney prices. In Example 13.1, we found the weekly returns of Disney stock to be consistent with a random process. What can we say about the time series of the weekly closing prices?(a) Using software, construct a time plot of weekly prices. Is the series consistent with a random process? If not,
Is it really Poisson? Certain manufacturing environments, such as semiconductor manufacturing and biotechnology, require a low level of environmental pollutants (for example, dust, airborne microbes, and aerosol particles). For such industries, manufacturing occurs in ultraclean environments known
Monitoring budgets. Control charts are used for a wide variety of applications in business.In the accounting area, control charts can be used to monitor budget variances. A budget variance is the difference between planned spending and actual spending for a given time period. Often, budget
Monitoring rare events. In certain SPC applications, we are concerned with monitoring the occurrence of events that can occur at any point within a continuous interval of time, such as the number of computer operator errors per day or plant injuries per month. However, for highly capable processes,
It’s all in the wrist. Consider the saga of a professional basketball player plagued with poor free-throw shooting performance. Here are the number of free throws he made out of 50 attempts on 20 consecutive practice days (read left to right): FTHROW 25 27 31 28 22 21 27 20 25 27 23 22 29 34 30
Even more signals. There are other out-ofcontrol signals that are sometimes used with x charts.One is “15 points in a row within the 1 level.”That is, 15 consecutive points fall between 2 yÏn and 1 yÏn. This signal suggests either that the value of used for the chart is too large or
Bone density revisited. Refer to Exercise 12.26(page 627), in which you were asked to construct x and R charts for the calibration data from a Lunar bone densitometer shown in Table 12.6. BONE(a) Make an s chart and comment on control of the process variation.(b) Based on the standard deviations,
Hospital losses revisited. Refer to Exercise 12.14 (page 614), in which you were asked to construct x and s charts for the hospital losses data shown in Table 12.4. HLOSS(a) Make an R chart and comment on control of the process variation.(b) Using the range estimate, make an x chart and comment on
Categorizing the output. Previously, control of the process was based on categorizing the thickness of each film inspected as satisfactory or not. Steady improvement in process quality has occurred, so that just 15 of the last 5000 films inspected were unsatisfactory.(a) What type of control chart
x chart. Interviews with the operators reveal that in Samples 1 and 10, mistakes in operating the interferometer resulted in one high-outlier thickness reading that was clearly incorrect. Recalculate s after removing Samples 1 and 10. Recalculate UCL for the s chart and add the new UCL to your s
s chart. Calculate control limits for s, make an s chart, and comment on control of short-term process variation.
Purchased material. At the present time, about five out of every 1000 lots of material arriving at a plant site from outside vendors are rejected because they are incorrect. The plant receives about 300 lots per week. As part of an effort to reduce errors in the system of placing and filling
Pareto charts. You manage the customer service operation for a maker of electronic equipment sold to business customers. Traditionally, the most common complaint is that equipment does not operate properly when installed, but attention to manufacturing and installation quality will reduce these
Enlighten management. A manager who knows no statistics asks you, “What does it mean to say that a process is in control? Is being in control a guarantee that the quality of the product is good?”Answer these questions in plain language that the manager can understand.
Implications of out-of-control signal. For attribute control charts, explain the difference in implications for a process and in actions to be taken when the plotted statistic falls beyond the upper control limit versus beyond the lower control limit.
Purchase order errors. Purchase orders are checked for two primary mistakes: incorrect charge account number and missing required information. Each day, 10 purchase orders are randomly selected, and the number of mistakes in the sample is recorded. Here are the numbers of mistakes observed for 20
Monitoring lead time demand. Refer to the lead time demand process discussed in Exercise 5.83(page 285). Assuming the Poisson distribution given in the exercise, what would be the appropriate control chart limits for monitoring lead time demand?
p charts and high-quality processes. A manufacturer of consumer electronic equipment makes full use not only of statistical process control but of automated testing equipment that efficiently tests all completed products. Data from the testing equipment show that finished products have only 3.5
School absenteeism. Here are data from an urban school district on the number of eighth-grade students with three or more unexcused absences from school during each month of a school year. Because the total number of eighth-graders changes a bit from month to month, these totals are also given for
Call center. A large nationwide retail chain keeps track of a variety of statistics on its service call center. One of those statistics is the length of time a customer has to wait before talking to a representative. Based on call center research and general experience, the retail chain has
Aircraft rivets. After completion of an aircraft wing assembly, inspectors count the number of missing or deformed rivets. There are hundreds of rivets in each wing, but the total number varies depending on the aircraft type. Recent data for wings with a total of 34,700 rivets show 208 missing or
Positive lower control limit? What values of c are associated with a positive lower control limit for the c chart?
Worker safety. An investigation of the out-of-control signal seen in Figure 12.20 revealed that not only were there new hires that month, but new machinery was installed. The combination of relatively inexperienced employees and unfamiliarity with the new machinery resulted in an unusually high
Setting up a p chart. After inspecting Figure 12.18 (page 633), you decide to monitor the future absenteeism rates using a center line and control limits calculated from the second two weeks of data recorded in Table 12.8. Find p for these 10 days and give the new values of CL, LCL, and UCL.
Unpaid invoices. The controller’s office of a corporation is concerned that invoices that remain unpaid after 30 days are damaging relations with vendors.To assess the magnitude of the problem, a manager searches payment records for invoices that arrived in the past 10 months. The average number
More on Six-Sigma quality. The originators of the Six-Sigma quality standard reasoned as follows.Short-term process variation is described by . In the long term, the process mean will also vary. Studies show that in most manufacturing processes, 61.5is adequate to allow for changes in . The
Six-Sigma quality. A process with Cp $ 2 is sometimes said to have “Six-Sigma quality.” Sketch the specification limits and a Normal distribution of individual measurements for such a process when it is properly centered. Explain from your sketch why this is called Six-Sigma quality.
Alloy composition process capability. Refer to Exercise 12.28 as it relates to the 20 preliminary subgroups on percents of aluminum content. The acceptable range for the percents of aluminum is 3.8%to 4.2%. ALLOY(a) Obtain the individual observations and make a Normal quantile plot of them. What do

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