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mathematics
business statistics

Questions and Answers of Business Statistics

If the correlation between number of customers and sales in dollars in retail stores is r = 0.6, then what would be the correlation if the sales were measured in thousands of dollars? In euros? (1
A fitness center weighed 53 male athletes and then measured the weight that they were able to lift. The correlation was found to be r = 0.75. Can you interpret this correlation without knowing
To inflate the correlation, a conniving manager added $200,000 to the actual sales amount for each store in Exercise 25. Would this trickery make the correlation larger?Data from exercises 25If the
1. The timeplot in Figure 9 shows the price at the end of the month of one share of stock in Pfizer.What seems to be happening? How could you verify your answer?2. Figure 10 tracks the value of an
These data compare the on-time arrival performance of American and US Airways shortly before their merger in 2015. The table shows the status of 9,350 arrivals during January 2015.(a) On the basis of
Bold names shown with a question identify the data table for the problem.Trust Gallup reported the following results from a survey in 2015. The survey asked 1,527 adults to state how much they trust
Suppose you were looking at the histogram of the incomes of all of the households in the United States. Do you think that the histogram would be bell shaped? Skewed to the left or right?
Match the brief description to the item or value.The square root of the variance(a) Median(b) Mean(c) Standard deviation(d) Variance(e) Z-score(f) Two-thirds(g) Mode(h) Interquartile range(i)
Match the brief description to the item or value.The average of the values of a numerical variable(a) Median(b) Mean(c) Standard deviation(d) Variance(e) Z-score(f) Two-thirds(g) Mode(h)
Match the brief description to the item or value.Length of the box in the boxplot(a) Median(b) Mean(c) Standard deviation(d) Variance(e) Z-score(f) Two-thirds(g) Mode(h) Interquartile range(i)
Match the brief description to the item or value.Position of a peak in the histogram(a) Median(b) Mean(c) Standard deviation(d) Variance(e Z-score(f) Two-thirds(g) Mode(h) Interquartile range(i)
Bold names shown with a question identify the data table for the problem.EmploymentThis table shows percentages of men and women employed in four industries.(a) Is there association between the
A study of purchases at a 24-hour supermarket recorded two categorical variables: the time of the purchase (8 a.m to 8 p.m vs. late night) and whether the purchase was made by someone with children
A survey found that the favorite color of everyone who bought a vehicle overall is silver. In this case, should a new car dealer order most pick-up trucks to stock on its lot in silver?
Executives at a retailer are comparing items chosen by shoppers who either saw or did not see its most recent television advertising. Do the managers in charge of advertising hope to find association
The title of each of the following exercises identifies the data table to be used for the problem.Tech Stocks These data give the monthly returns on stocks in three technology companies: HP, IBM, and
The title of each of the following exercises identifies the data table to be used for the problem.Another column in this data file gives the rated combined fuel economy (in miles per gallon) for 413
The title of each of the following exercises identifies the data table to be used for the problem.A column in this data file gives the engine displacement in liters of 413 vehicles sold in the United
The data in this chapter concern the amount of space needed to hold various songs. What about the length, in minutes? Suppose you get 60 seconds of music from every megabyte of recorded songs.
This histogram shows the price in dollars of 218 used cars.(a) Suppose we converted the prices of these cars from dollars to euros, with an exchange rate of 1.1 dollars per euro. Describe the
The September 2014 issue of the Federal Reserve Bulletin results from the Survey of Consumer Finances, a national economic survey conducted by the Federal Reserve every three years. The survey found
The Census Bureau reported that the median household net worth in the United States was $68,800 in 2011. In contrast, the mean household net worth was $339,000. How is it possible for the mean to be
The Energy Policy Act of 2005 mandates that gasoline sold in the United States must average at least 2.78% ethanol in 2006. Does this mean that every gallon of gas sold has to include ethanol?
Suppose sales representatives average 45 hours per week on the road with standard deviation 5. Would it be surprising to meet a representative who spent 51 hours on the road last week? Do you need to
The range measures the spread of a distribution. It is the distance from the smallest value to the largest value. Is the range sensitive to the presence of outliers?
Many athletes use interval training to improve their strength and conditioning. Interval training requires working hard for short periods, say a minute, followed by longer intervals, say five
For the incomes of all of the households in the United States, which do you expect to be larger, the mean or the median?
Compare the bar chart of the variable described in the previous question with the pie chart of the same data. Which makes it easier to see that each category has the same number of cases?
This pie chart shows the type of college attended by the CEOs of America€™s 50 largest companies.8 Which category is the mode? Which category is the median? Other Ivy League 4 Public 26
A categorical variable has two values, male and female. Would you prefer to see a bar chart, a pie chart, or a frequency table? Why?
A data table with 100 rows includes a categorical variable that has five levels. Each level has 20 rows. Describe the bar chart.
Sketch by hand the pie chart of the data in the previous question.Data from previous questionDescribe the bar chart of a categorical variable for which 900 of the 1,000 rows of data are in one
Describe the bar chart of a categorical variable for which 900 of the 1,000 rows of data are in one category and the remaining 100 are distributed evenly among five categories.
What would happen if we were to generate a bar chart for a column that measures the amount spent by the last 200 customers at a convenience store?
This table summarizes shares of the U.S. wireless telephone market in 2011. To summarize these percentages together in a pie chart, what needs to be added? Company
These percentages summarize the responses of 530 senior executives when asked the question, €œWhich strategies have proved successful in promoting a data-driven culture in your
The Wall Street Journal on January 19, 2016, used a chart resembling the following one to illustrate the rising amounts that Netflix spends to provide streaming content online. Is this the bar chart
Share of bank loans that are in good standing, 30 days past due, and in defaultMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and
Number of cellular telephone customers rating their service as Poor, OK, Good, and GreatMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are
Customer choices of compact, zoom, and high-end digital camerasMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are shares.
Share of software purchases devoted to games, office work, and designMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are
Brand of computer chosen by new students of a large universityMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are shares.
Excuses given for not finishing homework assignmentsMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are shares. If not
Reason for customers hanging up when calling a computer help deskMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are
Destinations for travelers leaving the United States and heading abroadMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are
Counts of the type of automobile involved in police traffic stopsMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are
Number of cash-back coupons returned by purchasers of cameras, computers, and stereo equipmentMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are
Number of different types of defects found in computer equipmentMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and others are shares.
Proportion of automobiles sold during the last quarter by eight major manufacturersMatch this description of variables to a bar chart, Pareto chart, pie chart, or frequency table. Some are counts and
Auto manufacturers are sensitive to the color preferences of consumers. Would they like to know the modal preference or the median preference?
A magazine wants a graphic that presents the sales of cars in the United States, broken down by the major manufacturers. To get the attention of readers, the graphic will show a car representing the
The data for this exercise derive from a sample of 5,000 visits to amazon.com, and, as in the example in this chapter, the data for each visit list the host that linked to Amazon. The key difference
The U.S. Census Bureau occasionally surveys business owners and learns which firms are predominantly owned by women. These data are a portion of the results reported in 2010 from the 2007 Survey of
List the criteria and model selection procedures we use to compare regression models.
List the tools that we use to identify an outlier with respect to its y value and/or x values.
For each of the following cases, use the indicated residual plots to check for any violations of the regression assumptions.a. The Tasty Sub Shop Case: For the model relating Revenue to Population
What two values does the dependent variable equal in logistic regression? What do these values represent?
When is neural network modeling most useful?
How do we define the output layer function g(L)?
United Oil is attempting to develop a middle-grade gasoline that will deliver high gasoline mileages. As part of its development process, United Oil will study the effect of three middle-grade
Although natural gas is currently inexpensive and nuclear power currently (and perhaps deservedly) does not have a good reputation, it is possible that more nuclear power plants will be constructed
Discuss how we model no trend and a linear trend.
In this exercise we consider annual U.S. lumber production over 30 years. The data were obtained from the U.S. Department of Commerce Survey of Current Business and are presented in Table 15.5. (The
Referring to the situation of Exercise 15.3, the mean and the standard deviation of the lumber production values can be calculated to be y̅ = 35,651.9 and s = 2,037.3599. Find a point forecast of
Use the Durbin€“Watson statistic given at the bottom of the Minitab output in Figure 15.9(c) to assess whether there is positive auto-correlation.Figure 15.9(c) SE Coef T-Value P-Value
Explain how the multiplicative decomposition model estimates seasonal factors.
Explain how the multiplicative decomposition method estimates the trend effect.
Discuss how the multiplicative decomposition method makes point forecasts of future time series values.
Find and identify the four seasonal factors for quarters 1, 2, 3, and 4.International Machinery, Inc., produces a tractor and wishes to use quarterly tractor sales data observed in the last four
Compute an approximate 95 percent prediction interval forecast of tractor sales for each of the quarters next year. Use the fact that the half-lengths of 95 percent prediction intervals for the
In general, when is it appropriate to use exponential smoothing?
What is the purpose of a smoothing constant in exponential smoothing?
When do we use double exponential smoothing?
When do we use the multiplicative Winters’ method?
Figure 15.20 gives the Minitab output of using double exponential smoothing in month 20 to forecast watch sales in months 21 through 26. Here we have used Minitab€™s default option that
Figure 15.21 on the next page gives the Minitab output of using multiplicative Winters€™ method in month 168 to forecast the monthly hotel room averages in months 169 through 180. Here we
Consider the monthly international passenger totals in Table 15.8 on page 690. Use Minitab and Winters€™ method in month 132 to find point predictions of and 95 percent prediction intervals
What is the MAD? What is the MSD? What is the MAPE? How do we use these quantities?
Why does the MSD penalize a forecasting method much more for large forecast errors than for small forecast errors?
Which method—method A or method B—gives the smallest MAD? The smallest MSD? The smallest MAPE?Compare two forecasting methods—method A and method B. Suppose that method A gives the point
Explain the difference between a simple index and an aggregate index.
Explain the difference between a Laspeyres index and a Paasche index.
Referring to the discussion of Figure 15.22, the CPI-U for March 2011 was 223.47, and the CPI-U for October 1963 was 30. Interpret these CPI-U€™s. FIGURE 15.22 Plot of the Monthly CPI-U
Recall that Table 15.16 gives the price of a gallon of regular gasoline in the United States (in dollars) for the years 2003 through 2011. Table 15.20 gives the price of a gallon of regular gasoline
Table 15.24 gives quarterly sales (in thousands of cases) of Tiger Sports Drink over the previous eight years. Plot the data and use an appropriate forecasting technique to find point predictions of
Write a paragraph explaining how common causes of process variation differ from assignable causes of process variation.
Explain (1) the purpose of an x̅ chart, (2) the purpose of an R chart, (3) why both charts are needed.
Explain why the initial control limits calculated for a set of subgrouped data are called “trial control limits.”
In an issue of Quality Progress, Gunter presents several control charts. Four of these charts are reproduced in Figure 16.17. For each chart, find any evidence of a lack of statistical control (that
In the book Tools and Methods for the Improvement of Quality, Gitlow, Gitlow, Oppenheim, and Oppenheim present several control charts in a discussion and exercises dealing with pattern analysis.
Write a short paragraph explaining why a process that is in statistical control is not necessarily capable of meeting customer requirements (specifications).
Explain the interpretation of the natural tolerance limits for a process. What assumptions must be made in order to properly make this interpretation? How do we check these assumptions?
For each of the following, explaina. Why it is important to have leeway between the natural tolerance limits and the specification limits.b. What is meant by the sigma level capability for a
Suppose that x̅ and R charts based on subgroups of size 3 are used to monitor the moisture content of a type of paper. The x̅ and R charts are found to be in statistical control with x̅̅ = 6.0
Suppose that a normally distributed process (centered at target) has three sigma capability. If the process shifts 1.5 sigmas to the right, show that the process will produce defective products at a
In your own words, define a nonconforming unit.
Explain the purpose behind constructing (a) A cause-and effect diagram(b) A defect concentration diagram.
In an issue of Quality Progress, Hoexter and Julien discuss the quality of the services delivered by law firms. One aspect of such service is the quality of attorney€“client communication.
What is a nonparametric test? Why would such a test be particularly useful when we must take a small sample?
When we perform the sign test, we use the sample data to compute a p-value. What probability distribution is used to compute the p-value? Explain why.

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