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Business Statistics 3rd Canadian Edition Norean D. Sharpe, Richard D. De Veaux, Paul F. Velleman, David Wright - Solutions
The following time series graph shows daily closing stock prices for Toyota Motor Manufacturing from April 1, 2008, through June 21, 2013.a) Which time series components seem to be present? The method of moving averages was applied to these data. Here are time series graphs showing moving average
The Paralyzed Veterans of America (PVA) is a philanthropic organization sanctioned by the U.S. government to represent the interests of veterans who are disabled. To generate donations, the PVA sends out greeting cards and mailing address labels periodically with its requests for donations. To
First Quantum Minerals Ltd., a mining and metals company based in Vancouver, produces copper, gold, and nickel. It’s listed on the Toronto and London stock exchanges. The data file ch21_MCSP_Quantum contains monthly commodity prices for copper, gold, and nickel together with the share price of
Each winter, many Canadians travel to the Caribbean for a winter vacation. Some people call them “snow birds,” including Jeff Mohammed who heads up a company offering all-inclusive packages. He has deals with a number of hotels and airlines and offers prices that depend on the quality of the
The Canadian exchange rate may be related to the TSX indices of performance of various sectors of the Canadian economy. The data file used in Exercise 25 contains monthly TSX indices for various sectors of the Canadian economy together with the exchange rate between Canadian and U.S. dollars for
Exercise 27 raised some questions about the regression model built to understand the effect of OECD regulation on GDP/ Capita in 24 OECD countries. Let’s look more deeply. Here’s a histogram of the Cook’s Distances for that model:The country with high Cook’s Distance is Ireland.a) What does
The following regression is based on weekly receipts from shows on Broadway in New York City:Dependent variable is: Receipts($M)R-squared = 93.3% R-squared (adjusted) = 93.1%s = 0.9589 with 92 = 88 degrees of freedomHere are some diagnostic plots:a) The two points plotted with “x” in the
Airlines strive to be on time, in part because customers can refer to government-published statistics to select f lights that are most often on time. We have data for 19 airlines for March 2006 reporting the following variables:On Time (number of on-time arrivals)Cancelled
A study by the U.S. Small Business Administration modelled the GDP per capita of 24 of the countries in the Organisation for Economic Co-operation and Development (OECD). One analysis estimated the effect on GDP of economic regulations using an index of the degree of OECD economic regulation and
The price ($/lb) of lobster harvested in the Maine lobster fishing industry is an important factor in the profitability of the industry. Here is a regression model to predict the Price from the number of Traps (millions), the number of Fishers, and the Catch/Trap (tonnes):Dependent variable is:
A major sector in the Canadian economy is minerals. Growth in that sector is associated with an increase in the value of the Canadian dollar. The data set contains monthly data for the Canadian exchange rate and stock indices for various sectors of the economy on the Toronto Stock Exchange.
Here are plots of two regression analyses of roller coaster Speed against Height. The first is for roller coasters that don’t have inversions and the second is for roller coasters that do.a) Would a single indicator variable for Inversions added to the regression equation enable us to obtain one
Here is a scatterplot of the residuals from the regression in Exercise 16:a) For Behemoth, the data value for Speed is 123, and the predicted value is 130.15. If we change the data value to 124 and recompute the regression, the predicted value becomes 130.89. What is the leverage for Behemoth?b)
Data on roller coasters at Canada’s Wonderland are available in the data file and include Speed, Height, and Number of Inversions. We performed a regression to investigate whetherSpeed is related to Height, and then added indicator variables to take into account the number of inversions: none,
For the regression model in Exercise 8, the leverage values look like this:The movie with the highest leverage of 0.219 is Walt Disney’s John Carter, which grossed $66M but had a budget of $300M. If the budget for John Carter had been $1M higher than it was (and everything else remained the
Professional sports, like many other professions, require a variety of skills for success. That makes it difficult to evaluate and predict success. Fortunately, sports provides examples we can use to learn about modelling success because of the vast amount of data that are available. Here’s an
Aeroplan, the loyalty program of Air Canada, has been in operation since 1984. Travellers on Air Canada flights receive Aeroplan miles, which can be redeemed for free travel, vacations, or merchandise. Aeroplan was originally owned by Air Canada, and was spun off as a separate company in 2002. Its
Exercise 42 analyzes whether weekly earnings are related to employment opportunities in Canada. Other factors that might impact people’s weekly earnings are their number of years of education (ED) and their number of years of work experience (EX). To investigate how important these factors are,
You’ve probably heard that earnings are generally higher in urban areas than in rural areas. But why is this so? Perhaps it’s because urban areas attract a cluster of employers, producing any employment opportunities. To test this possibility, Statistics Canada used census data to run a
EthicScan Canada monitors the social, labour, and environmental performance of 1500 companies in Canada, and makes comparisons between companies in the same industry sector. In the food industry, six companies are compared by giving a score for nine factors, including environmental performance
A study of the impact of the salary and stock options paid to executives of 77 Canadian companies on the company rating for corporate social responsibility (CSR) came up with the followingregression equation:CSR Rating = - 0.163 × Salary + 0.320 × Options + Several Other FactorsAll variables are
Here are some plots of residuals for the regression of Exercise 14:Which of the regression conditions can you check with these plots? Do you find that those conditions are met? 0.30 - 0.15+ 0.00+ -0.15+. -0.30 + 15 12 18 21 Predicted 25 20 15 10 0.32 -0.28 -0.08 0.12 Residuals 0.30+ 0.15+ 0.00+
Here are some plots of residuals for the regression of Exercise 13:Which of the regression conditions can you check with these plots? Do you find that those conditions are met? 400 + 200 -200 + 400 300 500 600 Predicted 400 200 -200 + -2 -1 1 Predicted Residuals 2.
In order to plan electric power generation, it is important to identify trends in generation from different sources, including wind. Statistics Canada reports the amount of renewable energy generated (in megawatt-hours) in each province and territory for several renewable sources, including wind
A company based in Kingston, Ontario, has been installing solar modules on residential roofs in Kingston and Ottawa and is planning to expand its operation in the smaller communities along Highway 401 toward Toronto to the southwest of Kingston. One reason for expansion in this direction is that
The altitude (in feet) of a Boeing 737 landing at Pearson International Airport in Toronto is shown as the average during consecutive one-minute intervals in the graph:Describe (without performing any quantitative analysis) how the concepts discussed in this chapter apply (or don’t apply) to
Building permits are a leading indicator of economic growth. But do non-residential permits follow the same pattern as residential permits? Statistics Canada provides us with the requisite data in Table 260-0003, Building Permits, Values by Activity Sector. The graph shows the value of each type of
How has the price of a lobster changed? Here’s a plot tracking the price of lobster per pound in constant year 2000 dollars:This plot isn’t straight. Would a transformation help? If so, which one? If not, why not? 3.75+ 3.00 + 2.25 + 1.50 + 0.75 1937.5 1950.0 1962.5 1975.0 1987.5 2000.0 Year
How has the number of licensed lobster fishers changed? Here’s a plot of the number of Fishers vs. Year:This plot isn’t straight. Would a transformation help? If so, which one? If not, why not? 10,500 + 9,000- 7,500 8agas 6,000 + 1990 2010 1950 1970 Year Fishers
Many professions use tables to determine key quantities. The value of a log is based on the number of board feet of lumber the log may contain. (A board foot is the equivalent of a piece of wood 1 inch thick, 12 inches wide, and 1 foot long. For example, a 20 × 40 piece that’s 12 feet long
Probe a little deeper into the analysis in Exercise 49 as follows: a) Plot the data and the residuals, calculate the Durbin-Watson statistic and comment on what these imply for the regression model.b) Would a transformation of the data improve the model: (i) for 2000–08; (ii) for 2009–12;
The data file gives quarterly gross domestic product (GDP) of Canada in billions of dollars for 1Q2000–2Q2015.a) Perform a linear regression analysis of this data.b) Interpret the slope, its P-value, and the R2.
Lobster are caught in traps, which are baited and left in the open ocean. Licences to fish for lobster are limited, there is a small additional fee for each trap in use, and there are limits on the numbers of traps that can be placed in each of seven fishing zones. But those limits have changed
A company selling wedding services needs to take into account the difference in age of the two partners when marketing its services. The graph shows the ages of both men and women at first marriage (www.census.gov):Clearly, the pattern for men is similar to the pattern for women. But are the two
The graph below shows the number of passengers travelling on major Canadian airlines month by month from November 2010 to September 2015. Time is shown as months since October 2010.a) Perform a linear regression analysis of this data.b) Interpret the slope, its P-value, and the R2.c) Plot the
You probably hope your earnings will increase if you spend time studying, but by how much? Statistics Canada answers this question in the research paper from which we have reprinted the following graph.a) Do you think there’s a clear pattern? Describe the trend.b) Is the association strong?c) Is
For the regression in Exercise 19: A student tries taking the reciprocal of customers and produces the plot shown below:a) Would you recommend this transformation? Why or why not?b) What would you suggest? 0.00012 - 0.00010 0.00008 0.00006 0.00004 0.00002 05 10 15 20 25 30 35 Month 1/Customers
A quickly growing company shows the following scatterplot of customers vs. time (in months).a) What re-expression might you suggest for the number of customers?b) What power in the Ladder of Powers does that correspond to? 140,000 - 120,000 * 100,000 E 80,000 60,000 40,000 20,000 + 5 10 15 20 25 30
One possible model for the manufacturing process of Exercise 17 is the following:Dependent variable is: Log (Cost per unit)R-squared = 90.1% R-squared (adjusted) = 89.3%s = 0.0841 with 15 - 2 = 13 degrees of freedomUsing this model, predict the cost per unit in a batch of 300. Variable Intercept
A small company has developed an improved process for making solar panels. The company needs to set its prices and wants those prices to ref lect the efficiencies of producing larger batches. The data show the following:#Units
A study of homes that looked at the relationship between Age of a home and Price produced the following scatterplot. A regression was fit to the data, as shown:On the basis of this plot, would you advise using this regression? Explain. 350,000 + 300,000 250,000 200,000 + 20 + 40 + 80 60 100 Age
A scatterplot of Salary against Years Experience for some employees and the scatterplot of residuals against predicted Salary from the regression line are shown in the figures. On the basis of these plots, would you recommend a re-expression of either Salary or Years Experience? 60 50 40+ 30 + 10
Trinus Pipes and Tubes, a small company in Barrie, Ontario, produces plastic pipes certified to meet the Canadian Standards Association C448 specification for use in geothermal systems. Trinus provides 50-year warranties on its products against leakage, so the thickness of the pipe wall needs to be
A Canadian clothing retailer needs to test whether the content of the fabric, as stated on the label, is within acceptable limits. It outsources this work to a testing company that inspects the fabric at the production facility. Suppose that a line of T-shirts claims to be 50% cotton and that tests
Encana Corporation, whose name is an acronym for ENergy, CANada, and Alberta, is a natural gas company based in Calgary with five major natural gas operations in Canada: Bighorn, Coalbed Methane, Cutbank Ridge, Greater Sierra in western Canada, and Deep Panuke, an offshore project in Nova
InterCon Travel Health is a Toronto-based company that provides services to health insurers of foreign tourists who travel to the United States and Canada.4 As described in the Guided Example in this chapter, the primary focus of InterCon is to act as an interface between local health providers and
A treaty between the United States and Canada guarantees that one-third of the water in the Niagara River should f low over the falls. One-third can be removed from the river to generate hydro-electric power by Canada and another third by the United States. Until 2013, Canada had a canal and a
The Beaufort Sea, located to the north of Nunavut and the Northwest Territories, is being explored for oil and natural gas by companies that conduct geological surveys and sell the resulting data to the energy companies that actually do the drilling. Alternatively, the survey company may do the
Exploration licences for energy companies to drill in the Beaufort Sea are overseen by Indigenous and Northern Affairs Canada. The licences typically grant the right to drill in a certain area of the seabed in return for pledging a sum of money that it plans to spend on drilling. If the company
A small Canadian mining company is issuing an initial public offering (IPO) of shares on the Vancouver Stock Exchange at $17 per share. A limited number of “early” investors were able to purchase these shares at $17 on the IPO date, and the shares were traded on the stock exchange for any
An investor is considering how to invest her money. She has two options—either a domestic mutual fund that only invests in blue chip stocks or an international aggressive mutual fund that invests in young technical firms. The payoff (profit) after one year for these investments depends on the
A bicycle shop owner is deciding which products to stock. His distributor will give him a deal if he buys more of one kind of bike. The payoff table shows monthly sales for a high-end bike (selling at $950) or a moderately priced bike (selling at $500). Based on past experience, the shop owner
Akbar, of Exercises 27, 29, and 31, could obtain long-range predictions of the growing conditions for next summer. He thinks they might show a probability of good growing conditions as low as 50% or as high as 80%. If he doesn’t obtain those predictions, he’ll make a decision based on his
Akbar Overgrowth, whom we met in Exercise 27, is an entrepreneur who is optimistic about the growing season. What choice should he make to maximize his return? His assistant, Lance Broadleaf, is very conservative, and argues that KickGrass should minimize its potential downside results. Which
Aaron, whom we met in Exercise 28, tends to be optimistic about business conditions. What is his maximax strategy that would maximize his results?In ExerciseDemand and price are related; raising prices typically lowers demand. Many companies understand that if they can segment their market and
Akbar Overgrowth, from Exercise 27, estimates that the probability of a good growing season is 0.70. On that basis,In Exercise 27KickGrass Lawncare is a service that cares for lawns in a large, affluent community. Akbar Overgrowth, the owner, is considering the purchase of new zero-turn riding lawn
Blueberries are the most important fruit in Canada. Not only do they taste good, but they also occupy over half of the land area devoted to fruit production, with blueberry exports valued at several hundred million dollars per year. There are two main varieties of blueberries: small, wild berries
In potash mining, large conveyors are used underground to haul ore from the rock face to shafts through which it can be lifted to the surface for processing. A conveyer hauling one tonne per second consumes about 250 kilowatts of electric power. Automatic control of conveyors can reduce electric
An organic produce company divides Canada into five regions: West, Prairies, Ontario, Quebec, and Atlantic. Each has its own greenhouses for growing organic produce and its own distribution system to retail outlets. The fruits and vegetables are produced without pesticides, thus reducing their
Referring to the regression in exercise 47.a) Interpret the meaning of R squared.b) Comment on how this meaning is consistent with the significance of the linear regression. Variable Coefficient SE(Coeff) t-ratio P-value Intercept 1.303 0.3211 4.06 0.0001 LogAssets 0.578 0.0919 6.28
Football team owners are constantly in competition for good players. The better the winning percentage, the more likely the team will provide good business returns for the owners. Of course, the resources that each of the 32 teams has in the National Football League (NFL) vary. Does the size of the
How does the production budget of a movie depend on its length? Data on the budgets (millions of dollars) and the running times (minutes) for major-release films in a recent year are summarized in these plots and computer output:Dependent variable is: Budget ($M)R squared = 15.4%s = 32.95 with 120
Concern over the weather associated with El Niño has increased interest in the possibility that the climate on Earth is getting warmer. The most common theory relates an increase in atmospheric levels of carbon dioxide (CO2), a greenhouse gas, to increases in temperature. Here is part of a
For a physical exam to qualify for company-provided insurance, 14 employees had their blood pressure measured. Their systolic and diastolic BP are given here:SBP
A study of 98 investment advisors asked them to predict the value of a “penny” stock a week ahead. The correlation between the values predicted and the actual value was 0.20. Was this evidence that they could predict penny stock performance?a) State the null and alternative hypotheses about the
A website that rents movies online recorded the age and the number of movies rented during the past month for some of its customers. Here are its data:Age
For the model found in Exercise 1, predict how much a person with a household income of $75,000 would be expected to spend eating out in a week. EatOut$/wk 17.28 + 0.354 HHIncome
You’re considering opening an Estonian cuisine restaurant and wonder how much people in your target community spend on eating out relative to their household incomes. You commission a telephone survey and build the following regression model for individual respondents:where household income is in
Use the data file Real-Estate to consider what factors might contribute to the price of a home. Specifically, consider:• Does the price for homes with a fireplace differ significantly from the price for homes without fireplaces? Select an appropriate nonparametric test to obtain your results.•
After emerging from bankruptcy protection in 2004, Air Canada worked with its employees at numerous measures to maintain profitability. However, its share price dropped from around $18 at the end of 2006 to around $3.50 at the end of 2010. Then, in 2011, Air Canada experienced labour-relations
A survey organization obtains the opinions of a random sample of Canadian adults as to how fair the Canadian tax system is on a five-point Likert scale, from “very fair” to “very unfair.” Five years later it surveys the same people and asks the same question in order to assess whether
A marketing executive tested two incentives to see what percentage of customers would enrol in a new web-based loyalty program. The customers were asked to log on to their accounts on the web and provide some demographic and spending information. As an incentive, they were offered either nothing
With the rising costs of U.S. medical insurance and the declining interest and ability of employers to maintain proper medical coverage for their employees, business owners and employees alike are wondering: Who will insure future workers in the United States? The government has spent decades
The Carbon Disclosure Project (CDP) acts on behalf of over 700 institutional investors (pension funds, mutual funds, etc.) with almost $100 trillion of investments to collect and distribute information on corporate greenhouse gas (carbon) emissions. These investors are interested in taking carbon
Nordion has developed a medical device that inserts a radioisotope inside a patient’s liver for the treatment of liver cancer. About half of the world’s liver cancer patients are in China, and Nordion is planning to market the technology there, using methods that include making presentations at
In a survey of 616 Canadian homeowners who have a wooden deck attached to their homes, Ipsos Reid found a substantial percentage had never inspected their decks for safety, 40% say they never really think about whether their deck is safe, and 11% say their deck “could collapse at any minute.”
Governments around the world implement measures to promote gender equality, and they need to know whether voters think they’re being successful. Angus Reid Strategies conducted a survey in Canada, the United States, and the United Kingdom to provide information on this issue. A key question asked
A councillor in the Vancouver Island region of Tofino proposed “discouraging the future development and location of large-format retail chains and fast-food chains.” Angus Reid Strategies interviewed 1003 adult Canadians to see whether they agreed with this proposal. (Note that “ATL” in the
How should governments deal with crime? Should they focus on punishing criminals, or should they aim to prevent crime happening in the first place? It’s important for government policy to take public opinion into account, so Angus Reid conducted a poll to determine public opinion on this issue.
The survey described in Exercise 21 also investigated the customers’ emphasis on Quality by asking them to respond to the statement, “For the same amount of money, I will generally buy one good item rather than several of lower price and quality.” Using the same definitions for Shopping
The survey described in Exercise 21 also investigated the customers’ marital status. Using the same definitions for Shopping Frequency as in that exercise, the calculations yielded the following table. Test an appropriate hypothesis for the relationship between marital status and the frequency of
A large company in New Brunswick that buys fish from local fisheries and distributes them to major companies and restaurants is considering launching a new ad campaign on the health benefits of fish. As evidence, it would like to cite the following study. Medical researchers followed 6272 Swedish
A female fashion study surveyed customers to determine characteristics of the “frequent” shoppers at different department stores. Suppose you’re a marketing manager at one of the department stores. You’d like to know if a customer’s shopping frequency and her age are related. Here are the
A sales representative who is on the road visiting clients thinks that, on average, he drives the same distance each day of the week. He keeps track of his driving distance for several weeks and discovers that he averages 122 kilometres on Mondays, 203 kilometres on Tuesdays, 176 kilometres on
Four professors teach Statistics at your university in classes of about 85 students each, and you need to choose a good one. You can check them out on Ratemyprofessors.com, but some professors don’t receive many ratings and you’d prefer a larger sample of opinions. And although your university
The IBM artificial intelligence system, Watson, achieved fame when it beat human champions at the TV trivia game Jeopardy. It works by being able to understand English text in a vast database of documents relating to a certain subject area. In the case of Jeopardy, the subject area is very broad,
Morgan Solar develops optical systems for concentrating sunlight on solar cells and sells the resulting solar systems in Southern California and other locations with intense direct sunlight. They continuously come up with new optical designs that need testing in a range of environmental conditions,
The experimental farm in Ottawa performs research on a wide range of crops including grains and oil seeds for farms across the country. About 30 million tonnes of wheat are produced each year in Canada but yields can be affected by Fusarium, a fungus. Antifungal agents can be researched by
Canola (CANada Oil Low Acid) was bred naturally at the University of Manitoba and today farms in the prairies produce about 20 million metric tonnes per year, higher than any other country in the world. The Canola Council of Canada organizes trials of new varieties of canola at multiple sites in
An airline monitors the number of seats sold in Executive class on flights from Calgary to Vancouver on weekday mornings, afternoons, and evenings, and obtains the boxplots shown below.a) What are the null and alternative hypotheses? Talk about passengers and f lights, not symbols.b) Do the
A wind farm is being proposed for the shore of Lake Superior to supply power to Thunder Bay and nearby mining operations. The farm operator is testing turbines from five different manufacturers and wants to select a single supplier for the whole wind farm. Wind conditions vary along the shore, and
Salmon farms in Atlantic Canada have a problem of sea lice that attack the fish. Three alternative pesticides have been developed to kill the lice and are being tested on three different farms. We want to select a single pesticide for use on all three farms since pesticide can be carried in the
For the following experiment, indicate whether it was single-blind, double-blind, or not blinded at all. Explain your reasoning.Does a “stop smoking” program work better if it costs more? Smokers responding to an advertisement offering to help them stop smoking were randomly offered a program
For the following observational studies, indicate whether they are prospective or retrospective.a) An airline was concerned that new security measures might discourage air travellers. A year after the new security restrictions were put into place, the airline compared the miles travelled by its
For the following observational studies, indicate whether they are prospective or retrospective.a) A company looked at a sample of returned registration cards to estimate the income level of households that purchased its product.b) A retail outlet encouraged customers to join its “frequent
The Organisation for Economic Co-operation and Development (OECD) surveyed 1000 people at random in each of its member countries in 2014 and found that the number of hours worked by Canadians was 1710 hours per year on average, whereas in the United States it was 1790. Assume that the standard
Partly as a result of a government incentive program, several businesses and residences in Ontario have installed solar panels so as to reduce their electricity bills. The amount of electricity (in kilowatthours) generated by each of these installations is recorded in a database each hour of each
Ontario is a world leader in the installation of smart electricity meters on residences. This has allowed the province to charge different rates for electricity at different times of day and has also resulted in the accumulation of a vast database of the amount of electricity (in kilowatt-hours)
The OECD conducts the Program for International Student Assessment and in 2012 tested 510,000 15-year-old high school students in 65 countries to assess their performance in math, reading, and science. We are interested in how Canada compares to Germany and Japan.a) What missing information do you
According to the OECD, life satisfaction measures how people evaluate their life as a whole rather than their current feelings. It captures a ref lective assessment of which life circumstances and conditions are important for subjective well-being. In 2014, they asked a random sample of 1000
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