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Business Statistics 3rd Canadian Edition Norean D. Sharpe, Richard D. De Veaux, Paul F. Velleman, David Wright - Solutions
In order to assist advertisers in targeting advertising to the appropriate age groups, Ipsos surveyed 9700 Canadian adults to record the amount of time they spent consuming media and obtained the following results:Assume that the number of people surveyed is proportional to the age range of each
Certain businesses and professions have reputations for being somewhat dishonest when dealing with customers. One area of concern is the honesty of auto repair shops. Many provinces require emissions checks; a vehicle that doesn’t pass the check must be repaired. In one province, the Department
The Organisation for Economic Co-operation and Development (OECD) surveyed 1000 homes at random in each of its member countries in 2014 and found that the number of rooms per person in Canadian homes was 2.5 on average, whereas in the United States it was 2.3. Assume that the standard deviation is
The managers for a sample of stores maintain that their businesses are doing better this year, despite relatively flat sales. Their argument is that they’ve been able to reduce costs through more efficient staffing and inventory management. Using the data provided in the file, determine if the
A company developing an ad campaign for its cola is investigating the impact of caffeine on studying in hopes of finding evidence of its claim that caffeine helps memory. The firm asked 30 subjects, randomly divided into two groups, to take a memory test. The subjects then each drank two cups of
Having done poorly on their final math exams in June, six students repeat the course in summer school and take another exam in August. If we consider these students to be representative of all students who might attend this summer school in other years, do these results provide evidence that the
The table on the next page gives the average high temperatures in January and July for several European cities. Find a 90% confidence interval for the mean temperature difference between summer and winter in Europe. Be sure to check conditions for inference, and clearly explain what your interval
After implementing the fitness program described in Exercise 48, another company found that a random sample of 48 employees increased their productivity score from 49 to 56 with a standard deviation of 6.2. This company believes that the fitness firm may have exaggerated the potential results of
A national fitness firm claims that a company may increase employee productivity by implementing one of the firm’s fitness programs at the job site. As evidence of this, the fitness firm reports that one company was able to increase job productivity of a random sample of 30 employees from 57 to
When we considered the Boston Marathon in Exercise 43, we were unable to check the Nearly Normal Condition. Here’s a histogram of the differences:Those three large differences are the first three years of wheelchair competition: 1977, 1978, and 1979. Often the startup years of new events are
A market analyst wants to know if the new website he designed is showing increased page views per visit. A customer is randomly sent to one of two different websites, which offer the same products but with different designs. He takes a random sample of customers from each website and records their
A philanthropic organization collects and buys data on its donor base. The full database contains about 4.5 million donors and over 400 variables collected on each, but the data set ch13_MCSP_Donor_Profiles is a sample of 916 donors and includes the following variables:• Age (in years)•
A real estate agent is trying to understand the pricing of homes in her area, a region in the United States comprising small to midsize towns and a small city. For each of 1200 homes recently sold in the region, the file ch13_MCSP_Real_Estate holds the following variables:• Sale Price (in $)•
Climate-change concerns are resulting in investment in fuels that don’t produce greenhouse gases. Although solar and wind power garner a lot of attention, nuclear power from uranium is also a possibility. China is investing in nuclear power, and even countries such as Sweden that previously
Citizens Bank of Canada operates a credit card program that supports not-forprofit initiatives aimed at effecting positive environmental and social change.The Shared Interest VISA card has no annual fee, and each time it’s used 10 cents is donated to a pool of not-for-profits.Suppose you work for
You’re on the financial planning team for monitoring a high-spending segment of a credit card. You know that customers tend to spend more during December before the holidays, but you’re not sure about the pattern of spending in the months after the holidays. Look at the data set
Rate My Professors6 records the opinions of students about their professors according to three criteria: clarity, easiness, and helpfulness. You and your friend want to choose between two professors for your Statistics class, and you see that the average ratings of these professors are as follows,
Larger homes generally fetch a higher price than smaller homes. How much can we learn about a house from the fact that it has a fireplace or more than the average number of bedrooms? Data for a random sample of 1047 homes can be found in the file ch14_MCSP_Real_Estate. There are six quantitative
Alternative sources of energy are of increasing interest throughout the energy industry. Wind energy has great potential, but appropriate sites must be found for the turbines. To select the site for an electricity-generating wind turbine, wind speeds were recorded at several potential sites every
Some sports arenas and ballparks are offering “all you can eat” sections where, for a higher ticket price, fans can feast on all the hot dogs and popcorn they want. (Alcohol and desserts are extra.) But, of course, the teams want to price those tickets appropriately. They want to design an
Some offices pipe in background music. The vendor claims this improves productivity, but might it cause more distraction? A firm’s HR department wants to learn whether productivity is affected by background music. The company hires a research firm to conduct an experiment. The researchers will
Online shopping statistics are routinely reported by www.shop.org. Of interest to many online retailers are gender-based differences in shopping preferences and behaviours. The average monthly online expenditures are reported for males and females:a) Find 95% confidence intervals for the average
Using the data in Exercise 2, test the hypothesis that the mean numbers of page views from the two websites are the same. You may assume that the number of page views from each website follows a Normal distribution.a) Calculate the P-value of the statistic, knowing that the approximation formula
The average house price in Canada in 2010 was $339,100, according to the Canadian Real Estate Association (CREA). Today, a consumer group randomly selected a sample of 54 house prices and found an average price of $418,200 with a standard deviation of $94,300. The group put out a press release
Via Rail recently installed new passing tracks and a Centralized Traffic Control system on the line between Kingston and Ottawa in order to reduce delays. Suppose that, before the improvements, trains between Kingston and Ottawa were on average 12.4 minutes late. After the improvements, a consumer
The Organisation for Economic Co-operation and Development (OECD) produces a “Better Life Index” based in part on a survey of 1000 people in each member country. They found that the number of hours worked by Canadians was 1710 hours per year on average, whereas for the average OECD country it
The Organisation for Economic Co-operation and Development (OECD) produces a “Better Life Index” based in part on a survey of 1000 homes in each member country. They found that the number of rooms per person in Canadian homes was 2.5 on average, whereas for the average OECD country it was 1.6.
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. The results are in the data file for the countries whose average score was 500 or more in
Ontario has installed a lot of wind turbines compared to other provinces, but should a landowner build some more? To produce enough energy, the site should have an annual average wind speed of at least 8 kilometres per hour. One candidate site was monitored for a year, with wind speeds recorded
Farmed salmon is much cheaper to bring to market than salmon caught in the wild, but consumers are concerned about several issues recently publicized about farmed salmon, including the type of food they are fed and the contaminants found in their meat (see www.healthcastle.com). Among the
Fancy pets are big business, so a young entrepreneur (age 12) decided to breed golden hamsters, a type well known to pet stores and collectors. (Oddly enough, nearly all the golden hamsters in captivity are descendants of one litter found in Syria in 1930.) Of 47 recent litters, there were an
A battery company claims that its batteries last an average of 100 hours under normal use. There have been several complaints that the batteries don’t last that long, so an independent testing agency is engaged to test them. For the 16 batteries the agency tested, the mean lifetime was 97 hours
The owner of the collection agency in Exercise 37 is quite certain that the agency can collect more than $200 per customer on average. He urges that the credit card company run a larger trial. Do you think a larger trial might help the company make a better decision? Explain.In Exercise 37Credit
A tire manufacturer is considering a newly designed tread pattern for its all-weather tires. Tests have indicated that these tires will provide better fuel efficiency and longer tread life. The last remaining test is for braking effectiveness. The company hopes the tire will allow a car travelling
Investment style plays a role in constructing a mutual fund. Many individual stocks can be grouped into two distinct categories: growth and value. A growth stock is one with high earning potential and often pays little or no dividends to shareholders. Conversely, value stocks are commonly viewed as
Consumer Reports tested 14 brands of vanilla yogurt and found the following numbers of calories per serving: 160, 200, 220, 230, 120, 180, 140, 130, 170, 190, 80, 120, 100, and 170.a) Check the assumptions and conditions for inference.b) Create a 95% confidence interval for the average calorie
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. The results are in the data file for the countries whose average score was 500 or more in math.
When homeowners fail to make mortgage payments, the bank forecloses and sells the home, often at a loss. In one large community, realtors randomly sampled 36 bids from potential buyers to determine the average loss in home value. The sample showed that the average loss was $11,560 with a standard
Hoping to attract more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. For a random sample of 44 weekdays, daily fees collected averaged $12,600 with a standard deviation of $1500.a) What
A sample of 20 CEOs from the Forbes 500 shows total annual compensations ranging from a minimum of $0.1 million to $62.24 million. The average for these 20 CEOs is $7.946 million. The histogram and boxplot are as follows:Based on these data, a computer program found that a 95% confidence interval
A confidence interval for the price of gasoline from a random sample of 30 gas stations in a region gives the following statistics:y̅ = $1.29 SE(y) = $0.06a) Find a 95% confidence interval for the mean price of regular gasoline in that region.b) Find the 90% confidence interval for the mean.c) If
A confidence interval for the price of gasoline from a random sample of 30 gas stations in a region gives the following statistics:y̅ = $1.49 s = $0.18a) Find a 95% confidence interval for the mean price of regular gasoline in that region.b) Find the 90% confidence interval for the mean.c) If we
Using the t tables, software, or a calculator, estimate the following:a) The critical value of t for a 95% confidence interval with df = 7.b) The critical value of t for a 99% confidence interval with df = 102.c) The P-value for t ≤ 2.19 with 41 degrees of freedom.d) The P-value for t > 2.33
Using the t tables, software, or a calculator, estimate the following:a) The critical value of t for a 90% confidence interval with df = 17.b) The critical value of t for a 98% confidence interval with df = 88.c) The P-value for t ≥ 2.09 with 4 degrees of freedom.d) The P-value for t > 1.78
The analyst in Exercise 2 wants to know if the mean purchase amount of all transactions is at least $40.a) What is the null hypothesis?b) Is the alternative one- or two-sided?c) What is the value of the test statistic?d) What is the P-value of the test statistic?e) What do you conclude at α =
The owner of the internet music site from Exercise 1 wants to know if the mean age of all customers is 25 years old.a) What is the null hypothesis?b) Is the alternative one- or two-sided?c) What is the value of the test statistic?d) What is the P-value of the test statistic?e) What do you conclude
For the data in Exercise 1:a) How many degrees of freedom does the t-statistic have?b) How many degrees of freedom would the t-statistic have if the sample size had been 100? 20 32 34 29 30 11 30 30 14 29 38 22 44 48 26 25 22 32 35 32 42 35 44 44 48
An airline marketing manager sent out 10,000 mail pieces to a random sample of customers to test a new web-based loyalty program. The customers received either nothing (No Offer), a free companion airline ticket (Free Flight), or free flight insurance on their next flight (Free Insurance). The
Ingots are huge pieces of metal, often weighing in excess of 9000 kilograms, made in a giant mould. They must be cast in one large piece for use in fabricating large structural parts for cars and planes. If they crack while being made, the crack may propagate into the zone required for the part,
According to a recent census, 29% of all families in Quebec were common-law couples. In order to test-market products to common-law couples, you need to select a city with a large percentage of this type of family. Suppose you survey 100 randomly selected families in Montreal and find that 35% of
McKinsey & Co. surveyed 12,000 Canadian households equally divided among low, middle, and high incomes as to whether they would be able to maintain their lifestyle after they stopped working, taking into account savings, pensions, and government payments. The results were that 93% of low income
Many fatal road accidents are due to preventable driver-related causes including drugs, alcohol, cell phone use, speeding, and failure to use a seatbelt or helmet. In 2014, 230 out of 265 fatal accidents were due to these driver-related causes. The deputy commissioner of the Ontario Provincial
Tangerine gives its banking customers a commission if they refer new people to open bank accounts at Tangerine. As a result, 55% of new customers at Tangerine came from referrals in 2014. Another Canadian bank had 14% referrals last year (out of a total of 65,000 new customers) and has increased
A company manufactures ceramic ball bearings, but customers complain that some of them are cracked. Some cracking is inevitable and the company accepts 0.2% cracked product. A random sample of ball bearings is collected from the manufacturing plant and tested to determine whether more than 0.2% are
A Nanos Research survey for the Globe and Mail on energy and the environment in December 2014 asked what is the most environmentally responsible way to transport oil. Of 205 Canadian adults in the age group 18–29, 50.8% answered “pipeline” as opposed to rail, road, etc. But for 178 people in
A Nanos Research survey for the Globe and Mail on energy and the environment in December 2014 asked whether Canadians believe cooperation between Canada and the United States on these issues is important. The percentages saying this is important or somewhat important were 87.3% for the 497 men
Ontario is the Canadian centre for solar panel manufacturing, with companies like Canadian Solar exporting around the world. A competing company manufactures 250 watt solar panels, but the manufacturing process does not guarantee that the panels will produce exactly 250 watts of electric power.
Angus Reid Strategies surveys Canadians as to whether they prefer an elected head of state instead of a monarch. The percentages preferring an elected head of state were 54% for men and 33% for women in a 2013 survey of 1008 Canadian adults. Test whether the percentage of men with this view was
The National Sample Survey identifies a segment of Indian households as the “Mature Middle Class” with an income of around 170,000 rupees per year. The rapid growth of the Indian economy has resulted in an increase in the proportion of households in this group, and the survey estimates that it
A random survey of 1000 Canadians aged 20–24 in 2008 found that 61.4% lived with their parents. In 2013 a similar survey found 65.3% of Canadians aged 20–24 lived with their parents. Is there a difference between the percentages of Canadians aged 20–24 living with their parents in 2008 and
A random sample of 1000 families in Alberta reported 14% single-parent families. Another random sample of 700 families in Nova Scotia reported 17% single-parent families. Is there a lower percentage of single-parent families in Alberta than in Nova Scotia at the 95% level of significance?
An Angus Reid survey of 1000 adult Canadians about reform of the Canadian Senate found that 32% of people in Ontario supported abolishing the Senate of Canada, whereas the percentage in Quebec was 43%. Do more people in Quebec support abolishing the Canadian Senate than in Ontario? (Assume that
Suppose a professional survey of 1016 Canadian adults (assume a 50/50 split between men and women) found that 65% of men and 45% of women support scrapping the nickel.a) At what level of significance can we conclude that more Canadian men than women support scrapping the nickel?b) If we wanted to
Suppose a professional survey of 1016 Canadian adults found that support for scrapping the nickel was high in British Columbia (62%) and Ontario (55%). Do these survey results lead to the conclusion that a greater percentage of British Columbian adults support scrapping the nickel than Ontarian
Suppose a professional survey of 1016 Canadian adults found that 55% were in favour of scrapping the nickel and a reporter commented, “Over half of Canadian adults want to scrap the nickel.”a) Analyze the statistical validity of this statement.b) Comment on the ethics of this statement as it
British Columbia introduced a carbon tax of $10 per tonne of carbon in 2008, rising by $5 per tonne each year until 2012. In 2011, with the tax at $25 per tonne, Environics surveyed 1025 British Columbians about the tax and found that 54% supported it. A politician claimed, “Over half of British
Molson has been in business in Canada for over two and a quarter centuries, a fact that speaks to the consistent quality of the beer. Suppose Molson’s aim is that at least 98% of customers say the taste hasn’t changed. One way to ensure consistency is to run taste tests with a random selection
In 2013, Angus Reid surveyed 1000 adult Canadians about reform of the Canadian Senate.a) 72% answered “Yes” to the question “Do you support allowing Canadians to directly elect their senators?” Does this indicate that the proportion of the adult Canadian population who would answer
During the entire history of Canada, 0.74% of the 4201 federal Members of Parliament have been Aboriginals. In 2015, 7 out of the 308 federal Members of Parliament were Aboriginal. Using the methods given in this chapter, compare these pieces of information to answer the question “Were
Aboriginals make up 3.9% of the Canadian population, and in 2015, 7 out of the 308 federal Members of Parliament were Aboriginal. Using the methods given in this chapter, compare these pieces of information to answer the question “Are Aboriginals underrepresented in Parliament?” State your
In May 2010, Public Safety Minister Vic Toews introduced a bill in Parliament proposing that sex offenders who have abused children should not be able to get a government pardon. Angus Reid conducted a survey of 1013 Canadian adults and found that 81% supported the bill.a) How sure can we be that
Angus Reid Strategies regularly surveys Canadians as to whether they prefer an elected head of state instead of a monarch. The percentage preferring an elected head of state was 43% in November 2009, 30% in July 2010, and 40% in April 2013 based on surveys of 1005 Canadian adults each year.a) Test
In 2002, the Liberal government introduced “harm reduction” programs for drug users, such as supervised injection sites and needle-exchange programs. However, a Conservative government was elected in 2006. The new government considered eliminating the harm reduction programs, and in 2007 Angus
The Liberal government that decriminalized the possession of small quantities of marijuana was replaced by a Conservative government in the 2006 federal election. The new government considered scrapping the legislation, and in 2007 Angus Reid conducted a survey of 1028 adult Canadians and found
A philanthropic organization knows that its donors have an average age near 60, and so is considering taking out an ad in the Canadian Association of Retired Persons (CARP) magazine. The head of Finance says that the CARP advertisement won’t be worth the money unless more than two-thirds of the
The data set provided contains last month’s credit card purchases of 500 customers randomly chosen from a segment of a major credit card issuer. The Marketing Department is considering a special offer for customers who spend more than $1000 per month on their card. Historically, the percentage
A nonprofit company concerned with high school dropout rates has designed a tutoring program aimed at students between 16 and 18 years of age. Nationally, the high school dropout rate for the year 2013 was 10.9%. One school district, which adopted the use of the nonprofit’s tutoring program and
The accounting department of a major Canadian university would like to advertise that more than 50% of its graduates obtained a job offer prior to graduation. A sample of 240 recent graduates indicated that 138 of these graduates had a job offer prior to graduation. Test an appropriate hypothesis
An internal report from a manufacturing company indicated that about 3% of all products were defective. Data from one batch found only 4 defective products out of 233 products. Is this consistent with the report? Test an appropriate hypothesis using a 5% significance level. Also calculate a
A company hopes to improve customer satisfaction, setting as a goal no more than 5% negative comments. A random survey of 350 customers found only 10 with complaints.a) Create a 95% confidence interval for the true level of dissatisfaction among customers.b) Does this provide evidence that the
In 2006, 34% of students had not been absent from school even once during the previous month. In a 2011 survey, responses from 8302 students showed that this figure had slipped to 33%. Officials would be concerned if student attendance were declining. Do these figures give evidence of a decrease in
In a telephone poll of 1302 randomly selected men, only 39 said that their most important measure of success was their work.a) Estimate the percentage of all males who measure success primarily by their work. Use a 98% confidence interval. Don’t forget to check the conditions first.b) Some
A newsletter reported that 90% of adults drink milk. A regional farmers’ organization planning a new marketing campaign across its multicounty area polls a random sample of 750 adults living there. In this sample, 657 people said that they drink milk. Do these responses provide strong evidence
The same Gallup Poll data from Exercise 29 also reported that 33% of those surveyed rated the economy as “Poor.” The same media outlet claimed the true proportion to be 30%. Does the Gallup Poll support this claim?a) Find a 95% confidence interval for the sample proportion of U.S. adults who
In 2008, a Gallup Poll asked 2336 U.S. adults aged 18 or over how they rated economic conditions. In a poll conducted from January 27 through February 1, 2008, 24% rated the economy as “Excellent/Good.” A recent media outlet claimed that the percentage of Americans who felt the economy was in
A young investor is concerned that investing in the stock market is actually gambling, since the chance of the stock market going up on any given day is 50%. She decides to track her favourite stock for 250 days and finds that on 140 days, the stock was “up.”a) Find a 95% confidence interval
A mutual fund manager claims that at least 70% of the stocks she selects will increase in price over the next year. We examined a sample of 200 of her selections over the past three years. Our P-value turns out to be 0.03. Test an appropriate hypothesis. Which conclusion is appropriate? Explain.a)
An information technology analyst believes that her company is losing customers on its website who find the checkout and purchase system too complicated. She adds a one-click feature to the website to make it easier, but finds that only about 10% of the customers are using it. She decides to launch
The clothing company in Exercise 19(a) looks at a sample of delivery reports. The company tests the hypothesis that 90% of the deliveries are on time against the alternative that greater than 90% are on time and finds a P-value of 0.22. Which of these conclusions is appropriate?a) There’s a 22%
In 2012, 14.8% of medium-sized businesses in Canada were foreign-controlled, according to Statistics Canada Table 1790005: “Corporations Returns Act (CRA), enterprise characteristics by country of control and operating revenue size.” These data are based on corporate tax returns and are
Last year, a luxury hotel chain operating across the Caribbean attracted 14% of Canadian snowbirds travelling to the Caribbean during February and found that 56% were “very satisfied” with their stay. This year, the chain has upgraded its properties, with the aim of achieving 70% “very
An Angus Reid survey of 1003 Canadian adults and 1980 British adults found that 59% of the Canadian sample and 56% of the British sample thought that homosexuality is something people are born with as opposed to being a preference they have chosen. Does a smaller percentage of Britons hold this
In an Angus Reid survey of opinions regarding same-sex marriage, 13% of a sample of 1003 Canadian adults said that same-sex couples should not have any legal recognition. The corresponding percentage for a survey of 1980 Britons was 15%. Does a greater percentage of Britons hold this view than
Utilities must forecast the demand for energy use far into the future, because it takes decades to plan and build new power plants. Ron Bears, who worked for a Maritime utility company, had the job of predicting the proportion of households that would choose to use electricity to heat their homes.
Suppose you’re working for Gallup Canada on a survey to estimate how many people believe that Canada should increase the amount of electric power generated by nuclear power stations. You conduct an initial survey of 250 adults, and 12.7% state that they support an increase in nuclear power. Your
In 2014, Nanos Research conducted a survey of 1000 adult Canadians to determine their favourability toward the Alberta oil sands project. The responses were “favourable,” “somewhat favourable,” “somewhat unfavourable,” “unfavourable,” and “unsure.” Grouping “favourable” and
The University of Calgary’s Hotchkiss Brain Institute has developed a new procedure for treating stroke using a retrievable stent. Initial trials indicate a positive outcome in 55% of patients compared to 30% with the previous treatment. Suppose they want to be 90% confident of a difference in
Ipsos-Reid asked 900 Canadian adults whether they approve of using illegal or unauthorized online methods to access online music. In their responses, 12% of men said they completely approve, whereas the corresponding percentage for women was 6%.a) Construct a 90% confidence interval for the
Suppose we surveyed 1006 Canadian adults and found that 41% believed that Canadian values were more right wing than 10 years previously.a) A newspaper reporting these results stated, “Canadian opinion on this issue ranges from 33% agreement for 18-to-34-year-olds to 48% agreement for those over
Suppose we surveyed 1016 Canadian adults (assume half men and half women) and found that 65% of men and 45% of women support scrapping the five-cent coin (the nickel).a) Construct a 90% confidence interval for the difference in support for scrapping the nickel between men and women.b) Construct a
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