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Business Statistics 3rd Canadian Edition Norean D. Sharpe, Richard D. De Veaux, Paul F. Velleman, David Wright - Solutions
Suppose we surveyed 1000 adult Canadians about reform of the Canadian Senate. We found that 32% of people in Ontario supported abolishing the Senate of Canada, whereas the percentage in Quebec was 43%. Construct a 90% confidence interval for the difference in support for abolishing the Senate
Research at the University of Manitoba has resulted in the development of high yielding, high protein soybeans particularly suited to the local climate. There has been rapid growth in the land area planted with these soybeans, many of which are not genetically modified (non-GMO), making them
Suppose we surveyed 1000 adult Canadians about reform of the Canadian Senate and 34% answered “Yes” to the question, “Do you support abolishing the Senate of Canada?”a) Construct a 95% confidence interval for this proportion and give a verbal explanation of what your interval means.b)
It’s not often that taxes are popular, but when Environics surveyed 1023 adult British Columbians in 2011, it found 54% in favour of the carbon tax in that province. At $25/tonne of carbon, the tax adds only 5¢ to the price of a litre of gasoline.a) Calculate a 90% confidence interval for the
Ipsos surveyed 1005 Canadian adults just after the Black Friday sale in 2014 and found that 24.7% of them had bought something during the Black Friday sales promotions.a) Calculate a 95% confidence interval for the proportion of Canadian adults buying something during the Black Friday sales
A survey of 1013 randomly selected Canadian adults asked whether they thought the government will impose a carbon tax on the oil sands in Alberta; only 12% thought that it would. Calculate a 90% confidence interval on this percentage and interpret the meaning of this interval.
Abortion is legal in Canada, but public opinion is divided on the circumstances in which it should be publicly funded. According to a survey of 1002 randomly selected Canadian adults, 43% said the healthcare system should fund abortions whenever they’re requested and 41% said the health-care
Results from a January 2008 telephone survey conducted by Gallup showed that 57% of urban Colombian adults support a free trade agreement (FTA) with the United States. Gallup used a cluster sample in which the cities of Bogotá, Cali, Barranquilla, and Medellín provided a representative sample of
ACT Inc. reported that 74% of 1644 randomly selected first-year college students returned to college the next year. Estimate the national first-year student retention rate.a) Check that the assumptions and conditions are met for inference on proportions.b) Construct a 98% confidence interval.c)
In a random survey of 226 selfemployed individuals, 20 reported having had their tax returns audited by the Canada Revenue Agency in the past year. Estimate the proportion of self-employed individuals nationwide who’ve been audited in the past year.a) Check the assumptions and conditions (to the
A real estate agent looks over the 15 listings she has in a particular postal code in Toronto and finds that 80% of them have swimming pools.a) Check the assumptions and conditions for inference on proportions.b) If it’s appropriate, find a 90% confidence interval for the proportion of houses in
A survey developed by Babson College and the Association of Women’s Business Centers (WBCs) was distributed to WBCs in the United States. Of a representative sample of 20 WBCs, 40% reported that they had received funding from the national Small Business Association (SBA).a) Check the assumptions
In 2008, a Gallup Poll asked 2335 Americans aged 18 or over how they rated economic conditions. In a poll conducted January 27–February 1, 2008, only 24% rated the economy as “Excellent/Good.” Construct a 95% confidence interval for the true proportion of Americans who rated the U.S. economy
For quality control purposes, 900 ceramic tiles were inspected to determine the proportion of defective (e.g., cracked, uneven finish) tiles. Assuming that these tiles are representative of all tiles manufactured by an Italian tile company, what can you conclude from the computer output?z-interval
A student is considering publishing a new magazine aimed directly at owners of Japanese automobiles. He wants to estimate the fraction of cars in Canada that are made in Japan. The computer output summarizes the results of a random sample of 50 autos. Explain carefully what it tells you.z-interval
Recently, two students made worldwide headlines by spinning a Belgian euro 250 times and getting 140 heads—that’s 56%. That makes the 90% confidence interval (51%, 61%). Can we draw any conclusions about Belgian euros in general from this information?
Consider each situation described below. Identify the population and the sample, explain what p and pn represent, and tell whether the methods of this chapter can be used to create a confidence interval.a) A large company with 10,000 employees at its main research site is considering moving its
A market researcher estimates that the percentage of adults between the ages of 21 and 39 who will see a particular television ad is 15%, adding that he believes his estimate has a margin of error of about 3%. Explain what the margin of error means.
A corporate executive reports the results of an employee satisfaction survey, stating that 52% of employees say they are either “satisfied” or “extremely satisfied” with their jobs. The executive then says, “The margin of error is plus or minus 4%.” Explain carefully what that means.
In a Nanos Research survey of 1000 Canadian adults about how favourable they were toward the Alberta oil sands project, 30.5% were unfavourable and 16.9% were somewhat unfavourable. Of those who were unfavourable, 72.0% agreed that the oil sands project was bad for the environment, whereas the
In a Nanos Research survey of 1000 Canadian adults about how favourable they were toward the Alberta oil sands project, 19.5% were favourable and 25.6% were somewhat favourable. Of those who were favourable, 15.4% agreed that the oil sands project creates jobs, whereas the corresponding percentage
Consider each situation described below. Identify the population and the sample, explain what p and p̂ represent, and tell whether the methods of this chapter can be used to create a confidence interval.a) A total of 240 potato plants in a field in Prince Edward Island are randomly checked, and
A sample of 200 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. The result of the survey is that 70 of the 200 students responded “yes.” You construct an approximate 95% confidence interval for the true proportion p by
MBNA Canada’s affiliates program allows other organizations to offer credit cards to their members. The Toronto Blue Jays and the Edmonton Eskimos both use MBNA’s affiliates program, as does the Canadian Automobile Association. Whenever a member of one of these organizations makes a purchase
The Economist Intelligence Unit says there were 32.5 broadband subscribers per 100 people in Canada in 2012.a) We ask 1000 randomly selected Canadian adults whether they have broadband internet access to their homes. In response, 325 of them say yes and 675 say no, so that the proportion of people
According to a survey from Statistics Canada (Table 2020107, “Earnings of Individuals, by Selected Characteristics and North American Industry Classification System (NAICS), 2011 Constant Dollars”), in 2011, the average earnings in Vancouver were $42,800 in Educational Services and $78,600 in
According to a survey from Statistics Canada (Table 2020107, “Earnings of Individuals, by Selected Characteristics and North American Industry Classification System (NAICS), 2011 Constant Dollars”), in 2011, the average earnings in manufacturing in Alberta were $66,700 and in Ontario were
According to the Canadian Census, the proportion of families with three or more children (aged less than 25) declined from 42% in 1961 to 19% in 2011. Suppose we estimate that this proportion is 17.5% this year. In order to market products to large families, we randomly select 1600 Canadian
On World Hepatitis Day, July 28, 2014, the BC Centre for Disease Control stated that 3% of British Columbians (about 130,000 people) were infected with hepatitis C. Although there is no vaccination against hepatitis C, it can be cured with a daily combination pill that cures 95% of patients.a) In a
Using the data in Exercises 54 and 55, what is the probability that a random sample of 1500 families from Nova Scotia contains more loneparent families than a random sample of 1500 families from Alberta?In Exercise 54In Exercise 55 Couple Families Lone-Parent Families Number of families 219,030
Statistics Canada divides families into two groups: couple families and lone-parent families. According to Statistics Canada’s Table 1110009 “Family Characteristics, Summary,” in 2012 in Alberta, the data were as follows:A surveyor calls 2000 families in Alberta at random in order to market
Statistics Canada divides families into two groups: couple families and lone-parent families. According to Statistics Canada’s Table 1110009 “Family Characteristics, Summary,” in 2012 in Nova Scotia, the data were as follows:A surveyor calls 1000 families in Nova Scotia at random in order to
When the British Columbia government introduced a carbon tax in 2008, it didn’t want to lose votes, as might easily happen with a new tax. It therefore guaranteed that revenue from the carbon tax would be channelled back into reducing income taxes. In 2011 Environics asked 1023 British Columbians
CREA puts the average price at which a house was sold in Canada in 2014 at $415,100. Let’s assume that the standard deviation of the house prices is $134,216. Suppose you’d done a survey of a random selection of 36 house sale prices in 2014 and obtained an average house price of $368,533.
The Economist Intelligence Unit says there were 132.6 computers per 100 people in Canada in 2012. We ask 1000 randomly selected Canadian adults how many computers they have; 100 of them say none; 500 of them say one; 200 of them say two, and 100 say three.a) Calculate the mean number of computers
Although most of us buy milk by the litre, quart, or gallon, farmers measure daily production in pounds. Ayrshire cows average 47 pounds of milk a day, with a standard deviation of 6 pounds. For Jersey cows, the mean daily production is 43 pounds, with a standard deviation of 5 pounds. Assume that
The weight of cement in a medium-size bag is stated to be 10 kilograms. The amount that the packaging machine puts in these bags is believed to have a Normal model with a mean of 10.2 kilograms and a standard deviation of 0.12 kilograms.a) What fraction of all bags sold are underweight?b) Some of
Grocery store receipts show that customer purchases have a skewed distribution with a mean of $32 and a standard deviation of $20.a) Explain why you cannot determine the probability that the next customer will spend at least $40.b) Can you estimate the probability that the next 10 customers will
Young cod are transferred from a hatchery to sea cages, and it then takes an average of 26 months for cod to reach market size, with a standard deviation of one month. The average weight of market-size cod is 3.75 kilograms with a standard deviation of 0.38 kilograms, and we’ll assume that it’s
Suppose that, according to a recent census, the income per capita measured in U.S. dollars was $41,287 in Canada and $43,298 in Norway. Let’s assume that income per capita is Normally distributed with a standard deviation equal to 31% of the mean for each country. You select a random sample of
Intact is the leading property and casualty (P&C) insurer in Canada and claimed 17% of the market in its “Quick Facts” report for 3Q14. The top five P&C insurers have 38% of the market. Suppose you work for a P&C insurer not currently in the top five, and you’d like to arrange
Suppose that, according to a recent census, 29% of all families in the province of Quebec are common-law couples. You survey 100 families in the city of Montreal in order to assess the purchasing preferences of common-law couples.a) What is the probability that the percentage of commonlaw couples
In 1150, it was recognized in England that coins should have a standard weight of precious metal as the basis for their value. A guinea, for example, was supposed to contain 128 grains of gold. (There are 360 grains in an ounce.) In the “trial of the pyx,” coins minted under contract to the
Many variables important to the real estate market are skewed, limited to only a few values or considered as categorical variables. Yet marketing and business decisions are often made based on means and proportions calculated over many homes. One reason these statistics are useful is the Central
When a very large star reaches the end of its life it explodes, causing a supernova, a very intense burst of radiation that is sufficient to destroy almost all life on planets of nearby stars. Some simple organisms may remain, but all animals and plants are destroyed and evolution has to start
Maria is starting a career as a professional wildlife photographer and plans to photograph Canada geese at one of their staging grounds during their migration in northeastern Manitoba. She booked a place in a hide at the edge of a lake and plans to photograph the geese as they land on the water.
Statistics Canada provides data on the number of reportable transport accidents involving dangerous goods. The probability that reportable transport accidents involving dangerous goods in Canada occur on the roads (as opposed to other forms of transport) is 0.295.a) Out of 10 reportable transport
A sales manager for a major pharmaceutical company analyzes last year’s sales data for 96 sales representatives, grouping them by region (1 = East Coast U.S.; 2 = Midwest U.S.; 3 = West U.S.; 4 = South U.S.; 5 = Canada; 6 = Rest of World). She plots Sales (in $1000) against Region (1–6) and
Mining companies purchase large and specialized equipment. The company specifies the features required for the product in a request for quotations (RFQ) and suppliers submit bids. Because of the complex nature of the equipment, an RFQ and each individual bid can run into hundreds of pages of
When a volcano erupts, it sends ash into the upper atmosphere, partially blocking out the sun, and thus reducing the amount of electric power generated by solar panels. During the 35- year period 1980–2015, there were four volcanic eruptions sufficiently powerful to reduce the amount of power
The elevator market is dominated by four suppliers: Otis of the United States, Kone of Finland, Thyssen-Krupp of Germany, and Schindler of Switzerland. Elevators are installed in buildings of a range of heights and incorporate a range of features, resulting in a range of prices from $50,000 to
North Korea conducted nuclear tests in 2009 and 2013, and South Korea’s defence ministry estimated their power at between 2 and 6 kilotonnes of TNT in 2009 and between 6 and 7 kilotonnes of TNT in 2013. “The power of North Korea’s nuclear tests increased between 2009 and 2013,” stated a
Canada extracts water from the Niagara River upstream of Niagara Falls and uses it to generate hydroelectric power at two generating stations downstream. Until 2013, water was taken to the generating stations in a tunnel and a canal, which were used to capacity 65% of the time. In 2006 work got
A survey of another area of Baffin Bay indicates that drilling will be successful with a probability of 0.4. Drilling a single well costs $0.65 billion and brings in a revenue of $2.2 billion. If the first well is successful, the chance of a second well being successful is increased from 0.4 to
Baffin Bay, located between Canada and Greenland, is being explored for oil and natural gas. First an energy company conducts a geological survey, and if the data look promising it starts drilling. A recent survey of one area cost $65 million and indicates that drilling will be successful with a
Since 1961, NRCan researchers have been visiting the Devon Island icecap in Nunavut to monitor the effects of global warming. They’ve found that the thickness of the ice has decreased by about five metres. Now they don’t have to travel to the icecap as frequently, since they also have available
During the entire history of Canada, 0.74% of the 4201 federal Members of Parliament have been Aboriginals. In 2014, 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 2014, 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 under-represented in Parliament?” State your
In July, on average, Ottawa has 4.2 thunderstorms. What is the probability that next Julya) Ottawa will have six thunderstorms?b) Ottawa will have fewer than four thunderstorms?c) State your assumptions clearly.
Bombardier designs and manufactures trains and planes and relies on large deals from its customers for these high-cost products. This series of large contracts makes for a very variable revenue stream compared with the more even income it derives from longterm service contracts. Nina Gupta, an
During May, young moose, unfamiliar with roads and traffic, are wandering around at night in Newfoundland, causing risk of road accidents. Suppose that in 2016 the average number of road accidents involving moose was 4.1 per day during May. The government increased the number of hunting licences
The website manager in Exercise 82 wants to model the time between purchases. Recall that the mean number of purchases in the evening is three per minute.a) What model would you use to model the time between events?b) What is the mean time between purchases?c) What is the probability that the time
Statistics Canada provides data on the number of reportable transport accidents involving dangerous goods. In a recent year the average rate of occurrence of such accidents was 8.15 per week.a) What probability distribution is appropriate for modelling the number of these accidents per week? State
Statistics Canada provides data on the number of cases in adult criminal court by type of crime. In a recent year the average number of homicide cases was 6.83 per month.a) What probability distribution is appropriate for modelling the number of cases per month? State your assumptions clearly.b)
For mutual funds with Normally distributed returns with a mean of 6.2% and a standard deviation of 1.8%, what are the cutoff values for thea) Highest 10% of these funds?b) Lowest 20%?c) Middle 40%?d) Highest 80%?
The bloodmobile in Exercise 64 received 300 donations in one day.a) Assuming that the frequency of AB blood is 4%, determine the mean and standard deviation of the number of donors who are AB.b) Justify why you can use a Normal model to approximate the distribution of Type AB blood.c) How likely
Suppose Serena continues to make 67% of her first serves, as in Exercise 61, and serves 80 times in a match.a) What are the mean and standard deviation of the number of good first serves expected?b) Justify why you can use a Normal model to approximate the distribution of the number of good first
Only 4% of people have Type AB blood. A bloodmobile has 12 vials of blood on a rack. If the distribution of blood types at this location is consistent with the general population, what’s the probability that Canadian Blood Services finds AB blood ina) None of the 12 samples?b) At least two
Based on the 74% national retention rate described in Exercise 25, does a college where 522 of the 603 freshman returned the next year as sophomores have a right to brag that it has an unusually high retention rate? Explain.
Best known for its testing program, ACT Inc. also compiles data on a variety of issues in education. In 2004 the company reported that the national college freshman-to-sophomore retention rate held steady at 74% over the previous four years. Consider colleges with freshman classes of 400 students.
When it sends out its fundraising letter, a philanthropic organization typically gets a return from about 5% of the people on its mailing list. To see what the response rate might be for future appeals, it did a simulation using samples of size 20, 50, 100, and 200. For each sample size, it
A tourist agency wants to know what proportion of visitors to the Eiffel Tower are from Asia. To find out, the agency surveys 100 people in the line to purchase tickets to the top of the tower one Sunday afternoon in May. Are all the assumptions and conditions for finding the sampling distribution
The proportion of adult women in Canada is approximately 51%. A marketing survey telephones 400 people at random.a) What proportion of women in the sample of 400 would you expect to see?b) How many women, on average, would you expect to find in a sample of that size?
The CAPE10 index is based on the price/earnings (P/E) ratios of stocks. We can examine the P/E ratios without applying the smoothing techniques used to find the CAPE10. The file CAPE10 holds the data, giving dates, CAPE10 values, and P/E values.Examine the P/E value. Would you judge that a Normal
Serena Williams made a successful first serve 67% of the time in a Wimbledon finals match against her sister, Venus. If she continues to serve at the same rate the next time they play and serves six times in the first game, determine the following probabilities. (Assume that each serve is
Cellophane that’s going to be formed into bags for items such as dried beans or bird seed is passed over a light sensor to test if the alignment is correct before it passes through the heating units that seal the edges. Small adjustments can be made by the machine automatically. But if the
University students are a major target for advertisements for credit cards. At a university, 65% of students surveyed said they had opened a new credit card account within the past year. If that percentage is accurate, how many students would you expect to survey before finding one who had not
Researchers testing a new medication find that 7% of users have side effects. To how many patients would a doctor expect to prescribe the medication before finding the first one who has side effects?
A real estate broker purchased three two-bedroom houses in a depressed market for a combined cost of $71,000. He expects the cleaning and repair costs on each house to average $3700, with a standard deviation of $1450. When he sells them, after subtracting taxes and other closing costs, he expects
An insurance company estimates that it should make an annual profit of $150 on each homeowner’s policy written, with a standard deviation of $6000.a) Why is the standard deviation so large?b) If the company writes only two of these policies, what are the mean and standard deviation of the annual
A small engine shop receives an average of 1.7 repair calls per hour, with a standard deviation of 0.6. What is the mean and standard deviation of the number of calls it receives for an eight-hour day? What, if anything, did you assume?
The computer help desk is staffed by students during the 7 p.m. to 11 p.m. shift. Let Y denote the random variable that represents the number of students seeking help during the 15-minute time slot 10 p.m. to 10:15 p.m.a) What are the possible values of Y?b) Is the random variable discrete or
Through the career services office, you have arranged preliminary interviews at four companies for summer jobs. Each company will either ask you to come to its site for a follow-up interview or not. Let X be the random variable equal to the total number of followup interviews you might have.a) List
You’ve just launched the website for your company that sells nutritional products online. Suppose X = the number of different pages that a customer hits during a visit to the website.a) Assuming that there are n different pages in total on your website, what are the possible values that this
A warehouse is lit by 1000 f luorescent tubes, each of which fails, on average, after 4250 hours of operation. It’s costly to send a technician to replace an individual tube when it fails, so the warehouse manager decides to replace all the tubes after 3000 hours of operation, whether they have
A manufacturer of a robot used on production lines for car manufacturing tests the accuracy of the robot operation and finds that, on average, the accuracy becomes unacceptable after 5850 hours of operation. The manufacturer specifies that the robot must be serviced to maintain its accuracy after
Speeds of cars were measured as they passed one point on a road to study whether traffic speed controls were needed. Here’s a histogram and normal probability plot of the measured speeds. Is a Normal model appropriate for these data? Explain. 20 32 15 28 24 10 20 + 15.0 22.5 30.0 -1.25 1.25
After examining a child at his two-year checkup, the boy’s pediatrician said that the z-score for his height relative to Canadian two-year-olds is -1.88. Write a sentence to explain to the parents what that means.
Your company’s Human Resources department administers a test of “executive aptitude.” It reports test grades as z-scores, and you got a score of 2.20. What does this mean?
Is a continuous Uniform distribution appropriate for the following situations? If so, state which variable is uniformly distributed.a) Subway trains depart every five minutes. You have just arrived on the platform to catch a train.b) The last four digits of your new phone number will be assigned at
Is a continuous Uniform distribution appropriate for the following situations? If so, state which variable is uniformly distributed.a) A manufacturer of cells for solar modules ordered some germanium, an essential element in one of the layers on the solar cell. The supplier said, “It will be
The 2000 Census showed that 26% of all firms in the United States are owned by women. You’re phoning local businesses, assuming that the national percentage is true in your area. You wonder how many calls you’ll have to make before you find one owned by a woman. What probability model should
As in Exercise 15, you’re phoning local businesses. You call three firms. What is the probability that all three are owned by women?In Exercise 15The 2000 Census showed that 26% of all firms in the United States are owned by women. You’re phoning local businesses, assuming that the national
At many airports, travellers entering a country are sent randomly to one of several stations where passports and visas are checked. If each of the six stations is equally likely, can the probabilities of which station a traveller will be sent to be modelled with a Uniform model?
Canada’s annual exports to India are $2.8 billion on average with a standard deviation of $0.35 billion. Canada’s annual imports from India are $3.1 billion on average with a standard deviation of $0.25 billion. Calculate the mean and standard deviation of Canada’s balance of trade with India
Find the standard deviation of the day trader’s option value in Exercise 4.In Exercise 4A day trader buys an option on a stock that will return $100 profit if the stock goes up today and lose $400 if it goes down. If the trader thinks there’s a 75% chance that the stock will go up
Find the standard deviation of the book purchases in Exercise 3. In Exercise 3Suppose that the probabilities of a customer purchasing zero, one, or two books at a bookstore are 0.2, 0.4, and 0.4, respectively. What is the expected number of books a customer will purchase?
Suppose that the probabilities of a customer purchasing zero, one, or two books at a bookstore are 0.2, 0.4, and 0.4, respectively. What is the expected number of books a customer will purchase?
The database also, of course, includes each employee’s compensation.a) Is this variable discrete or continuous?b) What are the possible values it can take on?
A company’s employee database includes data on whether the employee has a dependent child in his or her health insurance.a) Is this variable discrete or continuous?b) What are the possible values it can take on?
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