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Business Statistics 3rd Edition Norean Sharpe, Richard Veaux, Paul Velleman - Solutions

Occasionally, when I fill my car with gas, I figure out how many miles per gallon my car got. I wrote down those results after six fill-ups in the past few months. Overall, it appears my car gets 28.8 miles per gallon. a) What statistic have I calculated? b) What is the parameter I’m trying to
Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments on about 120 orders each day. The next day, the supervisor rechecks 10 of the transactions to be sure they were processed
A manufacturing company employs 14 project managers, 48 foremen, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a simple random sample of employees every month.a) Do you see any danger
Sammy’s Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number. To help maintain consistency, at the end of each day, Sammy selects three bottles of salsa, weighs the contents, and tastes the
Concerned about reports of discolored scales on fish caught downstream from a newly sited chemical plant, scientists set up a field station in a shoreline public park. For one week they asked fishermen there to bring any fish they caught to the field station for a brief inspection. At the end of
Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know what percentage of local doctors accept Medicaid patients. We call the offices of 50 doctors randomly selected from local Yellow Pages listings. b) We want to know what
As discussed in the chapter, GfK Roper Consulting con-ducts a global consumer survey to help multinational companies understand different consumer attitudes throughout the world. In India, the researchers interviewed 1000 people aged 13-65 (www.gfkamerica.com). Their sample is designed so that they
Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know if business leaders in the community support the development of an “incubator” site at a vacant lot on the edge of town. We spend a day phoning local businesses in the phone
For their class project, a group of Business students decides to survey the student body to assess opinions about a proposed new student coffee shop to judge how successful it might be. Their sample of 200 contained 50 first-year students, 50 sophomores, 50 juniors, and 50 seniors. a) Do you think
A business magazine mailed a questionnaire to the human resources directors of all Fortune 500 companies, and received responses from 23% of them. Those responding reported that they did not find that such surveys intruded significantly on their workday. a) The population b) The population
An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via “smart phones” so they want to estimate the proportion of users who access the site that way (even if they also use their computers
For each situation below identify the population and the sample and explain what p and p represent and what the value of p is. Would you trust a confidence interval for the true proportion based on these data? Explain briefly why or why not. a) A marketing analyst conducts a large survey of her
A survey 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.” a) What is the value of the sample proportion p? b) What is the standard error of the
From a survey of 250 coworkers you find that 155 would like the company to provide on-site day care. a) What is the value of the sample proportion p? b) What is the standard error of the sample proportion? c) Construct an approximate 95% confidence interval for the true proportion p by taking ± 2
From a survey of coworkers you find that 48% of 200 have already received this year’s flu vaccine. An approximate 95% confidence interval is (0.409, 0.551). Which of the following are true? If not, explain briefly. a) 95% of the coworkers fall in the interval (0.409, 0.551). b) We are 95%
From the survey in Exercise 11, which of the following are true? If they are not true, explain briefly why not. a) 95% of the 200 students are in the interval (0.283, 0.417). b) The true proportion of students who use laptops to take notes is captured in the interval (0.283, 0.417) with probability
From the survey in Exercise 11, a) How would the confidence interval change if the confidence level had been 90% instead of 95%? b) How would the confidence interval change if the sample size had been 300 instead of 200? (Assume the same sample proportion.) c) How would the confidence interval
As in Exercise 13, from a survey of coworkers you find that 48% of 200 have already received this year’s flu vaccine. An approximate 95% confidence interval is (0.409, 0.551). a) How would the confidence interval change if the sample size had been 800 instead of 200? b) How would the confidence
Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. You have no preconceived idea of what that proportion might be. a) What sample size is needed if you wish confident that your estimate is within 0.02 proportion? b) What sample size is
As in Exercise 17, you want to estimate the proportion of traditional college students on your campus who own their own car. However, from some research on other college campuses, you believe the proportion will be near 20%. a) What sample size is needed if you wish to be 95% confident that your
It’s believed that as many as 25% of adults over age 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. a) How many of this younger age group must we survey in order to estimate the proportion of nongrads to within 6% with 90%
The proportion of adult women in the United States 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?
In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days. a) How many randomly selected employers must we contact in order to create an estimate in which we are 98% confident with a margin of error of 5 % ? b)
The philanthropic organization in Exercise 21 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 21 you looked at the histograms showing distributions of sample proportions from 1000 simulated mailings for samples of size 20, 50, 100,
The automatic character recognition device discussed in Exercise 22 successfully reads about 85% of handwritten credit card applications. In Exercise 22 you looked at the histograms showing distributions of sample proportions from 1000 simulated samples of size 20, 50, 75, and 100. The sample
In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of “successes.” As a lesson, the professor has
Manufacturing companies strive to maintain production consistency, but it is often difficult for outsiders to tell whether they have succeeded. Sometimes, however, we can find a simple example. The candy company that makes M&M’s candies claims that 10% of the candies it produces are green and
The class in Exercise 25 expands its stock-picking experiment. a) The students use computer-generated random numbers to choose 25 stocks each. Use the 68-95-99.7 Rule to describe the sampling distribution model. b) Confirm that you can use a Normal model here. c) They increase the number of stocks
Would a bigger sample help us to assess manufacturing consistency? Suppose instead of the 50-candy bags of Exercise 26, we work with bags that contain 200 M&M’s each. Again we calculate the proportion of green candies found.a) Explain why it’s appropriate to use a Normal model to describe
One student in the class of Exercise 25 claims to have found a winning strategy. He watches a cable news show about investing and during the show throws his darts at the pages of the Journal. He claims that of 200 stocks picked in this manner, 58% were winners.a) What do you think of his claim?
The investment website of Exercise 1 draws a random sample of 200 investors from their customers. Suppose that the true proportion of smart phone users is 36%. a) What would the standard deviation of the sampling distribution of the proportion of smart phone users be? b) What is the probability
In a really large bag of M&M’s, we found 12% of 500 candies were green. Is this evidence that the manufacturing process is out of control and has made too many greens? Explain.
State police believe that 70% of the drivers traveling on a major interstate highway exceed the speed limit. They plan to set up a radar trap and check the speeds of 80 cars.a) Using the 68-95-99.7 Rule, draw and label the distribution of the proportion of these cars the police will observe
The most recent public health statistics available indicate that 19.0% of American adults smoke cigarettes. Using the 68-95-99.7 Rule, describe the sampling distribution model for the proportion of smokers among a randomly selected group of 50 adults. Be sure to discuss your assumptions and
It is generally believed that nearsightedness affects about 12% of all children. A school district has registered 170 incoming kindergarten children.a) Can you use the Normal Model to describe the sampling distribution model for the sample proportion of children who are nearsighted? Check the
In early 2013 Realty Trac reported that foreclosures had settled down to 1 in 859 homes per month for a rate of 0.116%, far below the 1.6% seen during the financial crisis of 2007-2008. Suppose a large bank holds 9455 of these mortgages.a) Can you use the Normal model to describe the sampling
Based on past experience, a bank believes that 7% of the people who receive loans will not make payments on time. The bank has recently approved 200 loans.a) What are the mean and standard deviation of the proportion of clients in this group who may not make timely payments?b) What assumptions
The campus representative for Lens.com wants to know what percentage of students at a university currently wear contact lens. Suppose the true proportion is 30%.a) We randomly pick 100 students. Let p represent the proportion of students in this sample who wear contacts. What’s the appropriate
Best known for its testing program, ACT, Inc., also compiles data on a variety of issues in education. In 2012 the company reported that the national college freshman-to-sophomore retention rate at four-year colleges was about 80.0%. Consider colleges with freshman classes of 400 students. Use the
A national study found that 44% of college students engage in binge drinking (5 drinks at a sitting for men, 4 for women). Use the 68-95-99.7 Rule to describe the sampling distribution model for the proportion of students in a randomly selected group of 200 college students who engage in binge
Based on the 80% national retention rate described in Exercise 37, does a college where 551 of the 603 freshmen returned the next year as sophomores have a right to brag that it has an unusually high retention rate? Explain.
The proportion of adult women in the United States is approximately 51 %. A marketing survey telephones 400 people at random. a) What is the sampling distribution of the observed proportion that are women? b) What is the standard deviation of that proportion? c) Would you be surprised to find 5 3 %
After hearing of the national result that 44% of students engage in binge drinking (5 drinks at a sitting for men, 4 for women), a professor surveyed a random sample of 244 students at his college and found that 96 of them admitted to binge drinking in the past week. Should he be surprised at this
Just before a referendum on a school budget, a local newspaper polls 400 voters in an attempt to predict whether the budget will pass. Suppose that the budget actually has the support of 52% of the voters. What’s the probability the newspaper’s sample will lead them to predict defeat? Be sure
Information on a packet of seeds claims that the germination rate is 92 %. What’s the probability that more than 95% of the 160 seeds in the packet will germinate? Be sure to discuss your assumptions and check the conditions that support your model.
When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truck- load will be rejected if more than 5% of the sample is unsatisfactory. Suppose that in fact 8% of the apples on the truck do not
It’s believed that 4% of children have a gene that may be linked to juvenile diabetes. Researchers hoping to track 20 of these children for several years test 732 newborns for the presence of this gene. What’s the probability that they find enough subjects for their study?
A catalog sales company promises to deliver orders placed on the Internet within 3 days. Follow-up calls to a few randomly selected customers show that a 95% confidence interval for the proportion of all orders that arrive on time is 88% ± 6%. What does this mean? Are the conclusions in parts a-e
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%). What does this mean? Are the conclusions in parts a-e correct? Explain your answers. a) Between 51% and 61% of all euros are
Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true?a) For a given sample size, higher confidence means a smaller margin of error.b) For a specified confidence level,
Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true?a) For a given sample size, reducing the margin of error will mean lower confidence.b) For a certain confidence level,
A real estate agent wants to know how many owners of homes worth over $1,000,000 might be considering putting their home on the market in the next 12 months. He surveys 40 of them and finds that 10 of them are considering such a move. Are all the assumptions and conditions for finding the sampling
A small company involved in e-commerce is interested in statistics concerning the use of e-mail. A poll found that 38% of a random sample of 1012 adults, who use a computer at their home, work, or school, said that they do not send or receive e-mail. a) Find the margin of error for this poll if we
A biotechnology firm in Boston is planning its investment strategy for future products and research labs. A poll found that only 8% of a random sample of 1012 U.S. adults approved of attempts to clone a human.a) Find the margin of error for this poll if we want 95% confidence in our estimate of the
An insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them.a) Create a 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.b) Explain what your interval means.c) Explain what
Direct mail advertisers send solicitations (“junk mail”) to thousands of potential customers in the hope that some will buy the company’s product. The response rate is usually quite low. Suppose a company wants to test the response to a new flyer and sends it to 1000 people randomly selected
Some food retailers propose subjecting food to a low level of radiation in order to improve safety, but sale of such “irradiated” food is opposed by many people. Suppose a grocer wants to find out what his customers think. He has cashiers distribute surveys at checkout and ask customers to fill
The mayor of a small city has suggested that the state locate a new prison there, arguing that the construction project and resulting jobs will be good for the local economy. A total of 183 residents show up for a public hearing on the proposal, and a show of hands finds 31 in favor of the prison
In a survey on downloading music, the Gallup Poll asked 703 Internet users if they “ever downloaded music from an Internet site that was not authorized by a record company, or not,” and 18% responded “yes.” Construct a 95% confidence interval for the true proportion of Internet users who
During the week of April 15, 2013, a Gallup Poll asked 1500 U.S. adults, aged 18 or over, how they rated economic conditions. Only 17% rated the economy as Excellent/Good. Construct a 95% confidence interval for the true proportion of Americans who rated the U.S. economy as Excellent/Good.
In Canada, the vast majority (90%) of companies in the chemical industry are ISO 14001 certified. The ISO 14001 is an international standard for environmental management systems. An environ-mental group wished to estimate the percentage of U.S. chemical companies that are ISO 14001 certified. Of
GfK Roper surveyed people worldwide asking them “how important is acquiring wealth to you.” Of 1535 respondents in India, 1168 said that it was of more than average importance. In the United States of 1317 respondents, 596 said it was of more than average importance. a) What proportion thought
In a survey on corporate ethics, a poll split a sample at random, asking 538 faculty and corporate recruiters the question: “Generally speaking, do you believe that MBAs are more or less aware of ethical issues in business today than five years ago?” The other half were asked: “Generally
In 2012, Gallup published a report entitled “Qatar’s Rising Entrepreneurial Spirit” in which they concluded that the 33% of 1057 Qatari youth they surveyed who responded that they plan to start their own business was the highest in the region. They conducted a variety of face to face and
A pharmaceutical company is considering investing in a “new and improved” vitamin D supplement for children. Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls upon the skin, is essential for strong, healthy bones. The bone disease rickets was largely
A real estate agent looks over the 15 listings she has in a particular zip code in California 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
A paralegal at the Vermont State Attorney General’s office wants to know how many companies in Vermont provide health insurance benefits to all employees. She chooses 12 companies at random and finds that all 12 offer benefits. a) Check the assumptions and conditions for inference on
A telemarketer at a credit card company is instructed to ask the next 18 customers that call into the 800 number whether they are aware of the new Platinum card that the company is offering. Of the 18, 17 said they were aware of the program. a) Check the assumptions and conditions for inference on
In a random survey of 226 self-employed individuals, 20 reported having had their tax returns audited by the IRS in the past year. Estimate the proportion of self- employed individuals nationwide who’ve been audited by the IRS in the past year. a) Check the assumptions and conditions (to the
A Gallup Poll (Exercise 57) asked Americans if the fact that they can make copies of songs on the Internet for free made them more likely or less likely to buy a performer’s CD. Only 13% responded that it made them “less likely.” The poll was based on a random sample of 703 Internet users. a)
A recent poll of 1005 U.S. adults split the sample into four age groups: ages 18-29, 30-49, 50-64, and 65+. In the youngest age group, 62% said that they thought the U.S. was ready for a woman president, as opposed to 35% who said “no, the country was not ready” (3% were undecided). The sample
A marketing researcher for a phone company surveys 100 people and finds that that proportion of clients who are likely to switch providers when their contract expires is 0.15. a) What is the standard deviation of the sampling distribution of the proportion? b) If she wants to reduce the standard
A random sample of 168 students was asked how many songs were in their digital music library and what fraction of them was legally purchased. Overall, they reported having a total of 117,079 songs, of which 23.1% were legal. The music industry would like a good estimate of the proportion of songs
A company manufacturing CDs is working on a new technology. A random sample of 703 Internet users were asked: “As you may know, some CDs are being manufactured so that you can only make one copy of the CD after you purchase it. Would you buy a CD with this technology, or would you refuse to buy
The research group that conducted the survey in Exercise 70 wants to provide the music industry with definitive information, but they believe that they could use a smaller sample next time. If the group is willing to have twice as big a margin of error, how many songs must be included?
As in Exercise 19, we hope to estimate the percentage of adults aged 25 to 30 who never graduated from high school. What sample size would allow us to increase our confidence level to 95% while reducing the margin of error to only 2 % ?
Editors of the business report in Exercise 20 are willing to accept a margin of error of 4% but want 99% confidence. How many randomly selected employers will they need to contact?
A state’s environmental agency worries that a large percentage of cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate that percentage with a margin of error of 3% and 90% confidence. To gauge the size of the problem, the agency
During routine conversations, the CEO of a new start-up reports that 22% of adults between the ages of 21 and 39 will purchase her new product. Hearing this, some investors decide to conduct a large-scale study, hoping to estimate the proportion to within 4% with 98% confidence. How many randomly
A newspaper reports that the governor’s approval rating stands at 65%. The article adds that the poll is based on a random sample of 972 adults and has a margin of error of 2.5%. What level of confidence did the pollsters use?
The Board of Directors of a publicly traded company says that a proposed amendment to their bylaws is likely to win approval in the upcoming election because a poll of 1505 stock owners indicated that 52% would vote in favor. The Board goes on to say that the margin of error for this poll was 3
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. From these data construct a 95%
A market researcher for a provider of iPod accessories wants to know the proportion of customers who own cars to assess the market for a new iPod car charger. A survey of 500 customers indicates that 76% own cars.a) What is the standard deviation of the sampling distribution of the proportion?b)
A philanthropic organization knows that its donors have an average age near 60 and is considering taking out an ad in the American Association of Retired People (AARP) magazine. An analyst wonders what proportion of their donors are actually 50 years old or older. He takes a random sample of the
For each situation below identify the population and the sample and identify p and p if appropriate and what the value of p is. Would you trust a confidence interval for the true proportion based on these data? Explain briefly why or why not. a) As concertgoers enter a stadium, a security guard
For each of the following situations, write the null and alternative hypotheses in terms of parameter values. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up days. H0:p = 0.5 vs. HA :p ≠ 0.5. a) A casino wants to know if their
A new drug can be an expensive process, resulting in high costs to patients. A pharmaceutical company has developed a new drug to reduce cholesterol, and it will conduct a clinical trial to compare the effectiveness to the most widely used current treatment. The results will be analyzed using a
Write the null and alternative hypotheses to test each of the following situations. a) An online clothing company is concerned about the timeliness of their deliveries. The VP of Operations and Marketing recently stated that she wanted the percentage of products delivered on time to be greater than
Write the null and alternative hypotheses to test each of the following situations. a) A 2010 Harvard Business Review article looked at 1109 CEOs from global companies and found that 32% had MBAs. Has the percentage changed? b) Recently, 20% of cars of a certain model have needed costly
Have harsher penalties and ad campaigns increased seat-belt use among drivers and passengers? Observations of commuter traffic have failed to find evidence of a significant change compared with three years ago. Explain what the study’s P-value of 0.17 means in this context.
A company developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner. The company made this decision based on a P-value of 0.03. Explain the meaning of the P-value in this context.
A pharmaceutical company’s old antacid formula provided relief for 70% of the people who used it. The company tests a new formula to see if it is better and gets a P-value of 0.27. Is it reasonable to conclude that the new formula and the old one are equally effective? Explain.
As in Exercise 1, for each of the following situations, write the null and alternative hypotheses in terms of parameter values. a) A recent UMass-Amherst study found that seat-belt compliance in Massachusetts was 73% in 2011. The state wants to know if it has changed. b) Last year, a survey found
A German automobile company is counting on selling more cars to the younger market segment drivers under the age of 20. The company’s market researchers survey to investigate whether or not the proportion of today’s high school seniors who own their own cars is higher than it was a decade ago.
A candy company claims that in a large bag of holiday M&M’s® half the candies are red and half the candies are green. You pick candies at random from a bag and discover that of the first 20 you eat, 12 are red.a) If it were true that half are red and half are green, what is the probability
A retail company offers a “scratch off” pro-motion. Upon entering the store, you are given a card. When you pay, you may scratch off the coating. The company advertises that half the cards are winners and have immediate cash-back savings of $5 (the others offer $1 off any future purchase of
Gallup reported in 2012 that 53% of American investors are likely to say the price of energy (including gas and oil) is hurting the U.S. investment climate “a lot,” according to a Wells Fargo/Gallup Investor and Retirement Optimism Index survey. The survey results are based on questions asked
Gallup tracks daily the percentage of Americans who approve or disapprove of the job Barack Obama is doing as President. Daily results are based on telephone interviews with approximately 1500 national adults. The Gallup Poll conducted April 29-May 1, 2013, reported that 50% of adults approve of
Since many people have trouble using all of the features on their smart phones, an executive training company has developed what it hopes will be easier instructions. The goal is to have at least 96% of customers succeed at being able to use any feature they wish. The company tests the new system
The Gallup-Healthways Well- Being Index tracks daily how Americans evaluate their lives, both now and in five years, on the Cantril Self-Anchoring Striving Scale, where “0” represents the worst possible life and “10” represents the best possible life. Respondents are classified by Gallup as

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