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business
business statistics in practice
Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions
=+a) Check the assumptions and conditions (to the extent you can) for constructing a confidence interval.
=+b) Construct a 95% confidence interval.c) Interpret your interval.
=+d) Explain what “95% confidence” means in this context.
=+. Internet music, again. 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
=+a) Check that the assumptions and conditions are met for inference on proportions.
=+b) Find the 95% confidence interval for the true proportion of all U.S. Internet users who are “less likely” to buy CDs.
=+69. Premarital affairs. A 2013 poll amongst1000 Mexican adults, as part of Pew’s research into Global Views on Morality, found that 44% of Mexican adults qualify sex between unmarried adults as morally unacceptable. In contrast, in a sample of 1004 French adults, only 6% of adults have the
=+a) Do you expect the 95% confidence interval for the true proportion of all Mexican adults who qualify premarital affairs as morally unacceptable to be wider or narrower than the 95% confidence interval for the true proportion of all French adults having the same view. Explain.
=+b) Find the 95% confidence interval for the true proportion of all Mexican adults who qualify premarital affairs as morally unacceptable.
=+70. More Internet music. 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
=+a) Think carefully. What is the parameter being estimated?
=+What is the population? What is the sample size?M09_SHAR8696_03_SE_C09.indd 330 14/07/14 7:31 AM
=+80. Advertising. 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
=+b) Use the 68–95–99.7 Rule to describe how this proportion might vary from bag to bag.
=+c) How many of these homeowners might the bank expect will default on their mortgages? Explain.
=+35. Loans. 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 underlie your model? Are the conditions met? Explain.
=+c) What’s the probability that over 10% of these clients will not make timely payments?
=+36. Contacts. 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 pn represent the proportion of students in this sample who wear contacts. What’s the appropriate model for the distribution of pn? Specify the name of the distribution, the mean, and the standard deviation. Be sure to verify that the conditions are met.
=+b) What’s the approximate probability that more than one third of this sample wear contacts?
=+37. Back to school? 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
=+. Binge drinking. 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
=+39. Back to school, again. 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.
=+40. Binge sample. 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
=+41. Polling. 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
=+42. Seeds. 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.
=+43. Apples. 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 truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that in fact 8% of the apples on the
=+b) Sketch and clearly label the sampling model, based on the 68–95–99.7 Rule.
=+a) Can you use the Normal model to describe the sampling distribution model for the sample proportion of defaults?Check the conditions and discuss any assumptions you need to make.
=+) How would this model change if the bags contained even more candies?
=+29. A winning investment strategy? 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? Explain.
=+b) If there are 100 students in the class, are you surprised that one was this successful? Explain.
=+30. Even more quality. 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.
=+31. Speeding. 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 speeding.
=+b) Do you think the appropriate conditions necessary for your analysis are met? Explain.
=+32. Smoking, 2013. 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
=+33. Vision. 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 conditions and discuss any assumptions you need to make.
=+b) Sketch and clearly label the sampling model, based on the 68–95–99.7 Rule.
=+c) How many of the incoming students might the school expect to be nearsighted? Explain.
=+34. Mortgages 2013. A December 2013 Bloomberg report on mortgage defaults in Spain reported that the level of defaults was 0.7% in 2007, rose to 3.5% in 2012, and increased further to 5% in 2013. Suppose a large Spanish bank holds 9455 of these mortgages.
=+44. Genetic defect. 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?
=+45. Catalog sales. 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
=+49. Cars. A student is considering publishing a new magazine aimed directly at owners of Japanese automobiles. He wanted to estimate the fraction of cars in the United States that are made in Japan. The computer output summarizes the results of a random sample of 50 autos. Explain carefully
=+50. Quality control. For quality control purposes, 900 ceramic tiles were inspected to determine the proportion of defective (e.g., cracked, uneven finish, etc.) tiles. Assuming that these tiles are representative of all tiles manufactured by an Italian tile company, what can you conclude based
=+51. E-mail. 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 want 90%confidence in our estimate of the percent of American adults who do not use e-mail.
=+b) Explain what that margin of error means.
=+c) If we want to be 99% confident, will the margin of error be larger or smaller? Explain.
=+d) Find that margin of error.
=+e) In general, if all other aspects of the situation remain the same, will smaller margins of error involve greater or less confidence in the interval?
=+52. Biotechnology. 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 percent of American adults who approve of cloning humans.
=+b) Explain what that margin of error means.
=+c) If we only need to be 90% confident, will the margin of error be larger or smaller? Explain.
=+d) Find that margin of error.M09_SHAR8696_03_SE_C09.indd 328 14/07/14 7:31 AM
=+e) In general, if all other aspects of the situation remain the same, would smaller samples produce smaller or larger margins of error?
=+53. Teenage drivers. An insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them.
=+d) For a given confidence level, a sample 9 times as large will make a margin of error one third as big.
=+c) For a fixed margin of error, smaller samples will mean lower confidence.
=+a) Between 82% and 94% of all orders arrive on time.
=+b) 95% of all random samples of customers will show that 88% of orders arrive on time.
=+c) 95% of all random samples of customers will show that 82% to 94% of orders arrive on time.
=+d) The company is 95% sure that between 82% and 94%of the orders placed by the customers in this sample arrived on time.
=+e) On 95% of the days, between 82% and 94% of the orders will arrive on time.
=+46. Belgian euro. 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 unfair.
=+b) We are 90% sure that in this experiment this euro landed heads between 51% and 61% of the spins.
=+c) We are 90% sure that spun euros will land heads between 51% and 61% of the time.d) If you spin a euro many times, you can be 90% sure of getting between 51% and 61% heads.
=+e) 90% of all spun euros will land heads between 51% and 61% of the time.
=+47. Confidence intervals. 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, larger samples provide smaller margins of error.
=+c) For a fixed margin of error, larger samples provide greater confidence.d) For a given confidence level, halving the margin of error requires a sample twice as large.
=+48. Confidence intervals, again. 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, you can get a smaller margin of error by selecting a bigger sample.
=+a) Create a 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.b) Explain what your interval means.
=+a) What is the population of interest?
=+b) What is the sampling frame?
=+c) Point out any problems you see either with the sampling procedure and/or the survey itself. What are the potential impacts of these problems?
=+12. The airline company in Exercise 4 has realized that some of its customers don’t have e-mail or don’t read it regularly. They decide to restrict the mailing only to customers who have recently registered for a “Win a trip to Miami” contest, figuring that those with Internet access are
=+you possibly think of traveling to Miami in the next six months on your way to one of your destinations?”
=+a) What is the population?
=+b) What is the sampling frame?
=+c) Point out any problems you see either with the sampling procedure and/or the survey itself. What are the potential impacts of these problems?
=+13. An intern is working for Pacific TV (PTV), a small cable and Internet provider, and has proposed some questions that might be used in the survey to assess whether customers are willing to pay $50 for a new service.
=+“As we learned in Burlington, climate change is a serious problem for farmers. Given the evidence of impact on crops, do you agree that the government should be doing more to fight global warming?”
=+11. An intern for the environmental group in Exercise 3 has decided to make the survey process simpler by calling 150 of the members who attended the recent symposium on coping with climate change that was recently held in Burlington, VT. He has all the phone numbers, so it will be easy to
=+10. A question posted on a university’s website asked potential new students whether or not the university should include health insurance plans in their student fees.Section 8.4
=+a) Are they using a simple random sample? How do you know?
=+b) What kind of design do you think they are using?
=+6. 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 the group was using an SRS? Why?
=+b) What kind of sampling design do you think they used?
=+7. The environmental advocacy group from Exercise 3 that was interested in gauging perceptions about climate change among organic farmers has decided to use a different method to sample. Instead of randomly selecting members from a shuffled list, they listed the members in alphabetical order and
=+8. The airline company from Exercise 4, interested in the opinions of their frequent flyer customers about their proposed new routes, has decided that different types of customers might have different opinions. Of their customers, 50% are silver-level, 30% are blue, and 20% are red. They first
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