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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
=+1. What proportion of customers would you expect to be package subscribers?
=+2. What is the standard deviation of the sample proportion?
=+3. What shape would you expect the sampling distribution of the proportion to have?
=+4. Would you be surprised to find out that in a sample of 100, 49 of the customers are package subscribers? Explain. What might account for this high percentage?
=+1. If the proportion of package subscribers in his region is 0.30, how many package subscribers, on average, would you expect in a sample of 20?
=+2. Would you expect the shape of the sampling distribution of the proportion to be Normal? Explain
=+a. Find a 95% confidence interval for the true proportion of voters who will vote for the measure. (Use the 68–95–99.7% Rule.)
=+b. What would you report to the president of the Chamber of Commerce?
=+Q uestion Were the assumptions and conditions for making this interval satisfied?
=+Find a 99% confidence interval. Would you reassure her that the measure will pass? Explain.
=+3. 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?
=+a) Find the standard deviation of the sampling distribution of the proportions?
=+b) How large would the standard deviation have been if the number of people surveyed was 150 customers (assume the proportion is about the same)?Section 9.2
=+9. For each situation below identify the population and the sample and identify p and pn if appropriate and what the value of pn 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 randomly inspects their backpacks for alcoholic beverages. Of the 130 backpacks checked so far, 17 contained alcoholic beverages of some kind. The guards want to estimate the percentage of all backpacks of concertgoers at this concert that
=+b) The website of the English newspaper The Guardian asked visitors to the site to say whether they approved of recent “bossnapping” actions by British workers who were outraged over being fired. Of those who responded, 49.2%said “Yes. Desperate times, desperate measures.”
=+c) An airline wants to know the weight of carry-on baggage that customers take on their international routes, so they take a random sample of 50 bags and find that the average weight is 17.3 pounds.
=+. For each situation below identify the population and the sample and explain what p and pn represent and what the value of pn 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 customers to find out how much money they plan to spend at the company website in the next 6 months. The average amount reported from the 534 respondents is $145.34.
=+b) A university survey (40,000 students) is trying to find out whether students are willing to use bicycle parking facilities at a somewhat further distance from the current, overcrowded bicycle garage. Surveys are sent out by e-mail to all students. Of the 243 surveys returned, 134 express
=+c) The human resources department of a large Fortune 100 company wants to find out how many employees would take advantage of an on-site day care facility. They send out an e-mail to 500 employees and receive responses from 450 of them. Of those responding, 75 say that they would take advantage
=+11. 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 pn?
=+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 SEs from the sample proportion.
=+12. From a survey of 250 coworkers you find that 155 would like the company to provide on-site day care.
=+8. A market researcher for the users of Apple products wants to know the proportion of people who own an Apple iPad. A survey of 600 people indicated that 86% own an iPad.
=+what sample size should be used?
=+b) What is the probability that the sample proportion of smart phone users is greater than 0.36?
=+c) What is the probability that the sample proportion is between 0.30 and 0.40?
=+d) What is the probability that the sample proportion is less than 0.28?
=+e) What is the probability that the sample proportion is greater than 0.42?
=+4. The proportion of adult women in Latvia is approximately 54%. 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 56% women in a sample of size 400? Explain.
=+d) Would you be surprised to find 51% women in a sample of size 400? Explain.
=+e) Would you be surprised to find that there were fewer than 180 women in the sample? Explain.
=+6. A European medical agency wants to know what proportion of their patients is from the Middle East. They surveyed 200 people who are scheduled for a medical appointment in different departments on a particular day.Are all the assumptions and conditions for finding the sampling distribution of
=+7. A marketing research firm for a water bottling company surveys 200 customers and finds that the proportion of clients who are willing to renew their water supply contracts by the end of the service period is 0.45.
=+a) What is the standard deviation of the sampling distribution of the proportion?
=+b) If it is desired to reduce the standard deviation by half,
=+a) What is the value of the sample proportion pn?
=+a) Explain why it’s appropriate to use a Normal model to describe the distribution of the proportion of green M&M’s they might expect.
=+c) Explain what “95% confidence” means.d) A politician urging tighter restrictions on drivers’ licenses issued to teens says, “In one of every five auto accidents, a teenager is behind the wheel.” Does your confidence interval support or contradict this statement? Explain.
=+) Each group consisted of 538 respondents. If we combine them, considering the overall group to be one larger random sample, what is a 95% confidence interval for the proportion of the faculty and corporate recruiters that believe MBAs are more aware of ethical issues today?
=+) How does the margin of error based on this pooled sample compare with the margins of error from the separate groups? Why?Exercises 329 M09_SHAR8696_03_SE_C09.indd 329 14/07/14 7:31 AM 330 CHAPTER 9 Sampling Distributions and Confidence Intervals for Proportions
=+. Middle Eastern entrepreneurs. 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) What kinds of bias might they be referring to?
=+) Does their margin of error suggest that this was a simple random sample? Explain.
=+63. Pharmaceutical company. 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
=+children in England who are deficient in vitamin D.
=+b) Explain carefully what your interval means.
=+c) Explain what “98% confidence” means.
=+d) Does the study show that computer games are a likely cause of rickets? Explain.
=+64. Real estate survey. A real estate agent looks over the 15 listings she has in a particular zip code in the province of Western Finland and finds that 80% of them have a sauna.
=+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 this zip code that have saunas. If it’s not appropriate, explain why.
=+65. National health insurance. An investigator at one of Japan’s 47 prefectures wants to know how many citizens are in the National Health Insurance system (KokuminKenko--Hoken) or in the Employees’ Health Insurance system (Kenko--Hoken). She chooses 12 citizens at random and finds that all
=+) Check the assumptions and conditions for inference on proportions.
=+a) What kind of bias may be present here?
=+. Business ethics. 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
=+54. Advertisers. 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
=+a) Create a 90% confidence interval for the percentage of people the company contacts who may buy something.
=+b) Explain what this interval means.
=+c) Explain what “90% confidence” means.
=+) The company must decide whether to now do a mass mailing. The mailing won’t be cost-effective unless it produces at least a 5% return. What does your confidence interval suggest? Explain.
=+55. Retailers. 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
=+56. Local news. 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
=+57. Internet music. 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
=+58. Economy worries. During the period of Sep 2 – Oct 10, 2013, a Gallup Poll asked 1500 Indian adults, aged 18 or over, how they rated economic conditions. Only 29% rated the economy as ‘Getting better’. Construct a 95% confidence interval for the true proportion of Indians who rated the
=+59. International business. 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 environmental group wished to estimate the percentage of U.S.chemical companies that
=+a) What proportion of the sample reported being certified?
=+) Create a 95% confidence interval for the proportion of U.S. chemical companies with ISO 14001 certification.(Be sure to check conditions.) Compare to the Canadian proportion.
=+60. Worldwide survey. 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 acquiring wealth was of more than average importance in each country’s sample?
=+b) Create a 95% confidence interval for the proportion who thought it was of more than average importance in India. (Be sure to test conditions.) Compare that to a confidence interval for the U.S. population.
=+) If conditions are met, find a 95% confidence interval for the true proportion of citizens participating in the National Health Insurance system. If conditions are not met, explain why.
=+66. Awareness survey. 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.
=+d) Explain what this interval means. Do you believe that you can be this confident about your result? Why or why not?
=+71. CDs. 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
=+a) Create a 90% confidence interval for this percentage.
=+b) If the company wants to cut the margin of error in half,
=+how many users must they survey?
=+72. Internet music, last time. 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
=+73. Graduation. 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%?
=+74. Better hiring info. 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?
=+75. Pilot study. 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
=+76. Another pilot study. 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%
=+77. Approval rating. 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?
=+78. Amendment. 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
=+a) Explain why the poll is actually inconclusive.
=+b) What confidence level did the pollsters use?
=+79. Customer spending. 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
=+c) Construct a 95% confidence interval for the fraction of legal digital music.
=+b) Check the conditions for making a confidence interval.
=+a) Check the assumptions and conditions for inference on proportions.
=+b) If conditions are met, find a 95% confidence interval for the true proportion of customers who are aware of the new card. If conditions are not met, explain why.
=+67. IRS. 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 selfemployed individuals nationwide who’ve been audited by the IRS in the past year.
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