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Questions and Answers of Statistics

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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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%
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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 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
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
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
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
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
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
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
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
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
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
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:
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
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
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.
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
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
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
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
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
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
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
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
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
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%
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

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