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Stats Data And Models 4th Edition Richard D. De Veaux, Paul D. Velleman, David E. Bock - Solutions

The waiter in Exercise 13 usually waits on about 40 parties over a weekend of work. a) Estimate the probability that he will earn at least $500 in tips. b) How much does he earn on the best 10% of such weekends? Exercise 13 A waiter believes the distribution of his tips has a model that is slightly
Suppose the store in Exercise 14 had 312 customers this Sunday. a) Estimate the probability that the store's revenues were at least $10,000. b) If, on a typical Sunday, the store serves 312 customers, how much does the store take in on the worst 10% of such days? Exercise 14 A grocery store's
In a large class of introductory Statistics students, the professor has each student toss a coin 16 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions. a) What shape would
The candy company claims that 10% of the M&M's it produces are green. Suppose that the candies are packaged at random in small bags containing about 50 M&M's. A class of elementary school students learning about percents opens several bags, counts the various colors of the candies, and calculates
Suppose the class in Exercise 17 repeats the coin-tossing experiment. a) The students toss the coins 25 times 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 tosses to 64 each. Draw and label
The proportion of adult women in the United States is approximately 51%. A marketing survey telephones 400 people at random. a) What proportion of the sample of 400 would you expect to be women? b) What would the standard deviation of the sampling distribution be? c) How many women, on average,
Suppose the class in Exercise 18 buys bigger bags of candy, with 200 M&M's each. Again the students calculate, the proportion of green candies they find. 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. b) Use the
One of the students in the introductory Statistics class in Exercise 19 claims to have tossed her coin 200 times and found only 42% heads. What do you think of this claim? Explain.
In a really large bag of M&M's, the students in Exercise 20 found 500 candies, and 12% of them were green. Is this an unusually large proportion of green M&M's? 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 Centers for Disease Control and Prevention estimated in 2014 that 18.1 % of American adults smoked cigarettes. Using the 68-95-99.7 Rule, describe the sampling distribution model for the proportion of smokers among a randomly selected group of 60 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 apply the Central Limit Theorem to describe the sampling distribution model for the sample proportion of children who are nearsighted?
In December, 2013, Lender Processing Services* reported that although mortgage defaults had fallen, in New York state, 12.4% of mortgages were still "noncurrent," meaning that payments had been missed. Suppose a New York bank holds 1731 mortgages. a) Can you apply the Central Limit Theorem to
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
Assume that 30% of students at a university wear contact lenses. a) We randomly pick 100 students. Let p̂ represent the proportion of students in this sample who wear contacts. What's the appropriate model for the distribution of p̂? Specify the name of the distribution, the mean, and the
Best known for its testing program, ACT, Inc., also compiles data on a variety of issues in education. In 2013, the company reported that the national college freshman-to-sophomore retention rate that had held steady at 74% over the previous several years had recently fallen from 74% to 72.2%.
As we learned in Chapter 14, 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
Based on the 72.2% national retention rate described in Exercise 29, does a college where 522 of the 603 freshmen returned the next year as sophomores have a right to brag that it has an unusually high retention rate? Explain.
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 to
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.
Exercise 13 in Chapter 1 describes a study that showed that heterosexual women, during ovulation, were significantly better at correctly identifying the sexual orientation of a man from a photograph of his face than women who were not ovulating. In other words, ovulation improves a woman's
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?
Some restaurant owners, at the request of some of their less tolerant customers, have stopped allowing children into their restaurant. This, naturally, outrages other customers. One restaurateur hopes to please both sets of customers by having a "no children" section. She estimates that in her
A restaurateur anticipates serving about 180 people on a Friday evening, and believes that about 20% of the patrons will order the chef's steak special. How many of those meals should he plan on serving in order to be pretty sure of having enough steaks on hand to meet customer demand? Justify your
A sample is chosen randomly from a population that can be described by a Normal model. a) What's the sampling distribution model for the sample mean? Describe shape, center, and spread. b) If we choose a larger sample, what's the effect on this sampling distribution model?
A sample is chosen randomly from a population that was strongly skewed to the left. a) Describe the sampling distribution model for the sample mean if the sample size is small. b) If we make the sample larger, what happens to the sampling distribution model's shape, center, and spread? c) As we
A study measured the Waist Size of 250 men, finding a mean of 36.33 inches and a standard deviation of 4.02 inches. Here is a histogram of these measurements.a) Describe the histogram of Waist Size. b) To explore how the mean might vary from sample to sample, they simulated by drawing many samples
The total compensation of the chief executive officers (CEOs) of the 800 largest U.S. companies (the Fortune 800) averaged (in thousands of dollars) 10,307.31 with a standard deviation (also in $1000) of 17,964.62. Here is a histogram of their annual compensations (in $1000):a) Describe the
Researchers measured the Waist Sizes of 250 men in a study on body fat. The true mean and standard deviation of the Waist Sizes for the 250 men are 36.33 in and 4.019 inches, respectively. In Exercise 41, you looked at the histograms of simulations that drew samples of sizes 2, 5, 10, and 20 (with
In Exercise 42, you looked at the annual compensation for 800 CEOs, for which the true mean and standard deviation were (in thousands of dollars) 10,307.31 and 17,964.62, respectively. A simulation drew samples of sizes 30, 50, 100, and 200 (with replacement) from the total annual compensations of
A college's data about the incoming freshmen indicates that the mean of their high school GPAs was 3.4, with a standard deviation of 0.35; the distribution was roughly mound-shaped and only slightly skewed. The students are randomly assigned to freshman writing seminars in groups of 25. What might
Assessment records indicate that the value of homes in a small city is skewed right, with a mean of $140,000 and standard deviation of $60,000. To check the accuracy of the assessment data, officials plan to conduct a detailed appraisal of 100 homes selected at random. Using the 68-95-99.7 Rule,
A reporter working on a story about the New York lottery contacted one of the authors of this book, wanting help analyzing data to see if some ticket sales outlets were more likely to produce winners. His data for each of the 966 New York lottery outlets are graphed below; the scatterplot shows the
Allstate Insurance Company identified the 10 safest and 10 least-safe U.S. cities from among the 200 largest cities in the United States, based on the mean number of years drivers went between automobile accidents. The cities on both lists were all smaller than the 10 largest cities. Using facts
Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 16 days. a) What percentage of pregnancies should last between 270 and 280 days? b) At least how many days should the longest 25% of all pregnancies last? c) Suppose a certain
According to a Pew Research survey, 27% of American adults are pessimistic about the future of marriage and the family. That is based on a random sample of about 1500 people. Is it reasonable for Pew Research to use a Normal model for the sampling distribution of the sample proportion? Why or why
Statistics from Cornell's Northeast Regional Climate Center indicate that Ithaca, New York, gets an average of 35.4" of rain each year, with a standard deviation of 4.2". Assume that a Normal model applies. a) During what percentage of years does Ithaca get more than40" of rain? b) Less than how
The duration of human pregnancies may not actually follow the Normal model described in Exercise 49. a) Explain why it may be somewhat skewed to the left. b) If the correct model is in fact skewed, does that change your answers to parts a, b, and c of Exercise 49? Explain why or why not for each.
Some business analysts estimate that the length of time people work at a job has a mean of 6.2 years and a standard deviation of 4.5 years. a) Explain why you suspect this distribution may be skewed to the right. b) Explain why you could estimate the probability that 100 people selected at random
You roll a die, winning nothing if the number of spots is odd, $1 for a 2 or a 4, and $10 for a 6. a) Find the expected value and standard deviation of your prospective winnings. b) You play twice. Find the mean and standard deviation of your total winnings. c) You play 40 times. What's the
You pay $10 and roll a die. If you get a 6, you win $50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times.
The College Board reported the score distribution shown in the table for all students who took the 2013 AP Statistics exam. Score Percent of Students 5 ……………………… 12.6 4 ……………………… 20.2 3 ……………………… 25.0 2 ……………………… 18.8 1
A museum offers several levels of membership, as shown in the table.a) Find the mean and standard deviation of the donations. b) During their annual membership drive, they hope to sign up 50 new members each day. Would you expect the distribution of the donations for a day to follow a Normal model?
An AP Statistics teacher had 63 students preparing to take the AP exam discussed in Exercise 55. Though they were obviously not a random sample, he considered his students to be "typical" of all the national students. What's the probability that his students will achieve an average score of at
One of the phone volunteers for the museum in exercise 56 sets a personal goal of getting an average donation of at least $ 100 from the new members she enrolls during the membership drive. If she gets 80 new members and they can be considered a random sample of all the museum's members, what is
The combined gas mileage of midsize cars varies with mean 24 miles per gallon (mpg) and a standard deviation of about 5.5 mpg. A particular rental car agency typically has 150 midsize cars in its lot. Let represent the mean combined gas mileage for all cars in the lot. a) What's the approximate
For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for Spring Break. From past years, she guesses that about 10% of the class goes. Is it reasonable for her to use a Normal model for the sampling distribution of the sample
The weight of potato chips in a medium-size bag is stated to be 10 ounces. The amount that the packaging machine puts in these bags is believed to have a Normal model with mean 10.2 ounces and standard deviation 0.12 ounces. a) What fraction of all bags sold are underweight? b) Some of the chips
Suppose that IQs of East State University's students can be described by a Normal model with mean 130 and standard deviation 8 points. Also suppose that IQs of students from West State University can be described by a Normal model with mean 120 and stand deviation 10. a) We select a student at
Although most of us buy milk by the quart or gallon, farmers measure daily production in pounds. Ayrshire cows average 55 pounds of milk a day, with a standard deviation of 6 pounds. For Jersey cows, the mean daily production is 52 pounds, with a standard deviation of 5 pounds. Assume that Normal
The philanthropic organization in Exercise 3 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 3, you looked at the histograms showing distribution of sample proportions from 1000 simulated mailings for samples of size 20, 50, 100,
The automatic character recognition device discussed in Exercise 4 successfully reads about 85% of handwritten credit card applications. In Exercise 4, you looked at the histograms showing distributions of sample proportions from 1000 simulated samples of size 20, 50, 75, and 100. The sample
The distribution of scores on a Statistics test for a particular class is skewed to the left. The professor wants to predict the maximum score and so wants to understand the distribution of the sample maximum. She simulates the distribution of the maximum of the test for 30 different tests (with n
Pew Research, in November 2011, polled a random sample of 799 U.S. teens about Internet use. 49% of those teens reported that they had misrepresented their age online to gain access to websites and online services. a) Explain the meaning of p̂ = 0.49 in the context of this situation. b) Calculate
For 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) Police set up an auto checkpoint at which drivers are stopped and their cars inspected for
Consider each situation described. 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 consumer group hoping to assess customer experiences with auto dealers surveys 167 people who
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 these conclusions correct?
In January 2002, 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 these conclusions correct? Explain. a) Between 51% and 61% of all euros are unfair. b) We 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,
In December 2011, Consumer Reports published their study of labeling of seafood sold in New York, New Jersey, and Connecticut. They purchased 190 pieces of seafood from various kinds of food stores and restaurants in the three states and genetically compared the pieces to standard gene fragments
Gallup regularly conducts a poll asking people to imagine a ladder with 10 rungs. Rung 0 represents the worst possible life and rung 10 represents the best possible life. Respondents are asked what rung they would say they are on. Responses are classified as "Thriving" (standing on rung 7 or
The December 2011 Consumer Reports study described in Exercise 19 also found that 12 of the 22 "red snapper" packages tested were a different kind of fish. a) Are the conditions for creating a confidence interval satisfied? Explain. b) Construct a 95% confidence interval. c) Explain what your
In a poll taken in December 2012, Gallup asked 1006 national adults whether they were baseball fans; 48% said they were. Three years earlier, in February 2008, only 35% of a similar-size sample had reported being baseball fans. a) Find the margin of error for the 2012 poll if we want 90% confidence
The Pew Research poll described in Exercise 1 found that 49% of a sample of 799 teens admitted to misrepresenting their age online to access websites and online services. (Treat this as a simple random sample.) a) Find the margin of error for this poll if we want 95% confidence in our estimate of
The Paralyzed Veterans of America is a philanthropic organization that relies on contributions. They send free mailing labels and greeting cards to potential donors on their list and ask for a voluntary contribution. To test a new campaign, they recently sent letters to a random sample of 100,000
First USA, a major credit card company, is planning a new offer for their current cardholders. The offer will give double airline miles on purchases for the next 6 months if the cardholder goes online and registers for the offer. To test the effectiveness of the campaign, First USA recently sent
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 (a.k.a. "junk mail") to thousands of potential customers in the hope that some will buy the company's product. The acceptance rate is usually quite low. Suppose a company wants to test the response to a new flyer, and sends it to 1000 people randomly
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 only 31 in favor of the
In the survey on the death penalty you read about in the chapter, the Gallup Poll actually split the sample at random, asking 510 respondents the question quoted earlier, "Generally speaking, do you believe the death penalty is applied fairly or unfairly in this country today?" The other 510 were
The 95% confidence interval for the number of teens in Exercise l who reported that they had misrepresented their age online is from 45.6% to 52.5%. a) Interpret the interval in this context. b) Explain the meaning of "95% confident" in this context.
A city ballot includes a local initiative that would legalize gambling. The issue is hotly contested, and two groups decide to conduct polls to predict the outcome. The local newspaper finds that 53% of 1200 randomly selected voters plan to vote "yes," while a college Statistics class finds 54% of
Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls on the skin, is essential for strong, healthy bones. The bone disease rickets was largely eliminated in England during the 1950s, but now there is concern that a generation of children more likely to watch
A 2011 Gallup poll found that 76% of Americans believe that high achieving high school students should be recruited to become teachers. This poll was based on a random sample of 1002 Americans. a) Find a 90% confidence interval for the proportion of Americans who would agree with this. b) Interpret
In January 2014 AP-GfK polled 1060 U.S. adults to find if people were more concerned with privacy or security. Privacy concerns outweighed concerns about being safe from terrorists for 646 out the 1060 polled. Of the 1060 adults about 180 are 65 and older whose concerns may be different from the
ACT, Inc. reported that 74% of 1644 randomly selected college freshmen returned to college the next year. The study was stratified by type of college—public or private. The retention rates were 71.9% among 505 students enrolled in public colleges and 74.9% among 1139 students enrolled in private
Wildlife biologists inspect 153 deer taken by hunters and find 32 of them carrying ticks that test positive for Lyme disease. a) Create a 90% confidence interval for the percentage of deer that may carry such ticks. b) If the scientists want to cut the margin of error in half, how many deer must
Suppose ACT, Inc. wants to update their information from Exercise 34 on the percentage of freshmen that return for a second year of college. a) They want to cut the stated margin of error in half. How many college freshmen must be surveyed? b) Do you have any concerns about this sample?
It's believed that as many as 25% of adults over 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 non-grads to within 6% with 90%
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)
As in Exercise 37, 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%? Exercise 37 It's believed that as many as 25% of adults over 50
In a 2010 Pew Research study on trends in marriage and family, 4% of randomly selected respondents said that the trend of more single women having children is "a good thing." The 95% confidence interval is from 2.9% to 5.1% (n = 1229). a) Interpret this interval in this context. b) Explain the
Editors of the business report in Exercise 38 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 many 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 first picks 60 cars
During routine screening, a doctor notices that 22% of her adult patients show higher than normal levels of glucose in their blood—a possible warning signal for diabetes. Hearing this, some medical researchers decide to conduct a large-scale study, hoping to estimate the proportion to within 4%
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?
A TV news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of 1505 likely voters indicated that 52% would vote in favor. The reporter goes on to say that the margin of error for this poll was 3%. a) Explain why the poll is
St. Norbert's College in Green Bay, Wisconsin, and Wisconsin Public Radio conduct an annual poll of Wisconsinites about political opinions. The Fall 2011 survey asked a random sample of 402 adult Wisconsin residents whether they think things in the country are going in the right direction or in the
In the Gallup poll described in Exercise 2, 49% of those polled considered themselves to be "thriving." a) Calculate the margin of error for the proportion of all American adults who were rated as "thriving" for 99% confidence. b) Would the margin of error be larger or smaller for 95% confidence?
Consider the St. Norbert's College poll of Exercise 5. a) Are the assumptions and conditions met? b) How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 2%? Exercise 5 St. Norbert's College in Green Bay, Wisconsin, and Wisconsin
In Exercise 4, we saw that 4% of people think the trend of more single women having children is a "good thing." a) Are the conditions for constructing a confidence interval met? b) How many people would need to be surveyed for a 95% confidence interval to ensure the margin of error would be less
A very large study showed that aspirin reduced the rate of first heart attacks by 44%. A pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug. a) What is the null hypothesis the company will use? b)
Developing 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
Write the null and alternative hypotheses you would use to test each of the following situations: a) A governor is concerned about his "negatives"—the percentage of state residents who express disapproval of his job performance. His political committee pays for a series of TV ads, hoping that
Write the null and alternative hypotheses you would use to test each situation. a) In the 1950s, only about 40% of high school graduates went on to college. Has the percentage changed? b) Twenty percent of cars of a certain model have needed costly transmission work after being driven between
A 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.
A survey investigating whether the proportion of today's high school seniors who own their own cars is higher than it was a decade ago finds a P-value of 0.017. Is it reasonable to conclude that more high schoolers have cars? Explain.

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