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intro stats

Intro Stats 4th International Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions

4. Non-profits, part 2 If the information in Exercise 2 is to be used to make inferences about all people who work at non-profits and for-profit companies, what conditions must be met before proceeding? List them and explain if they are met.
3. Canada, deux If the information in Exercise 1 is to be used to make inferences about the proportion all Canadians and all Americans born in other countries, what conditions must be met before proceeding? Are they met? Explain.
2. Non-profits Do people who work for non-profit organizations differ from those who work at for-profit companies when it comes to personal job satisfaction?Separate random samples were collected by a polling agency to investigate the difference. Data collected from 422 employees at non-profit
1. Canada Suppose an advocacy organization surveys 960 Canadians and 192 of them reported being born in another country (www.unitednorthamerica.org/simdiff.htm). Similarly, 170 out of 1250 Americans reported being foreign-born. Find the standard error of the difference in sample proportions.
Milk 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
IQs 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 standard deviation 10.a) We select a student
Potato chips The weight of potato chips in a mediumsize 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
Fuel economy again 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 y represent the mean combined gas mileage for all cars in the lot.a)
Joining the museum One of the museum’s phone volunteers 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
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 least 3?
AP Stats 2011, again An AP Statistics teacher had 63 students preparing to take the AP exam discussed in Exercise
Museum membership 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
AP Stats 2011 The College Board reported the score distribution shown in the table for all students who took the 2011 AP Statistics exam.a) Find the mean and standard deviation of the scores.b) If we select a random sample of 40 AP Statistics students, would you expect their scores to follow a
New game 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
Dice and dollars 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.
At work 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
Pregnant again 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 partsa, b, and c of Exercise 49?Explain why or why not
Rainfall 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 than 40 of rain?b) Less
Pregnancy 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
Safe cities 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.
Lucky spot? A reporter working on a story about the New York lottery contacted one of the authors of this text, 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
Home values 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
What might the mean GPA of one of these seminar groups be? Describe the appropriate sampling distribution model—shape, center, and spread—with attention to assumptions and conditions.Make a sketch using the 68–95–99.7 Rule.
GPAs 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
CEOs, revisited In Exercise 30, 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
Waist size, revisited 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,
CEO compensation 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)
Waist size 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
Sampling, part II 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
Sampling 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?
Meals 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?
“No Children” section 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.
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?
Gaydar A study 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 “gaydar.” Near ovulation, on
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.
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 defeat?
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 be
Back to school, again Based on the 74% 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.
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 students who
Back to school? Best known for its testing program, ACT, Inc., also compiles data on a variety of issues in education.In 2010, the company reported that the national college freshman-to-sophomore retention rate held steady at 74%over the previous several years.
Contacts Assume that 30% of students at a university wear contact lenses.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
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
Mortgages In July 2010, Lender Processing Services reported that homeowners were defaulting in record numbers;12.4% of mortgages were delinquent or in foreclosure.Suppose a large bank holds 1731 adjustable-rate mortgages.a) Can you apply the Central Limit Theorem to describe the sampling
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 apply the Central Limit Theorem to describe the sampling distribution model for the sample proportion of children who are
Smoking Public health statistics for 2009 indicate that 20.6% 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 50 adults. Be sure to discuss your assumptions and conditions.
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
Too many green ones? 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.
Just (un)lucky? 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.
Bigger bag 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
More coins 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.
M&M’s 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
Coin tosses 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
More groceries 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?
More tips 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?
Groceries A grocery store’s receipts show that Sunday customer purchases have a skewed distribution with a mean of $32 and a standard deviation of $20.a) Explain why you cannot determine the probability that the next Sunday customer will spend at least $40.b) Can you estimate the probability that
Tips A waiter believes the distribution of his tips has a model that is slightly skewed to the right, with a mean of$9.60 and a standard deviation of $5.40.a) Explain why you cannot determine the probability that a given party will tip him at least $20.b) Can you estimate the probability that the
Market research II 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
Market research A marketing researcher for a phone company surveys 100 people and finds that the proportion of customers who are likely to switch providers when their contract expires is 15%.a) What is the standard deviation of the sampling distribution of the proportion?b) If she wants to reduce
Soup A machine is supposed to fill cans with 16 oz of soup. Of course there, will be some variation in the amount actually dispensed, and measurement errors are often approximately normally distributed. The manager would like to understand the variability of the variances of the samples, so he
Sample maximum 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
The sample statistics and theoretical values for each simulation are as follows:a) Looking at the histograms in Exercise 4, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?b) What does the Success/Failure Condition say about the
Character recognition, again 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,
Here are both the theoretical and observed statistics for these simulated samples:a) Looking at the histograms of Exercise 3, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?b) What does the Success/Failure Condition say about
Send more money 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
Campus sample 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
Marriage 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
For each sample size, they simulated 1000 samples with success rate p = 0.85 and constructed the histogram of the 1000 sample proportions, shown here.Explain how these histograms demonstrate what the Central Limit Theorem says about the sampling distribution model for sample proportions. Be sure to
Character recognition An automatic character recognition device can successfully read about 85% of handwritten credit card applications. To estimate what might happen when this device reads a stack of applications, the company did a simulation using samples of size 20, 50, 75, and
Send money When they send out their fundraising letter, a philanthropic organization typically gets a return from about 5% of the people on their mailing list. To see what the response rate might be for future appeals, they did a simulation using samples of size 20, 50,100, and 200.For each sample
Marketing 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
Website 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 smartphones so they want to estimate the proportion of users who access the site that way (even if they also use their computers
Polygraphs Lie detectors are controversial instruments, barred from use as evidence in many courts. Nonetheless, many employers use lie detector screening as part of their hiring process in the hope that they can avoid hiring people who might be dishonest. There has been some research, but no
HIV testing In July 2005, the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large study suggested that among people with HIV, 99.7% of tests conducted were (correctly)positive, while for people without HIV 98.5% of the tests were (correctly)
Parts A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers. The company prefers to use supplier A because only 1% of those connectors prove to be defective, but supplier A can deliver only 70% of the connectors needed. The
Dishwashers Dan’s Diner employs three dishwashers. Al washes 40% of the dishes and breaks only 1% of those he handles. Betty and Chuck each wash 30% of the dishes, and Betty breaks only 1% of hers, but Chuck breaks 3%of the dishes he washes. (He, of course, will need a new job soon. . . .) You go
No-shows An airline offers discounted “advancepurchase”fares to customers who buy tickets more than 30 days before travel and charges “regular” fares for tickets purchased during those last 30 days. The company has noticed that 60% of its customers take advantage of the advance-purchase
Drunks Police often set up sobriety checkpoints—roadblocks where drivers are asked a few brief questions to allow the officer to judge whether or not the person may have been drinking. If the officer does not suspect a problem, drivers are released to go on their way. Otherwise, drivers are
E-readers II Given the e-reader data presented in Exercise 52, if a randomly selected American has read 3 or more books, what’s the probability that he or she owns an e-reader?
Absenteeism, part II At the company described in Exercise 51, what percent of the absent employees are on the night shift?
E-readers In 2011, 12% of Americans owned an electronic reader of some sort. Suppose that 43% of people with e-readers read at least 3 books last year, while people without an e-reader, only 11% read 3 or more books in the course of the year.a) Explain how these statistics indicate that owning an
Absenteeism A company’s records indicate that on any given day about 1% of their day-shift employees and 2% of the night-shift employees will miss work. Sixty percent of the employees work the day shift.a) Is absenteeism independent of shift worked? Explain.b) What percent of employees are absent
Graduation, part II What percent of students who graduate from the college in Exercise 48 attended a public high school?
Late luggage Remember Leah (Exercise 47)? Suppose you pick her up at the Denver airport, and her luggage is not there. What is the probability that Leah’s first flight was delayed?
Graduation A private college report contains these statistics:70% of incoming freshmen attended public schools.75% of public school students who enroll as freshmen eventually graduate.90% of other freshmen eventually graduate.a) Is there any evidence that a freshman’s chances to graduate may
Luggage Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that
Cars A random survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table. Is country of origin independent of type of driver? Origin American Driver Student Staff 107 105 European 33 Asian 12 55 47
Gender A 2009 poll conducted by Gallup classified respondents by sex and political party, as shown in the table. Is party affiliation independent of the respondents’sex? Explain. Democrat Republican Independent Male 32 28 34 Female 41 25 26
Snoring After surveying 995 adults, 81.5% of whom were over 30, the National Sleep Foundation reported that 36.8% of all the adults snored. 32% of the respondents were snorers over the age of 30.a) What percent of the respondents were under 30 and did not snore?b) Is snoring independent of age?
Phone service According to estimates from the federal government’s 2010 National Health Interview Survey, based on face-to-face interviews in 16,676 households, approximately 63.6% of U.S. adults have both a landline in their residence and a cell phone, 25.4% have only cell phone service but no
Politics Given the table of probabilities from Exercise 24, are party affiliation and position on immigration independent?Explain. Party Stronger Immigration Enforcement Favor Oppose No Opinion Republican 0.30 0.04 0.03 Democrat 0.22 0.11 0.02 Other 0.16 0.07 0.05
Men’s health again Given the table of probabilities from Exercise 23, are high blood pressure and high cholesterol independent? Explain. Cholesterol Blood Pressure High OK High 0.11 0.21 OK 0.16 0.52
Birth order, finis In Exercises 20 and 26, we looked at the birth orders and college choices of some Intro Stats students. For these students:a) Are enrolling in Agriculture and Human Ecology disjoint? Explain.b) Are enrolling in Agriculture and Human Ecology independent? Explain.c) Are being
Unsafe food Early in 2010, Consumer Reports published the results of an extensive investigation of broiler chickens purchased from food stores in 23 states. Tests for bacteria in the meat showed that 62% of the chickens were contaminated with campylobacter, 14% with salmonella, and 9% with both.a)
Pets, again The local animal shelter in Exercise 22 reported that it currently has 24 dogs and 18 cats available for adoption; 8 of the dogs and 6 of the cats are male. Are the species and sex of the animals independent? Explain.
Cards If you draw a card at random from a well-shuffled deck, is getting an ace independent of the suit? Explain.
On the road again According to Exercise 16, the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04.a) What’s the probability that someone who has traveled to Mexico has visited Canada too?b) Are traveling to Mexico and to Canada
Cell phones in the home A survey found that 73% of Americans have a home phone, 83% have a cell phone and 58% of people have both.a) If a person has a home phone, what’s the probability that they have a cell phone also?b) Are having a home phone and a cell phone independent events? Explain.c) Are
Benefits Fifty-six percent of all American workers have a workplace retirement plan, 68% have health insurance, and 49% have both benefits. We select a worker at random.a) What’s the probability he has neither employersponsored health insurance nor a retirement plan?b) What’s the probability he
Eligibility A university requires its biology majors to take a course called BioResearch. The prerequisite for this course is that students must have taken either a Statistics course or a computer course. By the time they are juniors, 52% of the Biology majors have taken Statistics, 23% have had a
Shirts The soccer team’s shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 4 medium, 10 large, and 6 extra-large shirts. You want a medium for you and one for your sister. Find the probability of each event described.a) The first

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