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intro stats
Stats Data And Models 4th Global Edition Richard D. De Veaux, Paul Velleman, David E. Bock - Solutions
Satisfactory satisfaction samples For each scenario, determine the sampling method used by the managers from Exercise 2.a) Use the company e-mail directory to contact 150 employees from among those employed for less than 5 years, 150 from among those employed for 5–10 years, and 150 from among
Sampling A&M students For each scenario, identify the kind of sample used by the university administrators from Exercise 1:a) Select several dormitories at random and contact everyone living in the selected dorms.b) Using a computer-based list of registered students, contact 200 freshmen, 200
Sampling satisfaction A company hoping to assess employee satisfaction surveys employees by assigning computer-generated random numbers to each employee on a list of all employees and then contacting all those whose assigned random number is divisible by 7. Is this a simple random sample?
Sampling students A professor teaching a large lecture class of 350 students samples her class by rolling a die.Then, starting with the row number on the die (1 to 6), she passes out a survey to every fourth row of the large lecture hall. She says that this is a Simple Random Sample because
Satisfied respondents The company’s annual report states, “Our survey shows that 87.34% of our employees are ‘very happy’ working here.” Comment on that claim.Use appropriate statistics terminology.
A&M again The president of the university plans a speech to an alumni group. He plans to talk about the proportion of students who responded in the survey that they are the first in their family to attend college, but the first draft of his speech treats that proportion as the actual proportion of
Satisfied workers The managers of a large company wished to know the percentage of employees who feel“extremely satisfied” to work there. The company has roughly 24,000 employees. They contacted a random sample of employees and asked them about their job satisfaction, obtaining 437 completed
Texas A&M Administrators at Texas A&M University were interested in estimating the percentage of students who are the first in their family to go to college. The A&M student body has about 46,000 members. How might the administrators answer their question by applying the three Big Ideas ?
There are 80 students enrolled in an introductory Statistics class; you are to select a sample of 5.Question: How can you select an SRS of 5 students using these random digits found on the Internet: 05166 29305 77482?
Here are summary statistics comparing two samples of 8000 drawn at random from a company’s database of 3.5 million customers:QUESTION: Do you think these samples are representative of the population of the company’s customers? Explain. Mean Mean White Female # of Bracket Age (yr) (%) (%)
Smartphones A proud legislator claims that your state’s new law banning texting and hand-held phones while driving reduced occurrences of infractions to less than 10% of all drivers. While on a long drive home from your college, you notice a few people seemingly texting. You decide to count
Job discrimination? A company with a large sales staff announces openings for three positions as regional managers.Twenty-nine of the current salespersons apply, 15 men and 14 women. After the interviews, when the company announces the newly appointed managers, all three positions go to women. The
Second team Suppose the couples in Exercise 41 choose the teams by having one member of each couple write their names on the cards and the other people each pick a card at random. How likely is it that every person will be teamed with someone other than the person he or she came with?
Teammates Four couples at a dinner party play a board game after the meal. They decide to play as teams of two and to select the teams randomly. All eight people write their names on slips of paper. The slips are thoroughly mixed, then drawn two at a time. How likely is it that every person will be
The World Series The World Series ends when a team wins 4 games. Suppose that sports analysts consider one team a bit stronger, with a 55% chance to win any individual game. Estimate the likelihood that the underdog wins the series.
The hot hand A basketball player with a 78% shooting percentage has just made 6 shots in a row. The announcer says this player “is hot tonight! She’s in the zone!” Assume the player takes about 20 shots per game. Is it unusual for her to make 6 or more shots in a row during a game?
Parcheesi You are three spaces from a win in Parcheesi.On each turn, you will roll two dice. To win, you must roll a total of 3 or roll a 3 on one of the dice. How many turns might you expect this to take?
Dice game You are playing a children’s game in which the number of spaces you get to move is determined by the rolling of a die. You must land exactly on the final space to win. If you are 10 spaces away, how many turns might it take you to win?
A bigger family Suppose a couple will continue having children until they have at least two children of each sex(two boys and two girls). How many children might they expect to have?
The family Many couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each sex, what would the average family size be? Assume that boys and girls are equally likely.
Find the ace A technology store holds a contest to attract shoppers. Once an hour, someone at checkout is chosen at random to play in the contest. Here’s how it works:An ace and four other cards are shuffled and placed face down on a table. The customer gets to turn over cards one at a time,
Free groceries To attract shoppers, a supermarket runs a weekly contest that involves “scratch-off ” cards. With each purchase, customers get a card with a black spot obscuring a message. When the spot is scratched away, most of the cards simply say, “Sorry—please try again.”But during
Blood donors A person with type O-positive blood can receive blood only from other type O donors. About 39%of the U.S. population has type O blood. At a blood drive, how many potential donors do you expect to examine in order to get four units of type O blood?
Basketball strategy Late in NCAA basketball games, foul shots are often “one and one,” meaning a player gets a second shot only if he makes the first shot. Suppose a player has made 62% of his foul shots this season Estimate the number of points he will score in a one-andone situation.
Still learning? As in Exercise 29, assume that your chance of passing the driver’s test is 34% the first time and 72% for subsequent retests. Estimate the percentage of those tested who still do not have a driver’s license after two attempts.
Driving test You are about to take the road test for your driver’s license. You hear that only 28% of candidates pass the test the first time, but the percentage rises to 66% on subsequent retests. Estimate the average number of tests drivers take in order to get a license. Your simulation should
Play the winner? Another strategy for beating the lottery is the reverse of the system described in Exercise 27.Simulate the simplified lottery described in Exercise 25.Each time, bet the number that just turned up. The website suggests that this method should do worse. Does it?Play many games and
It evens out in the end The “beat the lottery” website of Exercise 25 notes that in the long run we expect each value to turn up about the same number of times. That leads to their recommended strategy. First, watch the lottery for a while, recording the winners. Then bet the value that has
Random is as random does The “beat the lottery”website discussed in Exercise 25 suggests that because lottery numbers are random, it is better to select your bet randomly. For the same simple lottery in Exercise 25(random values from 0 to 9), generate each bet by choosing a separate random
Beat the lottery Many states run lotteries to raise money.A website advertises that it knows “how to increase YOUR chances of Winning the Lottery.” They offer several systems and criticize others as foolish. One system is called Lucky Numbers. People who play the Lucky Numbers system just pick
Lucky guessing? A friend of yours who took the multiple choice quiz in Exercise 23 got all 6 questions right, but now claims to have guessed blindly on every question.If each question offered 4 possible answers, do you believe her? Explain, basing your argument on a simulation involving at least 10
Multiple choice You take a quiz with 6 multiple choice questions. After you studied, you estimated that you would have about an 80% chance of getting any individual question right. What are your chances of getting them all right? Use at least 20 trials.
Cereal, again Suppose you really want the Hope Solo picture. How many boxes of cereal do you need to buy to be pretty sure of getting at least one? First, define what“pretty sure” means to you. Then run a simulation with at least 10 trials.
Cereal In the chapter’s example, 20% of the cereal boxes contained a picture of Hope Solo, 30% Danica Patrick, and the rest Blake Griffin. Suppose you buy five boxes of cereal. Estimate the probability that you end up with a complete set of the pictures. Your simulation should have at least 20
Two pair or three of a kind? When drawing five cards randomly from a deck, which is more likely, two pairs or three of a kind? A pair is exactly two of the same denomination.Three of a kind is exactly 3 of the same denomination.(Don’t count three 8’s as a pair—that’s 3 of a kind. And
Election You’re pretty sure that your candidate for class president has about 65% of the votes in the entire school.But you’re worried that only 100 students will show up to vote. How often will the underdog (the one with 35%support) win? To find out, you set up a simulation.a) Describe how you
Another wrong conclusion After simulating the spread of a disease, a researcher wrote, “24% of the people contracted the disease.” What should the correct conclusion be?
Wrong conclusion A Statistics student properly simulated the length of checkout lines in a grocery store and then reported, “The average length of the line will be 3.2 people.” What’s wrong with this conclusion?
More bad simulations Explain why each of the following simulations fails to model the real situation:a) Use random numbers 2 through 12 to represent the sum of the faces when two dice are rolled.b) Use a random integer from 0 through 5 to represent the number of boys in a family of 5 children.c)
Bad simulations Explain why each of the following simulations fails to model the real situation properly:a) Use a random integer from 0 through 9 to represent the number of heads when 9 coins are tossed.b) A basketball player takes a foul shot. Look at a random digit, using an odd digit to
Play it again, Sam In Exercise 12, you imagined playing the lottery by using random digits to decide what numbers to play. Is this a particularly good or bad strategy?Explain.
Play the lottery Some people play state-run lotteries by always playing the same favorite “lucky” numbers.Assuming that the lottery is truly random, is this strategy better, worse, or the same as choosing different numbers for each play? Explain.
Get rich Your state’s BigBucks Lottery prize has reached$100,000,000, and you decide to play. You have to pick five numbers between 1 and 60, and you’ll win if your numbers match those drawn by the state. You decide to pick your “lucky” numbers using a random number table.Which numbers do
Geography An elementary school teacher with 25 students plans to have each of them make a poster about two different states. The teacher first numbers the states(in alphabetical order, from 1-Alabama to 50-Wyoming), then uses a random number table to decide which states each student gets. Here are
Colorblind By some estimates, about 10% of all males have some color perception defect, most commonly red–green colorblindness. How would you assign random numbers to conduct a simulation based on this percentage?
Birth defects A study says that out of every 200 babies born in the world, 14 have some kind of major birth defect.How would you assign random numbers to conduct a simulation based on this proportion?
Games Many kinds of games people play rely on randomness.Cite three different methods commonly used in the attempt to achieve this randomness, and discuss the effectiveness of each.
The lottery Many states run lotteries, giving away millions of dollars if you match a certain set of winning numbers. How are those numbers determined? Do you think this method guarantees randomness? Explain.
Response variable, take two For the burger joint contest described in Exercise 4, how will you combine components to model a trial? What is the response variable?
Response variable For the board game described in Exercise 3, how will you combine components to model a trial? What is the response variable?
More components Your local burger joint gives away a game piece with each purchase. Game pieces are labeled Burger, Fries, and Shake and are equally likely to be received. You will simulate to estimate how many purchases you will need to collect the entire set to win a free meal. Identify the
Components Playing a board game, you are stuck in jail until you roll “doubles” (same numbers) on a pair of dice. You will simulate using random digits to estimate how many turns you expect to remain in jail. Identify the component if you were to run a simulation.
More random outcomes For each of the following scenarios, decide if the outcome is random.a) You enter a contest in which the winning ticket is selected from a large drum of entries. Was the winner of the contest random?b) When playing a board game, the number of spaces you move is decided by
Random outcomes For each of the following scenarios, decide if the outcome is random.a) Flip a coin to decide who takes out the trash. Is who takes out the trash random?b) A friend asks you to quickly name a professional sports team. Is the sports team named random?c) Names are selected out of a
Fifty-seven students participated in a lottery for a particularly desirable dorm room—a large triple close to the student center. Twenty of the participants were members of the same varsity team. When all three winners were members of the team, the other students cried foul.Question: Could an
The game of 21 can be played with an ordinary 6-sided die. Competitors each roll the die repeatedly, trying to get the highest total less than or equal to 21. If your total exceeds 21, you lose.Suppose your opponent has rolled an 18. Your task is to try to beat him by getting more than 18 points
Chips A start-up company has developed an improved electronic chip for use in laboratory equipment. The company needs to project the manufacturing cost, so it develops a spreadsheet model that takes into account the purchase of production equipment, overhead, raw materials, depreciation,
Down the drain Most water tanks have a drain plug so that the tank may be emptied when it’s to be moved or repaired. How long it takes a certain size of tank to drain depends on the size of the plug, as shown in the table.Create a model Plug Dia (in.) Drain Time (min.) -IN 314 11 1 2 1112 140 80
Profit How are a company’s profits related to its sales?Let’s examine data from 71 large U.S. corporations.All amounts are in millions of dollars.a) Histograms of Profits and Sales and histograms of the logarithms of Profits and Sales are seen below. Why are the re-expressed data better for
Vehicle weights The Minnesota Department of Transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed “weigh-in-motion” scale. After installation of the scale, a study was conducted to find out whether the scale’s
Williams vs. Texas Here are the average weights of the football team for the University of Texas for various years in the 20th century.a) Fit a straight line to the relationship of Weight by Year for Texas football players.b) According to these models, in what year will the predicted weight of the
Models Find the predicted value of y, using each model for x = 10. a) 20.8 In .x b) log 5 0.23x 17.1 - 1.66x
Football weights The Sears Cup was established in 1993 to honor institutions that maintain a broad-based athletic program, achieving success in many sports, both men’s and women’s. Since its Division III inception in 1995, the cup has been won by Williams College 15 of 17 years.Their football
Tobacco and alcohol Are people who use tobacco products more likely to consume alcohol? Here are data on household spending (in pounds) taken by the British government on 11 regions in Great Britain. Do tobacco and alcohol spending appear to be related? What questions do you have about these data?
Gasoline Since clean-air regulations have dictated the use of unleaded gasoline, the supply of leaded gas in New York state has diminished. The following table was given on the August 2001 New York State Math B exam, a statewide achievement test for high school studentsa) Create a linear model and
Lunchtime Does how long toddlers sit at the lunch table help predict how much they eat? The table and graph show the number of minutes the kids stayed at the table and the number of calories they consumed. Create and interpret a model for these data. Calories Time Calories Time 472 21.4 450 42.4
Twins Twins are often born at less than 9 months gestation.The graph from the Journal of the American Medical Association (JAMA) shows the rate of preterm twin births in the United States over the past 20 years.In this study, JAMA categorized mothers by the level of prenatal medical care they
French Consider the association between a student’s score on a French vocabulary test and the weight of the student. What direction and strength of correlation would you expect in each of the following situations?Explain.a) The students are all in third grade.b) The students are in third through
Modeling jumps 2012 Here are the summary statistics for the Olympic long jumps and high jumps displayed in the previous exercise.a) Write the equation of the line of regression for estimating High Jump from Long Jump.b) Interpret the slope of the line.c) In a year when the long jump is 8.9 m, what
Jumps 2012 How are Olympic performances in various events related? The plot shows winning long-jump and high-jump distances, in meters, for the Summer Olympics from 1912 through 2012.a) Describe the association.b) Do long-jump performances somehow influence the high-jumpers? How do you account for
Depression The September 1998 issue of the American Psychologist published an article by Kraut et al. that reported on an experiment examining “the social and psychological impact of the Internet on 169 people in 73 households during their first 1 to 2 years online.”In the experiment, 73
Winter in the city Summary statistics for the data relating the latitude and average January temperature for 55 large U.S. cities are given bea) What percent of the variation in January Temperature can be explained by variation in Latitude?b) What is indicated by the fact that the correlation is
Correlations The study of U.S. cities in Exercise 25 found the mean January Temperature (degrees Fahrenheit), Altitude (feet above sea level), and Latitude(degrees north of the equator) for 55 cities. Here’s the correlation matrix:a) Which seems to be more useful in predicting January
U.S. cities Data from 50 large U.S. cities show the mean January Temperature and the Latitude. Describe what you see in the scatterplot. + 60 60 45 + Avg. Jan. Temp (F) 30 30 15+ + 30 35 40 45 Latitude (N)
Tips It’s commonly believed that people use tips to reward good service. A researcher for the hospitality industry examined tips and ratings of service quality from 2645 dining parties at 21 different restaurants. The correlation between ratings of service and tip percentages was 0.11. (Source:
No smoking? The downward trend in smoking you saw in the last exercise is good news for the health of babies, but will it ever stop?a) Explain why you can’t use the linear model you created in Exercise 22 to see when smoking during pregnancy will cease altogether.b) Create a model that could
Smoking and pregnancy 2011 The Child Trends Data Bank monitors issues related to children. The table shows a 50-state average of the percent of expectant mothers who smoked cigarettes during their pregnanciesa) Create a scatterplot and describe the trend you see.b) Find the correlation.c) How is
Big screen An electronics website collects data on the size of new HD flat panel televisions (measuring the diagonal of the screen in inches) to predict the cost(in hundreds of dollars). Which of these is most likely to be the slope of the regression line: 0.03, 0.3, 3, 30?Explain.
Improving trees In the last exercise, you saw that the linear model had some deficiencies. Let’s create a better model.a) Perhaps the cross-sectional area of a tree would be a better predictor of its age. Since area is measured in square units, try re-expressing the data by squaring the
How old is that tree? One can determine how old a tree is by counting its rings, but that requires either cutting the tree down or extracting a sample from the tree’s core.Can we estimate the tree’s age simply from its diameter?A forester measured 27 trees of the same species that had been cut
Crocodile lengths The ranges inhabited by the Indian gharial crocodile and the Australian saltwater crocodile overlap in Bangladesh. Suppose a very large crocodile skeleton is found there, and we wish to determine the species of the animal. Wildlife scientists have measured the lengths of the heads
Old Faithful again There is evidence that eruptions of Old Faithful can best be predicted by knowing the duration of the previous eruption.a) Describe what you see in the scatterplot of Intervals between eruptions vs. Duration of the previous eruptionb) Write the equation of the line of best fit.
Colorblind Although some women are colorblind, this condition is found primarily in men. Why is it wrong to say there’s a strong correlation between Sex and Colorblindness?
Cars, one more time! Can we predict the Horsepower of the engine that manufacturers will put in a car by knowing the Weight of the car? Here are the regression analysis and residuals plot:a) Write the equation of the regression line.b) Do you think the car’s Weight is measured in pounds or
Cars, revisited Look again at the correlation table for cars in the previous exercise.a) Which two variables in the table exhibit the strongest association?b) Is that strong association necessarily cause-and-effect?Offer at least two explanations why that association might be so strong.c) Engine
Cars, correlations What factor most explains differences in Fuel Efficiency among cars? Below is a correlation matrix exploring that relationship for the car’s Weight, Horsepower, engine size (Displacement), and number of Cylinders. (Data in Cars)a) Which factor seems most strongly associated
Cramming One Thursday, researchers gave students enrolled in a section of basic Spanish a set of 50 new vocabulary words to memorize. On Friday, the students took a vocabulary test. When they returned to class the following Monday, they were retested—without advance warning. Here are the test
Traffic Highway planners investigated the relationship between traffic Density (number of automobiles per mile)and the average Speed of the traffic on a moderately large city thoroughfare. The data were collected at the same location at 10 different times over a span of 3 months.They found a mean
Grades A Statistics instructor created a linear regression equation to predict students’ final exam scores from their midterm exam scores. The regression equation was Fin = 10 + 0.9 Mid.a) If Susan scored a 70 on the midterm, what did the instructor predict for her score on the final?b) Susan got
A manatee model 2013 Continue your analysis of the manatee situation from the previous exercise.a) Create a linear model of the association between Manatee Deaths and Powerboat Registrations.b) Interpret the slope of your model.c) Interpret the y-intercept of your model.d) How accurately did your
Manatees 2013 Marine biologists warn that the growing number of powerboats registered in Florida threatens the existence of manatees. The data below come from the Florida Fish and Wildlife Conservation Commission(myfwc.com/research/manatee/) and the National Marine Manufacturers Association
Acid rain Biologists studying the effects of acid rain on wildlife collected data from 163 streams in the Adirondack Mountains. They recorded the pH (acidity) of the water and the BCI, a measure of biological diversity, and they calculated R2 = 27%. Here’s a scatterplot of BCI against pH:a) What
Dow Jones 2014 The Dow Jones stock index measures the performance of the stocks of America’s largest companies(finance.yahoo.com). A regression of the Dow prices on years 1972–2014 looks like this:a) What is the correlation between Dow Index and Year?b) Write the regression equation.c) Explain
More twins 2014? In January 2012, the New York Times published a story called Twin Births in the U.S., Like Never Before, in which they reported a 76 percent increase in the rate of twin births from 1980 to 2009. Here are the number of twins born each year (per 1000 live births).
Vineyards again Instead of Age, perhaps the Size of the vineyard (in acres) is associated with the price of the wines. Look at the scatterplot (Data in Vineyards full):a) Do you see any evidence of an association?b) What concern do you have about this scatterplot?c) If the red “+” data point is
Vineyards, more information Here are the scatterplot and regression analysis for Case Prices of 36 wines from vineyards in the Finger Lakes region of New York State and the Ages of the vineyards. (Data in Vineyards full):a) Does it appear that vineyards in business longer get higher prices for
Togetherness Are good grades in high school associated with family togetherness? A random sample of 142 high school students was asked how many meals per week their families ate together. Their responses produced a mean of 3.78 meals per week, with a standard deviation of 2.2. Researchers then
College Every year, US News and World Report publishes a special issue on many U.S. colleges and universities. The scatterplots below have Student/Faculty Ratio (number of students per faculty member) for the colleges and universities on the y-axes plotted against 4 other variables. The correct
Tree growth A 1996 study examined the growth of grapefruit trees in Texas, determining the average trunk Diameter (in inches) for trees of varying Ages:a) Fit a linear model to these data. What concerns do you have about the model?b) If data had been given for individual trees instead of averages,
Years to live, 2013 Insurance companies and other organizations use actuarial tables to estimate the remaining lifespans of their customers. On the next page are the estimated additional years of life for black males in the United States, according to a 2013 National Vital Statistics Report.
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