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business statistics in practice
The Practice Of Statistics 5th Edition Daren S. Starnes, Josh Tabor - Solutions
The most important advantage of experiments over observational studies is that(a) experiments are usually easier to carry out.(b) experiments can give better evidence of causation.(c) confounding cannot happen in experiments.(d) an observational study cannot have a response variable.(e)
A TV station wishes to obtain information on the TV viewing habits in its market area. The market area contains one city of population 170,000, another city of 70,000, and four towns of about 5000 inhabitants each.The station suspects that the viewing habits may be different in larger and smaller
Bias in a sampling method is(a) any difference between the sample result and the truth about the population.(b) the difference between the sample result and the truth about the population due to using chance to select a sample.(c) any difference between the sample result and the truth about the
You wonder if TV ads are more effective when they are longer or repeated more often or both. So you design an experiment. You prepare 30-second and 60-second ads for a camera. Your subjects all watch the same TV program, but you assign them at random to four groups. One group sees the 30-second ad
A researcher wishes to compare the effects of two fertilizers on the yield of soybeans. She has 20 plots of land available for the experiment, and she decides to use a matched pairs design with 10 pairs of plots.To carry out the random assignment for this design, the researcher should(a) use a
You want to know the opinions of American high school teachers on the issue of establishing a national proficiency test as a prerequisite for graduation from high school. You obtain a list of all high school teachers belonging to the National Education Association(the country’s largest
Elephants sometimes damage trees in Africa. It turns out that elephants dislike bees. They recognize beehives in areas where they are common and avoid them. Can this be used to keep elephants away from trees? Will elephant damage be less in trees with hives? Will even empty hives keep elephants
A New York Times article on public opinion about steroid use in baseball discussed the results of a sample survey. The survey found that 34% of adults think that at least half of Major League Baseball(MLB) players “use steroids to enhance their athletic performance.” Another 36% thought that
Many people start their day with a jolt of caffeine from coffee or a soft drink. Most experts agree that people who take in large amounts of caffeine each day may suffer from physical withdrawal symptoms if they stop ingesting their usual amounts of caffeine.Researchers recruited 11 volunteers who
You look at real estate ads for houses in Sarasota, Florida. Many houses range from $200,000 to$400,000 in price. The few houses on the water, however, have prices up to $15 million. Which of the following statements best describes the distribution of home prices in Sarasota?(a) The distribution is
A child is 40 inches tall, which places her at the 90th percentile of all children of similar age. The heights for children of this age form an approximately Normal distribution with a mean of 38 inches. Based on this information, what is the standard deviation of the heights of all children of
A large set of test scores has mean 60 and standard deviation 18. If each score is doubled, and then 5 is subtracted from the result, the mean and standard deviation of the new scores are(a) mean 115; std. dev. 31. (d) mean 120; std. dev. 31.(b) mean 115; std. dev. 36. (e) mean 120; std. dev.
For a certain experiment, the available experimental units are eight rats, of which four are female(F1, F2, F3, F4) and four are male (M1, M2, M3, M4). There are to be four treatment groups, A, B, C, and D. If a randomized block design is used, with the experimental units blocked by gender, which
For a biology project, you measure the weight in grams (g) and the tail length in millimeters (mm) of a group of mice. The equation of the least-squares line for predicting tail length from weight is predicted tail length = 20 + 3 × weight Which of the following is not correct?(a) The slope is 3,
The figure below shows a Normal density curve.Which of the following gives the best estimates for the mean and standard deviation of this Normal distribution?(a) m = 200, s = 50 (d) m = 225, s = 25 (b) m = 200, s = 25 (e) m = 225, s = 275 (c) m = 225, s = 50 0.010 0.008 0.006 0.004 0.002 0.000 50
The owner of a chain of supermarkets notices that there is a positive correlation between the sales of beer and the sales of ice cream over the course of the previous year. During seasons when sales of beer were above average, sales of ice cream also tended to be above average. Likewise, during
Here are the IQ scores of 10 randomly chosen fifthgrade students:145 139 126 122 125 130 96 110 118 118 Which of the following statements about this data set is not true?(a) The student with an IQ of 96 is considered an outlier by the 1.5 × IQR rule.(b) The five-number summary of the 10 IQ scores
Before he goes to bed each night, Mr. Kleen pours dishwasher powder into his dishwasher and turns it on. Each morning, Mrs. Kleen weighs the box of dishwasher powder. From an examination of the data, she concludes that Mr. Kleen dispenses a rather consistent amount of powder each night.Which of the
The General Social Survey (GSS), conducted by the National Opinion Research Center at the University of Chicago, is a major source of data on social attitudes in the United States. Once each year, 1500 adults are interviewed in their homes all across the country. The subjects are asked their
You are planning an experiment to determine the effect of the brand of gasoline and the weight of a car on gas mileage measured in miles per gallon. You will use a single test car, adding weights so that its total weight is 3000, 3500, or 4000 pounds. The car will drive on a test track at each
A linear regression was performed using the five following data points: A(2, 22), B(10, 4), C(6, 14), D(14, 2), E(18, −4). The residual for which of the five points has the largest absolute value?(a) A (b) B (c) C (d) D (e) E
The frequency table below summarizes the times in the last month that patients at the emergency room of a small-city hospital waited to receive medical attention.Waiting time Frequency Less than 10 minutes 5 At least 10 but less than 20 minutes 24 At least 20 but less than 30 minutes 45 At least 30
Boxplots of two data sets are shown.Based on the boxplots, which statement below is true?(a) The range of both plots is about the same.(b) The means of both plots are approximately equal.(c) Plot 2 contains more data points than Plot 1.(d) The medians are approximately equal.(e) Plot 1 is more
The manufacturer of exercise machines for fitness centers has designed two new elliptical machines that are meant to increase cardiovascular fitness.The two machines are being tested on 30 volunteers at a fitness center near the company’s headquarters. The volunteers are randomly assigned to one
Those who advocate for monetary incentives in a work environment claim that this type of incentive has the greatest appeal because it allows the winners to do what they want with their winnings.Those in favor of tangible incentives argue that money lacks the emotional appeal of, say, a weekend for
In retail stores, there is a lot of competition for shelf space. There are national brands for most products, and many stores carry their own line of in-house brands, too. Since shelf space is not infinite, the question is how many linear feet to allocate to each product and which shelf (top,
Interpret probability as a long-run relative frequency.
Use simulation to model chance behavior.
According to the Book of Odds Web site www.bookofodds.com, the probability that a randomly selected U.S. adult usually eats breakfast is 0.61.(a) Explain what probability 0.61 means in this setting.(b) Why doesn’t this probability say that if 100 U.S. adults are chosen at random, exactly 61 of
Probability is a measure of how likely an outcome is to occur. Match one of the probabilities that follow with each statement. Be prepared to defend your answer.0 0.01 0.3 0.6 0.99 1(a) This outcome is impossible. It can never occur.(b) This outcome is certain. It will occur on every trial.(c) This
Refer to the golden ticket parking lottery example. At the following month’s school assembly, the two lucky winners were once again members of the AP® Statistics class.This raised suspicions about how the lottery was being conducted. How would you modify the simulation in the example to estimate
Refer to the NASCAR and breakfast cereal example. What if the cereal company decided to make it harder to get some drivers’ cards than others? For instance, suppose the chance that each card appears in a box of the cereal is Jeff Gordon, 10%; Dale Earnhardt, Jr., 30%; Tony Stewart, 20%; Danica
Liar, liar! Sometimes police use a lie detector (also known as a polygraph) to help determine whether a suspect is telling the truth. A lie detector test isn’t foolproof—sometimes it suggests that a person is lying when he or she is actually telling the truth (a“false positive”). Other
Mammograms Many women choose to have annual mammograms to screen for breast cancer after age 40. A mammogram isn’t foolproof. Sometimes the test suggests that a woman has breast cancer when she really doesn’t (a “false positive”). Other times the test says that a woman doesn’t have breast
Genetics Suppose a married man and woman both carry a gene for cystic fibrosis but don’t have the disease themselves. According to the laws of genetics, the probability that their first child will develop cystic fibrosis is 0.25.(a) Explain what this probability means.(b) If the couple has 4
Texas hold ’em In the popular Texas hold ’em variety of poker, players make their best five-card poker hand by combining the two cards they are dealt with three of five cards available to all players. You read in a book on poker that if you hold a pair (two cards of the same rank) in your hand,
Spinning a quarter With your forefinger, hold a new quarter (with a state featured on the reverse)upright, on its edge, on a hard surface. Then flick it with your other forefinger so that it spins for some time before it falls and comes to rest. Spin the coin a total of 25 times, and record the
Nickels falling over You may feel it’s obvious that the probability of a head in tossing a coin is about 1/2 because the coin has two faces. Such opinions are not always correct. Stand a nickel on edge on a hard, flat surface. Pound the surface with your hand so that the nickel falls over. Do
Free throws The figure below shows the results of a virtual basketball player shooting several free throws.Explain what this graph says about chance behavior in the short run and long run. % Hits 50 100 0 1 100 Shots
Keep on tossing The figure below shows the results of two different sets of 5000 coin tosses. Explain what this graph says about chance behavior in the short run and the long run. Proportion of heads 1.0 0.9 0.8 T 0.7- 0.6- 0.5 0.4- 0.3 0.2- 0.1 0.0 1 5 10 50 100 500 1000 5000 Number of tosses
Due for a hit A very good professional baseball player gets a hit about 35% of the time over an entire season. After the player failed to hit safely in six straight at-bats, a TV commentator said, “He is due for a hit by the law of averages.” Is that right? Why?
Cold weather coming A TV weather man, predicting a colder-than-normal winter, said, “First, in looking at the past few winters, there has been a lack of really cold weather. Even though we are not supposed to use the law of averages, we are due.” Do you think that “due by the law of
Playing “Pick 4” The Pick 4 games in many state lotteries announce a four-digit winning number each day. You can think of the winning number as a four-digit group from a table of random digits. You win (or share) the jackpot if your choice matches the winning number. The winnings are divided
An unenlightened gambler(a) A gambler knows that red and black are equally likely to occur on each spin of a roulette wheel. He observes five consecutive reds occur and bets heavily on black at the next spin. Asked why, he explains that black is “due by the law of averages.” Explain to the
Free throws A basketball player has probability 0.75 of making a free throw. Explain how you would use each chance device to simulate one free throw by the player.(a) A standard deck of playing cards(b) Table D of random digits(c) A calculator or computer’s random integer generator
Stoplight On her drive to work every day, Ilana passes through an intersection with a traffic light.The light has probability 1/3 of being green when she gets to the intersection. Explain how you would use each chance device to simulate whether the light is red or green on a given day.(a) A
Simulation blunders Explain what’s wrong with each of the following simulation designs.(a) A roulette wheel has 38 colored slots—18 red, 18 black, and 2 green. To simulate one spin of the wheel, let numbers 00 to 18 represent red, 19 to 37 represent black, and 38 to 40 represent green.(b) About
Simulation blunders Explain what’s wrong with each of the following simulation designs.(a) According to the Centers for Disease Control and Prevention, about 36% of U.S. adults were obese in 2012. To simulate choosing 8 adults at random and seeing how many are obese, we could use two digits.Let
Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer.(a) According to a recent poll, 75% of American adults regularly recycle. To simulate choosing a random sample of 100 U.S. adults and seeing how many of them recycle, roll a 4-sided die 100
Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer.(a) According to a recent survey, 50% of people aged 13 and older in the United States are addicted to texting. To simulate choosing a random sample of 20 people in this population and seeing how
Airport security The Transportation Security Administration(TSA) is responsible for airport safety.On some flights, TSA officers randomly select passengers for an extra security check prior to boarding. One such flight had 76 passengers—12 in first class and 64 in coach class. Some passengers
Scrabble In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles.There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Cait chooses her 7 tiles and is surprised to discover that all of them are vowels. We can use a simulation to see if this result
The birthday problem What’s the probability that in a randomly selected group of 30 unrelated people, at least two have the same birthday? Let’s make two assumptions to simplify the problem.First, we’ll ignore the possibility of a February 29 birthday. Second, we assume that a randomly chosen
Monty Hall problem In Parade magazine, a reader posed the following question to Marilyn vos Savant and the “Ask Marilyn” column:Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the
Recycling Do most teens recycle? To find out, an AP® Statistics class asked an SRS of 100 students at their school whether they regularly recycle. In the sample, 55 students said that they recycle. Is this convincing evidence that more than half of the students at the school would say they
Brushing teeth, wasting water? A recent study reported that fewer than half of young adults turn off the water while brushing their teeth. Is the same true for teenagers? To find out, a group of statistics students asked an SRS of 60 students at their school if they usually brush with the water
Color-blind men About 7% of men in the United States have some form of red-green color blindness.Suppose we randomly select 4 U.S. adult males. What’s the probability that at least one of them is red-green color-blind? Design and carry out a simulation to answer this question. Follow the
Lotto In the United Kingdom’s Lotto game, a player picks six numbers from 1 to 49 for each ticket. Rosemary bought one ticket for herself. She had the lottery computer randomly select the six numbers. When the six winning numbers were drawn, Rosemary was surprised to find that none of these
Color-blind men Refer to Exercise 25. Suppose we randomly select one U.S. adult male at a time until we find one who is red-green color-blind. Should we be surprised if it takes us 20 or more men? Design and carry out a simulation to answer this question. Follow the four-step process.
Scrabble Refer to Exercise 20. About 3% of the time, the first player in Scrabble can “bingo” by playing all 7 tiles on the first turn. Should we be surprised if it takes 30 or more games for this to happen?Design and carry out a simulation to answer this question. Follow the four-step process.
Random assignment Researchers recruited 20 volunteers—8 men and 12 women—to take part in an experiment. They randomly assigned the subjects into two groups of 10 people each. To their surprise, 6 of the 8 men were randomly assigned to the same treatment. Should they be surprised? Design and
Taking the train According to New Jersey Transit, the 8:00 a.m. weekday train from Princeton to New York City has a 90% chance of arriving on time. To test this claim, an auditor chooses 6 weekdays at random during a month to ride this train. The train arrives late on 2 of those days. Does the
You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0.11. This means that(a) in every 100 bridge deals, each player has one ace exactly 11 times.(b) in 1 million bridge deals, the number of deals on which each player has one ace will
If I toss a fair coin five times and the outcomes are TTTTT, then the probability that tails appears on the next toss is(a) 0.5. (c) greater than 0.5. (e) 1.(b) less than 0.5. (d) 0.
To simulate the number of makes in 10 shot attempts, you would perform the simulation as follows:(a) Use 10 random one-digit numbers, where 0–4 are a make and 5–9 are a miss.(b) Use 10 random two-digit numbers, where 00–46 are a make and 47–99 are a miss.(c) Use 10 random two-digit numbers,
Twenty-five repetitions of the simulation were performed.The simulated number of makes in each set of 10 shots was recorded on the dotplot below. What is the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts?(a) 5/10 (b) 3/10 (c) 12/25 (d) 3/25 (e) 47/100 2 3 4 5
Suppose this player attempts 10 shots in a game and only makes 3 of them. Does this provide convincing evidence that she is less than a 47% shooter?(a) Yes, because 3/10 (30%) is less than 47%.(b) Yes, because she never made 47% of her shots in the simulation.(c) No, because it is plausible that
Ten percent of U.S. households contain 5 or more people. You want to simulate choosing a household at random and recording “Yes” if it contains 5 or more people. Which of these are correct assignments of digits for this simulation?(a) Odd = Yes; Even = No(b) 0 = Yes; 1–9 = No(c) 0–5 = Yes;
Are you feeling stressed? (4.1) A Gallup Poll asked whether people experienced stress “a lot of the day yesterday.” About 41 percent said they did. Gallup’s report said, “Results are based on telephone interviews conducted … Jan. 1–Dec. 31, 2012, with a random sample of 353,564 adults
Waiting to park (1.3, 4.2) Do drivers take longer to leave their parking spaces when someone is waiting?Researchers hung out in a parking lot and collected some data. The graphs and numerical summaries below display information about how long it took drivers to exit their spaces.(a) Write a few
Describe a probability model for a chance process.
Use basic probability rules, including the complement rule and the addition rule for mutually exclusive events.
Use a two-way table or Venn diagram to model a chance process and calculate probabilities involving two events.
Use the general addition rule to calculate probabilities.
Role-playing games Computer games in which the players take the roles of characters are very popular. They go back to earlier tabletop games such as Dungeons&Dragons. These games use many different types of dice.A four-sided die has faces with 1, 2, 3, and 4 spots.(a) List the sample space for
Tossing coins Imagine tossing a fair coin 3 times.(a) What is the sample space for this chance process?(b) What is the assignment of probabilities to outcomes in this sample space?
Role-playing games Refer to Exercise 39. Define event A: sum is 5. Find P(A).
Tossing coins Refer to Exercise 40. Define event B:get more heads than tails. Find P(B).
Probability models? In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. If not, give specific reasons for your answer.(a) Roll a 6-sided die and record the count of spots
Rolling a die The following figure displays several possible probability models for rolling a die. Some of the models are not legitimate. That is, they do not obey the rules. Which are legitimate and which are not? In the case of the illegitimate models, explain what is wrong. Probability Outcome
Blood types All human blood can be typed as one of O, A, B, or AB, but the distribution of the types varies a bit with race. Here is the distribution of the blood type of a randomly chosen black American:Blood type: O A B AB Probability: 0.49 0.27 0.20 ?pg 308(a) What is the probability of type AB
Languages in Canada Canada has two official languages, English and French. Choose a Canadian at random and ask, “What is your mother tongue?” Here is the distribution of responses, combining many separate languages from the broad Asia/Pacific region:7 Language: English French Asian/Pacific
Education among young adults Choose a young adult (aged 25 to 29) at random. The probability is 0.13 that the person chosen did not complete high school, 0.29 that the person has a high school diploma but no further education, and 0.30 that the person has at least a bachelor’s degree.(a) What
Preparing for the GMAT A company that offers courses to prepare students for the Graduate Management Admission Test (GMAT) has the following information about its customers: 20% are currently undergraduate students in business; 15% are undergraduate students in other fields of study; 60% are
Who eats breakfast? Students in an urban school were curious about how many children regularly eat breakfast. They conducted a survey, asking, “Do yo eat breakfast on a regular basis?” All 595 students in the school responded to the survey. The resulting data are shown in the two-way table
Sampling senators The two-way table below describes the members of the U.S Senate in a recent year.Male Female Democrats 47 13 Republicans 36 4 If we select a U.S. senator at random, what’s the probability that the senator is(a) a Democrat?(b) a female?(c) a female and a Democrat?(d) a female or
Roulette An American roulette wheel has 38 slots with numbers 1 through 36, 0, and 00, as shown in the figure. Of the numbered slots, 18 are red, 18 are black, and 2—the 0 and 00—are green. When the wheel is spun, a metal ball is dropped onto the middle of the wheel. If the wheel is balanced,
Playing cards Shuffle a standard deck of playing cards and deal one card. Define events J: getting a jack, and R: getting a red card.(a) Construct a two-way table that describes the sample space in terms of events J and R.(b) Find P(J) and P(R).(c) Describe the event “J and R” in words. Then
Who eats breakfast? Refer to Exercise 49.(a) Construct a Venn diagram that models the chance process using events B: eats breakfast regularly, and M: is male.(b) Find P(B ∪ M). Interpret this value in context.(c) Find P(BC ∩ MC). Interpret this value in context.54. Sampling senators Refer to
Facebook versus YouTube A recent survey suggests that 85% of college students have posted a profile on Facebook, 73% use YouTube regularly, and 66% do both. Suppose we select a college student at random.(a) Make a two-way table for this chance process.(b) Construct a Venn diagram to represent this
Mac or PC? A recent census at a major university revealed that 40% of its students mainly used Macintosh computers (Macs). The rest mainly used PCs. At the time of the census, 67% of the school’s students were undergraduates. The rest were graduate students.In the census, 23% of respondents were
In government data, a household consists of all occupants of a dwelling unit. Choose an American household at random and count the number of people it contains. Here is the assignment of probabilities for the outcome:Number of persons: 1 2 3 4 5 6 7+Probability: 0.25 0.32 ??? ??? 0.07 0.03 0.01 The
In a sample of 275 students, 20 say they are vegetarians.Of the vegetarians, 9 eat both fish and eggs, 3 eat eggs but not fish, and 7 eat neither. Choose one of the vegetarians at random. What is the probability that the chosen student eats fish or eggs?(a) 9/20 (c) 22/20 (e) 22/275(b) 13/20 (d)
The most common bet in craps is the “pass line.” A pass line bettor wins immediately if either a 7 or an 11 comes up on the first roll. This is called a natural.What is the probability of a natural?(a) 2/36 (c) 8/36 (e) 20/36(b) 6/36 (d) 12/36
If a player rolls a 2, 3, or 12, it is called craps. What is the probability of getting craps or an even sum on one roll of the dice?(a) 4/36 (c) 20/36 (e) 32/36(b) 18/36 (d) 22/36
Crawl before you walk (3.2) At what age do babies learn to crawl? Does it take longer to learn in the winter, when babies are often bundled in clothes that restrict their movement? Perhaps there might even be an association between babies’ crawling age and the average temperature during the month
Treating low bone density (4.2) Fractures of the spine are common and serious among women with advanced osteoporosis (low mineral density in the bones). Can taking strontium ranelate help? A large medical trial assigned 1649 women to take either strontium ranelate or a placebo each day. All of the
Calculate and interpret conditional probabilities.
Use the general multiplication rule to calculate probabilities.
Use tree diagrams to model a chance process and calculate probabilities involving two or more events.
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