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Questions and Answers of
Business Statistics
Rolling dice. Suppose you roll two casino dice, as in Example 2. What is the probability that the sum of the spots on the up-faces is 7? 11? 7 or 11?
Web-based exercise. Search the Web for a recent poll in which the sample statistic is a proportion, for example, the proportion in the sample responding “Yes” to a question. Calculate a 95%
Web-based exercise. Results from the Behavioral Risk Factor Surveillance System (BRFSS) can be found at apps.nccd.cdc.gov/brfss/.Find the sample proportion of college graduates in your state who
Web-based exercise. If you go to the Centers for Disease Control and PreventionWeb site, you will find that the proportion of college graduates in California who engaged in binge drinking in 2006 is
A sampling distribution, continued. Exercise 21.33 presents 50 sample means x from 50 random samples of size 100. Using a calculator, find the mean and standard deviation of these 50 values. Then
Will they charge more? In Exercise 21.32, you carried out the calculations for a confidence interval based on a bank’s experiment in changing the rules for its credit cards. You ought to ask some
A sampling distribution. Exercise 21.31 concerns the mean of the random numbers generated by a computer program. The mean is supposed to be 0.5 because the numbers are supposed to be spread at random
Will they charge more? A bank wonders whether omitting the annual credit card fee for customers who charge at least $2500 in a year will increase the amount charged on its credit cards. The bank
Testing a random number generator. Our statistical software has a “random number generator” that is supposed to produce numbers scattered at random between 0 to 1. If this is true, the numbers
Blood pressure. A randomized comparative experiment studied the effect of diet on blood pressure. Researchers divided 54 healthy white males at random into two groups. One group received a calcium
Averages versus individuals. Scores on the ACT college entrance examination vary Normally with mean μ = 18 and standard deviation σ = 6. The range of reported scores is 1 to 36.(a) What range
IQ test scores. Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:114 100 104 89 102 91 114 114 103 105 108 130 120 132 111 128 118 119 86 72 111 103 74 112 107 103
The idea of a sampling distribution. Figure 21.1 (page 458) shows the idea of the sampling distribution of a sample proportion ^p in picture form.Draw a similar picture that shows the idea of the
Safe margin of error. The margin of error z∗^p(1−^p)/n is 0 when^p is 0 or 1 and is largest when ^p is 1/2. To see this, calculate ^p(1 − ^p) for^p= 0, 0.1, 0.2, . . . , 0.9, and 1. Plot your
Estimating unemployment. The Bureau of Labor Statistics (BLS)uses 90% confidence in presenting unemployment results from the monthly Current Population Survey (CPS). The January 2008 survey
Unhappy HMO patients. How likely are patients who file complaints with a health maintenance organization (HMO) to leave the HMO? In one year, 639 of the more than 400,000 members of a large New
The effect of confidence level. An October 2007 Los Angeles Times Poll found that 52% of its sample of 1209 adults preferred social spending to cutting taxes. Use this poll result and Table 21.1 to
Illegal immigrants. Exercise 21.8 reports a New York Times Poll that found that 776 in a random sample of 1125 American adults said they believe illegal immigrants should “be prosecuted and
Gun safety. Exercise 21.7 reports a Gallup Poll in which 425 of a random sample of 1012 adults thought that having a gun in the house makes it a safer place. Give a 90% confidence interval for the
Simulating confidence intervals. In Exercise 21.19, you found the recipe for a 68% confidence interval for a population proportion p. Suppose that (unknown to anyone) 60% of the voters in her
68% confidence. We used the 95 part of the 68–95–99.7 rule to give a recipe for a 95% confidence interval for a population proportion p.(a) Use the 68 part of the rule to give a recipe for a 68%
The quick method. The quick method of Chapter 3 (pages 42–43) uses^p± 1/√n as a rough recipe for a 95% confidence interval for a population proportion.The margin of error from the quick method
Do you jog? Suppose that 10% of all adults jog. An opinion poll asks an SRS of 400 adults if they jog.(a) What is the sampling distribution of the proportion ^p in the sample who jog?(b) According to
Harley motorcycles. Harley-Davidson motorcycles make up 14% of all the motorcycles registered in the United States. You plan to interview an SRS of 600 motorcycle owners.(a) What is the sampling
Teens and their TV sets. The New York Times and CBS News conducted a nationwide poll of 1048 randomly selected 13- to 17-yearolds.Of these teenagers, 692 had a television in their room. Also, of the
Count Buffon’s coin. The 18th-century French naturalist Count Buffon tossed a coin 4040 times. He got 2048 heads. Give a 95% confidence interval for the probability that Buffon’s coin lands heads
Don’t forget the basics. The Behavioral Risk Factor Surveillance System(BRFSS) survey found that 279 individuals in its 2006 random sample of 2166 college graduates in California said they had
Tossing a thumbtack. If you toss a thumbtack on a hard surface, what is the probability that it will land point up? Estimate this probability p by tossing a thumbtack 100 times. The 100 tosses are an
Random digits. We know that the proportion of 0s among a large set of random digits is p = 0.1 because all 10 possible digits are equally probable.The entries in a table of random digits are a sample
The effect of sample size. An October 2007 Los Angeles Times Poll found that 52% of its sample preferred social spending to cutting taxes. Give a 95% confidence interval for the proportion of all
Gun safety. In Exercise 21.7, you gave a 95% confidence interval based on a random sample of n = 1012 adults. How large a sample would be needed to get a margin of error half as large as the one in
Illegal immigrants. A May 2007 New York Times Poll on illegal immigrants interviewed 1125 randomly selected American adults.Of those in the sample, 776 said they believe illegal immigrants
Gun safety. An October 2004 Gallup Poll asked a sample of 1012 adults whether they thought that having a gun in the house makes it a safer place to be or a more dangerous place to be. The number who
The schools’ most serious problem. Results from a Gallup Youth Survey reveal that teens most often mention “violence, fighting, and school safety” when asked to name the biggest problem their
Fire the coach? A college president says, “99% of the alumni support my firing of Coach Boggs.” You contact an SRS of 200 of the college’s 15,000 living alumni and find that 66 of them support
A student survey. Tonya wants to estimate what proportion of the students in her dormitory like the dorm food. She interviews an SRS of 50 of the 175 students living in the dormitory. She finds that
Blood pressure of executives. The medical director of a large company looks at the medical records of 72 executives between the ages of 35 and 44 years. He finds that the mean systolic blood pressure
Gambling on sports. A December 2007 Gallup Poll consisting of a random sample of 1027 adult Americans found that 17% had gambled on sports in the last 12 months. Find a 99% confidence interval for
Gambling on sports. A December 2007 Gallup Poll consisting of a random sample of 1027 adult Americans found that 17% had gambled on sports in the last 12 months. Find a 95% confidence interval for
Web-based exercise. Oddsmakers often list the odds for certain sporting events on the Web. For example, one can find the current odds of winning the next Super Bowl for each NFL team. We found a list
Generating a sampling distribution. Let us illustrate the idea of a sampling distribution in the case of a very small sample from a very small Notes and Data Sources 409 population. The population is
Applying to college. You ask an SRS of 1500 college students whether they applied for admission to any other college. Suppose that in fact 35% of all college students applied to colleges besides the
Do you jog? An opinion poll asks an SRS of 1500 adults, “Do you happen to jog?” Suppose (as is approximately correct) that the population proportion who jog is p = 0.15. In a large number of
Airplane safety (optional). In the setting of Exercise 18.16, what is the probability of getting a sample in which fewer than 60% think that airplanes would be safer if pilots carried guns? (Use
Immigration (optional). In the setting of Exercise 18.15, what is the probability of getting a sample in which more than 51% of those sampled think that the level of immigration to this country
Airplane safety. Suppose that 62% of all adults think that airplanes would be safer places if pilots carried guns. An opinion poll plans to ask an SRS of 1009 adults about airplane safety. The
Immigration. Suppose that 55% of all adult American think that the level of immigration to this country should be decreased. An opinion poll interviews 1007 randomly chosen Americans and records the
Legitimate probabilities? 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
Colors of M&M’s. If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of
Roulette. A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36.The slots 0 and 00 are colored green, 18 of the others are red, and 18 are black.The dealer spins the wheel and at the same time
More tetrahedral dice. Tetrahedral dice are described in Exercise 18.9.Give a probability model for rolling two such dice. That is, write down all possible outcomes and give a probability to each.
Birth order. A couple plan to have three children. There are 8 possible arrangements of girls and boys. For example, GGB means the first two children are girls and the third child is a boy. All 8
High school academic rank. Select a first-year college student at random and ask what his or her academic rank was in high school. Here are the probabilities, based on proportions from a large sample
Our next president? A Gallup Poll on Presidents Day 2008 interviewed a random sample of 1007 adult Americans. Those in the sample were asked which former president they would like to bring back as
Land in Canada. Choose an acre of land in Canada at random. The probability is 0.45 that it is forest and 0.03 that it is pasture.(a) What is the probability that the acre chosen is not forested?(b)
Causes of death. Government data assign a single cause for each death that occurs in the United States. The data show that the probability is 0.27 that a randomly chosen death was due to heart
Moving up. A sociologist studying social mobility in Denmark finds that the probability that the son of a lower-class father remains in the lower class is 0.46. What is the probability that the son
Teen opinion poll. Refer to Example 4. Using the 68–95–99.7 rule, what is the probability that more than 54.4%say “Yes”?
Selling cars. Bill sells new cars for a living. On a weekday afternoon, he will deal with 1 customer with probability 0.2, 2 customers with probability 0.5, and 3 customers with probability 0.3. Each
Predicting the winner. There are 11 teams in the Big Ten athletic conference. Here’s one set of personal probabilities for next year’s basketball Part III Projects 451 champion: Michigan State
Mendel’s peas. Gregor Mendel used garden peas in some of the experiments that revealed that inheritance operates randomly. The seed color of Mendel’s peas can be either green or yellow. Suppose
Models legitimate and not. A bridge deck contains 52 cards, four of each of the 13 face values ace, king, queen, jack, ten, nine, . . . , two. You deal a single card from such a deck and record the
An IQ test (optional). How high must a person score on the WAIS test to be in the top 10% of all scores? Use the information in Exercise III.14 and Table B to answer this question.
We like opinion polls (optional). Use the information in Exercise III.15 and Table B to find the probability that one sample misses the truth about the population by 4% or more. (This is the
An IQ test (optional). Use the information in Exercise III.14 and Table B to find the probability that a randomly chosen person has aWAIS score 112 or higher.
We like opinion polls. Are Americans interested in opinion polls about the major issues of the day? Suppose that 40% of all adults are very interested in such polls. (According to sample surveys that
An IQ test. TheWechsler Adult Intelligence Scale (WAIS) is a common IQ test for adults. The distribution of WAIS scores for persons over 16 years of age is approximately Normal with mean 100 and
Satisfaction with colleges. The National Center for Public Policy and Higher Education asked randomly chosen adults, “Are the colleges in your state doing an excellent, good, fair, or poor job, or
Choosing at random. Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm’s public relations office. Their employer must choose two of them to attend a conference in Paris. To avoid unfairness,
Language study. Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of results:Language: Spanish French German All
How much education? The 2008 Statistical Abstract gives this distribution of education for a randomly chosen American over 25 years old:Less than High school College, Associate’s Bachelor’s
Poker. Deal a five-card poker hand from a shuffled deck. The probabilities of several types of hand are approximately as follows:Hand: Worthless One pair Two pairs Better hands Probability: 0.50 0.42
Profit from a risky investment. Rotter Partners is planning a major investment. The amount of profit X is uncertain, but a probabilistic estimate gives the following distribution (in millions of
Dice. What is the expected number of spots observed in rolling a carefully balanced die once? (Hint: See pages 429–432.)
Course grades. Choose a student at random from the course described in Exercise III.2 and observe what grade that student earns (A = 4, B = 3, C =2, D = 1, F = 0).(a) What is the expected grade of a
Blood types. People with Type B blood can receive blood donations from other people with either Type B or Type O blood. Tyra has Type B blood. What is the probability that 2 or more of Tyra’s 6
Course grades. If you choose 5 students at random from all those who have taken the course described in Exercise III.2, what is the probability that all the students chosen got a B or better?
Blood types. Choose a person at random and record his or her blood type. Here are the probabilities for each blood type:Blood type: Type O Type A Type B Type AB Probability: 0.4 0.3 0.2 ?(a) What
Course grades. Choose a student at random from all who took Math 101 in recent years. The probabilities for the student’s grade are Grade: A B C D F Probability: 0.2 0.4 0.2 0.1 ?(a) What must be
What’s the probability? Open your local telephone directory to any page in the residential listing. Look at the last four digits of each telephone number, the digits that specify an individual
Web-based exercise. The Web abounds in applets that simulate various random phenomena. One amusing probability problem is named Buffon’s needle. Draw lines 1 inch apart on a piece of paper, then
Web-based exercise. The basketball player LeBron James makes about 70% of his free throws over an entire season. At the end of a game, an announcer states that “LeBron had a hot hand tonight. He
The multiplication rule. Here is another basic rule of probability: if several events are independent, the probability that all of the events happen is the product of their individual
The birthday problem. A famous example in probability theory shows that the probability that at least two people in a room have the same birthday is already greater than 1/2 when 23 people are in the
More on the airport van. Let’s continue the simulation of Exercise 19.19. You have a backup van, but it serves several stations. The probability that it is available to go to the airport at any one
A multiple-choice exam. Matt has lots of experience taking multiplechoice exams without doing much studying. He is about to take a quiz that has 10 multiple-choice questions, each with four possible
The airport van. Your company operates a van service from the airport to downtown hotels. Each van carries 7 passengers. Many passengers who reserve seats don’t show up—in fact, the probability
Playing craps. The game of craps is played with two dice. The player rolls both dice and wins immediately if the outcome (the sum of the faces) is 7 or 11. If the outcome is 2, 3, or 12, the player
Two warning systems. An airliner has two independent automatic systems that sound a warning if there is terrain ahead (that means the airplane is about to fly into a mountain). Neither system is
The Asian stochastic beetle. We can use simulation to examine the fate of populations of living creatures. Consider the Asian stochastic beetle.Females of this insect have the following pattern of
Gambling in ancient Rome. Tossing four astragali was the most popular game of chance in Roman times. Many throws of a present-day sheep’s astragalus show that the approximate probability
A better model for repeating an exam. A more realistic probability model for Elaine’s attempts to pass an exam in the previous exercise is as follows. On the first try she has probability 0.2 of
Repeating an exam. Elaine is enrolled in a self-paced course that allows three attempts to pass an examination on the material. She does not study and has probability 2/10 of passing on any one
Tonya’s free throws. Tonya makes 80% of her free throws in a long season. In a tournament game she shoots 5 free throws late in the game and misses 3 of them. The fans think she was nervous, but
LeBron’s free throws. The basketball player LeBron James makes about 70% of his free throws over an entire season. Take his probability of a success to be 0.7 on each shot. Using line 122 of Table
More on class rank. In Exercise 19.8 you explained how to simulate the high school class rank of a randomly chosen college student. The Random Foundation decides to offer 8 randomly chosen students
More on course grades. In Exercise 19.7 you explained how to simulate the grade of a randomly chosen student in a statistics course. Five students on the same floor of a dormitory are taking this
Class rank. Choose a college student at random and ask his or her class rank in high school. Probabilities for the outcomes are Top quarter but Top half but Bottom Class rank: Top 10% not top 10% not
Course grades. Choose a student at random from all who took beginning statistics at Upper Wabash Tech in recent years. The probabilities for the student’s grade are Grade: A B C D or F Probability:
Simulating an opinion poll. A Gallup Poll on Presidents Day 2008 interviewed a random sample of 1007 adult Americans. Those in the sample were asked which former president they would like to bring
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