Draw a Venn diagram portraying four mutually exclusive events.
> According to the Congressional Directory, the official directory of the U.S. Congress, prepared by the Joint Committee on Printing, the age distribution for senators in the U.S. Congress as of Fall 2013, is as shown in the following table. Suppose that a
> R. Reifen et al. studied various nutritional measures of Ethiopian school children and published their findings in the paper “Ethiopian-Born and Native Israeli School Children Have Different Growth Patterns” (Nutrition, Vol. 19, pp. 427– 431). The study,
> Suppose that A and B are events such that P(A) = 1/4, P(B) = 1/3, and P(A or B) = 1/2. a. Are events A and B mutually exclusive? Explain your answer. b. Find P(A & B).
> Suppose that A and B are events such that P(A) = 1/3, P(A or B) = 1/2, and P(A & B) = 1/10. a. Are events A and B mutually exclusive? Explain your answer. b. Find P(B).
> In a designed experiment, there is one factor with four levels. How many treatments are there?
> Suppose that A and B are events such that P(A) = 0.84, P(B) = 0.46, and P(A & B) = 0.38. Determine P(A or B).
> Suppose that C and D are events such that P(C) = 0.35, P(D) = 0.40, and P(C & D) = 0.30. Determine P(C or D).
> Let F be an event with probability 0.72. Find the probability of (not F).
> Let E be an event with probability 0.35. Find the probability of (not E).
> Suppose that C and D are mutually exclusive events such that P(C) = 0.14 and P(D) = 0.32. Determine P(C or D).
> Interpret each of the following probability statements, using the frequentist interpretation of probability. a. The probability is 0.487 that a newborn baby will be a girl. b. The probability of a single ticket winning a prize in the Powerball lottery is
> Suppose that A and B are mutually exclusive events such that P(A) = 0.25 and P(B) = 0.40. Determine P(A or B).
> The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60 miles per hour (mph) and, according to the online document “Cheetah Conservation in Southern Africa” (Trade & Env
> A bowl contains 12 poker chips—3 red, 4 white, and 5 blue. One of these poker chips is selected at random from the bowl. Let B denote the event that the chip selected is blue. Find the probability that a blue chip is selected, and express your answer in
> An ordinary deck of playing cards has 52 cards. There are four suits—spades, hearts, diamonds, and clubs— with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. One of these cards is selected at random. Let R denote the even
> Let A, B, and C be events of a sample space. Complete the following table.
> In this section, we discussed two types of statistical designs. Identify and explain the meaning of each one.
> Suppose that A, B, and C are three events that cannot all occur simultaneously. Does this condition necessarily imply that A, B, and C are mutually exclusive? Justify your answer and illustrate it with a Venn diagram.
> Construct a Venn diagram that portrays four events, A, B, C, and D that have the following properties: Events A, B, and C are mutually exclusive; events A, B, and D are mutually exclusive; no other three of the four events are mutually exclusive.
> Let A and B be events of a sample space. a. Suppose that A and (not B) are mutually exclusive. Explain why B occurs whenever A occurs. b. Suppose that B occurs whenever A occurs. Explain why A and (not B) are mutually exclusive.
> From 10 men and 8 women in a pool of potential jurors, 12 are chosen at random to constitute a jury. Suppose that you observe the number of men who are chosen for the jury. Let A be the event that at least half of the 12 jurors are men, and let B be the
> Consider the following random experiment: First, roll a die and observe the number of dots facing up; then, toss a coin the number of times that the die shows and observe the total number of heads. Thus, if the die shows three dots facing up and the coin
> Refer to Exercise 5.66. Among the events A, B, C, and D, identify the collections of events that are mutually exclusive. Data from Exercise 5.66: A survey was conducted in Canada to ascertain public opinion about a major national park region in the Banf
> A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is 98.6◦F. The results of the study by P. Mackowiak et al. appeared in the article “A Critical Appraisal of 98.6◦F, the Upper Limit
> State the frequentist interpretation of probability.
> Refer to Exercise 5.65. Among the events A, B, C, and D, identify the collections of events that are mutually exclusive. Data from Exercise 5.65: The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. Th
> Each part of this exercise contains events from Exercise 5.54. In each case, decide whether the events are mutually exclusive. a. A and B b. B and C c. A, B, and C d. A, B, and D e. A, B, C, and D
> Refer to Exercise 5.53. a. Are events A and B mutually exclusive? b. Are events B and C mutually exclusive? c. Are events A, C, and D mutually exclusive? d. Are there three mutually exclusive events among A, B, C, and D? four? Data from Exercise 5.53: W
> Define each of the following terms in the context of experimental design. a. Response variable b. Factor c. Levels d. Treatments
> A survey was conducted in Canada to ascertain public opinion about a major national park region in the Banff-Bow Valley. One question asked the amount that respondents would be willing to contribute per year to protect the environment in the Banff-Bow Va
> The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. The following table provides a frequency distribution for the number of rooms in U.S. housing units. The frequencies are in thousands. For a U.S. hou
> The NBA Finals of basketball is played in a best of seven series. The number of games necessary to decide a winner can range from four to seven. Wikipedia lists the NBA Finals winners and number of games played per series. The following table provides th
> The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919–1921 World Series, when it was a best of nine). Thus it takes at least four games and no more than seven games to establish a winner. From the document Wo
> The following table provides a frequency distribution for the ages of adult women seeking pregnancy tests at public health facilities in Missouri during a 3-month period. It appeared in the article “Factors Affecting Contraceptive Use in Women Seeking Pr
> Body mass index (BMI) is a measure of body fat based on height and weight. According to the document Dietary Guidelines for Americans published by the U.S. Department of Agriculture and the U.S. Department of Health and Human Services, for adults, a BMI
> In a report titled Behavioral Risk Factor Surveillance System Summary Prevalence Report, the Centers for Disease Control and Prevention discusses the prevalence of diabetes in the United States. The following table provides a diabetes prevalence frequenc
> For each of the following events, list the outcomes that constitute the event, and describe the event in words. a. (not B) b. (A & B) c. (C or D)
> An experiment has 40 possible outcomes, all equally likely. An event can occur in 25 ways. The probability that the event occurs is____.
> For each of the following events, list the outcomes that constitute the event, and describe the event in words. a. (not A) b. (B & D) c. (B or C)
> For each of the following events, list the outcomes that constitute the event and describe the event in words. a. (not C) b. (C & D) c. (A or C)
> State and explain the significance of the three basic principles of experimental design.
> We presented cognition data obtained by researchers studying the effects of early postnatal dexamethasone therapy for the prevention or treatment of chronic lung disease of prematurity. The study included 146 school-age children of which 72 had been in a
> For each of the following events, list the outcomes that constitute the event and describe the event in words. a. (not A) b. (A & B) c. (B or C)
> When a dime is tossed four times, there are the following 16 possible outcomes. Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes constituting each
> A committee consists of five executives, three women and two men. Their names are Maria (M), John (J), Susan (S), Will (W), and Holly (H). The committee needs to select a chairperson and a secretary. It decides to make the selection randomly by drawing s
> The inferential procedures discussed in this book are intended for use with only one particular sampling procedure. What sampling procedure is that?
> Construct a dotplot for the following exam scores of the students in an introductory statistics class.
> In a horse race, the odds against winning are as shown in the following table. For example, the odds against winning are 8 to 1 for horse #1. List the outcomes constituting A = event one of the top two favorites wins (the top two favorites are the two ho
> When one die is rolled, the following six outcomes are possible: List the outcomes constituting A = event the die comes up even, B = event the die comes up 4 or more, C = event the die comes up at most 2, and D = event the die comes up 3.
> Answer true or false to the following statement and justify your answer: If event A and event B are mutually exclusive, so are events A, B, and C for every event C.
> Answer true or false to the following statement and justify your answer: If event A and event B are not mutually exclusive, neither are events A, B, and C for every event C.
> An experiment has 20 possible outcomes, all equally likely. An event can occur in five ways. The probability that the event occurs is ___.
> What does it mean for three events to be mutually exclusive?
> In a designed experiment, a. what are the experimental units? b. if the experimental units are humans, what term is often used in place of experimental unit?
> What does it mean for two events to be mutually exclusive?
> Consider the set consisting of the first 10 positive whole numbers (i.e., 1–10). Determine explicitly the numbers in the set that satisfy each of the following conditions: a. at least 6 b. at most 3 c. between 2 and 5, inclusive
> Iron is essential to most life forms and to normal human physiology. It is an integral part of many proteins and enzymes that maintain good health. Recommendations for iron are provided in Dietary Reference Intakes, developed by the Institute of Medicine
> Consider the set consisting of the first 12 positive whole numbers (i.e., 1–12). Determine explicitly the numbers in the set that satisfy each of the following conditions: a. at least 9 b. at most 10 c. between 5 and 8, inclusive
> Construct a Venn diagram representing the event a. (A & (not B)). b. ((A or B) & (not (A & B)))
> Construct a Venn diagram representing the event a. (A or B or C). b. ((not A) & B).
> Construct a Venn diagram representing the event a. (A & B). b. (A & B & C).
> Construct a Venn diagram representing the event a. (not E). b. (A or B).
> What type of graphical displays are useful for portraying events and relationships among events?
> An issue of Travel + Leisure Golf magazine reported several facts about lightning. Here are three of them. - The odds of an individual being struck by lightning in a year in the United States are about 280,000 to 1 (against). - The odds of an individual
> If a member is selected at random from a finite population, probabilities are identical to ___ .
> In simple random sampling, it is also true that each member of the population is equally likely to be selected, the chance for each member being equal to the sample size divided by the population size. Show that this fact is also true for stratified rand
> A study was conducted by the firm Coleman & Associates, Inc. to determine who curses at their computer. The results, which appeared in USA TODAY, indicated that 46% of people age 18–34 years have cursed at their computer. What are the odds against a rand
> Dementia is the loss of intellectual and social abilities severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer’s disease is the most common type of dementia. In the article “Living with Early Onset Dementia: Exploring the
> The Belmont Stakes is the third leg, after the Kentucky Derby and Preakness Stakes, of the Triple Crown of thoroughbred horseracing. The morning-line betting odds of the two favorites, Orb and Revolutionary, for the 2013 Belmont Stakes were 7 to 2 (again
> As found in USA TODAY, results of a survey by International Communications Research revealed that roughly 75% of adult women believe that a romantic relationship over the Internet while in an exclusive relationship in the real world is cheating. What are
> An American roulette wheel contains 38 numbers, of which 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any of the 38 numbers. For a bet on red, the house pays even odds (i.e., 1 to 1). W
> Consider the random experiment of tossing a coin once. There are two possible outcomes for this experiment, namely, a head (H) or a tail (T). a. Repeat the random experiment five times—that is, toss a coin five times—and record the information required i
> At a certain university in the United States, 62% of the students are at least bilingual—speaking English and at least one other language. Of these students, 80% speak Spanish and, of the 80% who speak Spanish, 10% also speak French. Determine the probab
> Explain what is wrong with the following argument: When two balanced dice are rolled, the sum of the dice can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, giving 11 possibilities. Therefore the probability is 1/11 that the sum is 12.
> In 2013, according to the National Governors Association, 30 of the 50 state governors were Republicans. Suppose that on each day of 2013, one U.S. state governor was randomly selected to read the invocation on a popular radio program. On approximately h
> The probability is 0.667 that the favorite in a horse race will finish in the money (first, second, or third place). In 500 horse races, roughly how many times will the favorite finish in the money?
> The probability is 0.314 that the gestation period of a woman will exceed 9 months. In 4000 human gestation periods, roughly how many will exceed 9 months?
> In simple random sampling, it is also true that each member of the population is equally likely to be selected, the chance for each member being equal to the sample size divided by the population size. a. Under what circumstances is that fact also true f
> Objects such as asteroids and comets that come into proximity with the Earth are called near-Earth objects (NEOs). The National Aeronautics and Space Administration (NASA) tracks and catalogues all NEOs that are at least 1 kilometer wide. Data on NEOs ca
> What is the difference between selecting a member at random from a finite population and taking a simple random sample of size 1?
> Refer to Exercise 5.24. a. Which, if any, of the events in parts (a)–(e) are certain? impossible? b. Determine the probability of each event identified in part (a). Data from Exercise 5.24: A family is defined to be a group of two or more persons relate
> Refer to Exercise 5.19. a. Which, if any, of the events in parts (a)–(e) are certain? impossible? b. Determine the probability of each event identified in part (a). Data from Exercise 5.19: The U.S. Census Bureau publishes data on housing units in Ameri
> A balanced dime is tossed three times. The possible outcomes can be represented as follows. Here, for example, HHT means that the first two tosses come up heads and the third tails. Find the probability that a. exactly two of the three tosses come up hea
> Two balanced dice are rolled. Refer to Fig. and determine the probability that the sum of the dice is a. 6. b. even. c. 7 or 11. d. 2, 3, or 12.
> A family is defined to be a group of two or more persons related by birth, marriage, or adoption and residing together in a household. According to Current Population Survey, published by the U.S. Census Bureau, the size distribution of U.S. families is
> According to Survey of Graduate Science Engineering Students and Postdoctorates, published by the U.S. National Science Foundation, the distribution of graduate science students in doctorate-granting institutions is as follows. Frequencies are in thousan
> From Wikipedia and the article “Which Country Has the Best Brains?” from BBC News Magazine, we obtained a frequency distribution of the number of Nobel Prize winners, by country. Suppose that a recipient of a Nobel Prize is selected at random. Find the p
> The population of Seoul was studied in an article by B. Lee and J. McDonald, “Determinants of Commuting Time and Distance for Seoul Residents: The Impact of Family Status on the Commuting of Women” (Urban Studies, Vol. 40, No. 7, pp. 1283–1302). The auth
> As reported by the Federal Bureau of Investigation in Crime in the United States, the age distribution of murder victims between 20 and 59 years old is as shown in the following table. A murder case in which the person murdered was between 20 and 59 year
> Consider the following sample of exam scores, arranged in increasing order. The sample mean and sample standard deviation of these exam scores are 85 and 16.1, respectively. Modeling your solutions after those in Example 3.15 on pages 117–118, solve the
> In simple random sampling, all samples of a given size are equally likely. Is that true in systematic random sampling? Explain your answer.
> Concerning the equal-likelihood model of probability, a. what is it? b. how is the probability of an event found?
> Another important discrete probability distribution is the Poisson distribution, named in honor of the French mathematician and physicist Simeon Poisson (1781–1840). This probability distribution is often used to model the frequency with which a specifie
> The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. The following table provides a frequency distribution for the number of rooms in U.S. housing units. The frequencies are in thousands. A U.S. housing
> In this exercise, we discuss the geometric distribution, the probability distribution for the number of trials until the first success in Bernoulli trials. The geometric probability formula is where X denotes the number of trials until the first success
> In this exercise, we discuss the hypergeometric distribution in more detail. When sampling is done without replacement from a finite population, the hyper geometric distribution is the exact probability distribution for the number of members sampled that
> Following is a gender frequency distribution for students in Professor Weiss’s introductory statistics class. Two students are selected at random. Find the probability that both students are male if the selection is done a. with replacement. b. without r
> Refer to the discussion on the binomial approximation to the hypergeometric distribution. a. If sampling is with replacement, explain why the trials are independent and the success probability remains the same from trial to trial—always the proportion of
> A success, s, in Bernoulli trials is often derived from a collection of outcomes. For example, an American roulette wheel consists of 38 numbers, of which 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally lik
> In the Scientific American article “Reducing Crime: Rehabilitation is Making a Comeback,” R. Doyle examined rehabilitation of felons. One aspect of the article discussed recidivism of juvenile prisoners between 14 and 17 years old, indicating that 82% of
