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Introduction To Statistics And Data Analysis 5th Edition Roxy Peck, Chris Olsen, Jay L Devore - Solutions

6.67 The authors of the paper “Do Physicians Know when Their Diagnoses Are Correct?” (Journal of General Internal Medicine [2005]: 334–339) presented detailed case studies to medical students and to faculty at medical schools. Each participant was asked to provide a diagnosis in the case and
6.66 Refer to the information given in the previous exercise about customers of a large cable company.a. Suppose two customers are to be selected at random. Would it be reasonable to consider the events C1 5 event that the first customer selected subscribes to cable TV and C2 5 event that the
6.65 A large cable company reports the following:● 80% of its customers subscribe to cable TV service● 42% of its customers subscribe to Internet service● 32% of its customers subscribe to telephone service● 25% of its customers subscribe to both cable TV and Internet service● 21% of its
6.64 Blue Cab operates 15% of the taxis in a certain city, and Green Cab operates the other 85%. After a nighttime hit-and-run accident involving a taxi, an eyewitness said the vehicle was blue. Suppose, though, that under night vision conditions, only 80% of individuals can correctly distinguish
6.63 According to a July 31, 2013, posting on cnn.com, a 2010 study in the journal Pediatrics found that 8%of children younger than age 18 in the United States have at least one food allergy. Among those with food allergies, about 39% had a history of severe reaction.a. If a child younger than 18
6.62 Let F denote the event that a randomly selected registered voter in a certain city has signed a petition to recall the mayor. Also, let E denote the event that the randomly selected registered voter actually votes in the recall election. Describe the event E > F in words. If PsFd 5 .10 and
6.61 There are two traffic lights on the route used by a certain individual to go from home to work. Let E denote the event that the individual must stop at the first light, and define the event F in a similar manner for the second light. Suppose that PsEd 5 .4, PsFd 5 .3, and PsE > Fd 5 .15.a.
6.60 A construction firm bids on two different contracts.Let E1 be the event that the bid on the first contract is successful, and define E2 analogously for the second contract. Suppose that P(E1) 5 .4 and P(E2) 5 .3 and that E1 and E2 are independent events.a. Calculate the probability that both
6.59 ▼ A certain university has 10 vehicles available for use by faculty and staff. Six of these are vans and four are cars. On a particular day, only two requests for vehicles have been made. Suppose that the two vehicles to be assigned are chosen in a completely random fashion from among the
6.58 Refer to the previous exercise. Suppose now that for a probability question, 100 answers are submitted, of which 50 are correct. Calculate the probabilities in Parts (a) and (b) of the previous exercise for the probability question.
6.57 The National Public Radio show Car Talk has a feature called “The Puzzler.” Listeners are asked to send in answers to some puzzling questions—usually about cars but sometimes about probability (which, of course, must account for the incredible popularity of the program!).Suppose that for
6.56 A store sells two different brands of dishwasher soap, and each brand comes in three different sizes: small(S), medium (M), and large (L). The proportions of the two brands and of the three sizes purchased are displayed as marginal totals in the following table.Size S M L B1 .40 Brand B2
6.55 A shipment of 5000 printed circuit boards contains 40 that are defective. Two boards will be chosen at random, without replacement. Consider the two events E1 5 event that the first board selected is defective and E2 5 event that the second board selected is defective.a. Are E1 and E2
6.54 Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that P(A beats B) 5 .7 P(A beats C) 5 .8 P(B beats C) 5 .6 and that the outcomes of the three matches are independent of one another.a. What is the probability that A
6.53 The following case study was reported in the article“Parking Tickets and Missing Women,” which appeared in an early edition of the book Statistics: A Guide to the Unknown. In a Swedish trial on a charge of overtime parking, a police officer testified that he had noted the position of the
Components 1 and 2 form a series subsystem, as do Components 3 and 4. The two subsystems are connected in parallel. Suppose that P(1 works) 5 .9 P(2 works) 5 .9 P(3 works) 5 .9 P(4 works) 5 .9 and that the four components work independently of one another.a. The 1–2 subsystem works only if both
6.51 Consider a system consisting of four components, as pictured in the following diagram:1 2 3 4
6.50 ▼ Approximately 30% of the calls to an airline reservation phone line result in a reservation being made.a. Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls result in a reservation?b. What assumption did you make to calculate the probability in
6.48 In a small city, approximately 15% of those eligible are called for jury duty in any one calendar year.People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year.a. What is the probability that a particular eligible
6.47 A Gallup survey of 2002 adults found that 46% of women and 37% of men experience pain daily (San Luis Obispo Tribune, April 6, 2000). Suppose that this information is representative of adult Americans.If an adult American is selected at random, are the events selected adult is male and
6.46 The article “SUVs Score Low in New Federal Rollover Ratings” (San Luis Obispo Tribune, January 6, 2001)gave information on death rates for various kinds of accidents by vehicle type for accidents reported to the police. Suppose that we randomly select an accident reported to the police and
6.45 The report “TV Drama/Comedy Viewers and Health Information” (www.cdc.gov/Healthmarketing) describes the results of a large survey involving approximately 3500 people that was conducted for the Center for Disease Control. The sample was selected in a way that the Center for Disease Control
6.44 The paper “Predictors of Complementary Therapy Use Among Asthma Patients: Results of a Primary Care Survey” (Health and Social Care in the Community[2008]: 155–164) included the accompanying table. The table summarizes the responses given by 1077 asthma patients to two questions:Question
6.43 Many fire stations handle emergency calls for medical assistance as well as calls requesting firefighting equipment. A particular station says that the probability that an incoming call is for medical assistance is .85. This can be expressed as P(call is for medical assistance) 5 .85.a. Give a
6.42 The paper “Good for Women, Good for Men, Bad for People: Simpson’s Paradox and the Importance of Sex-Specific Analysis in Observational Studies” (Journal of Women’s Health and Gender-Based Medicine [2001]:867–872) described the results of a medical study in which one treatment was
A1 5 event that a randomly selected individual is in age group 18–24, and A6 5 event that a randomly selected individual is in age group 65 and older.a. Convert the counts to proportions and then use them to compute the following probabilities:i. PsA1 d ii. PsA1 > Sd iii. PsA1uSd iv. Psnot A1 d
6.41 The USA Today article referenced in the previous exercise also gave information on seat belt usage by age, which is summarized in the following table:Age Does Not Use Seat Belt Regularly Uses Seat Belt Regularly 18–24 59 41 25–34 73 27 35–44 74 26 45–54 70 30 55–64 70 30 65 and older
6.40 USA Today (June 6, 2000) gave information on seat belt usage by gender. The proportions in the following table are based on a survey of a large number of adult men and women in the United States.Male Female Uses Seat Belts Regularly .10 .175 Does Not Use Seat Belts Regularly .40 .325 Assume
6.39 The table at the top of the next page summarizes data on smoking status and perceived risk of smoking and is consistent with summary quantities obtained in a Gallup Poll conducted in November 2002. Assume that it is reasonable to consider these data as representative of the adult American
6.38 ▼ Is ultrasound a reliable method for determining the gender of an unborn baby? The accompanying data on 1000 births are consistent with summary values that appeared in the Journal of Statistics Education(“New Approaches to Learning Probability in the First Statistics Course,”
6.37 Suppose that an individual is randomly selected from the population of all adult males living in the United States. Let A be the event that the selected individual is over 6 feet in height, and let B be the event that the selected individual is a professional basketball player.Which do you
6.36 The newspaper article “Folic Acid Might Reduce Risk of Down Syndrome” (USA Today, September 29, 1999)makes the following statement: “Older women are at a greater risk of giving birth to a baby with Down Syndrome than are younger women. But younger women are more fertile, so most children
6.35 The events E and Ti are defined as E 5 the event that someone who is out of work and actively looking for work will find a job within the next month and Ti 5 the event that someone who is currently out of work has been out of work for i months. For example, T2 is the event that someone who is
6.34 Delayed diagnosis of cancer is a problem because it can delay the start of treatment. The paper “Causes of Physician Delay in the Diagnosis of Breast Cancer”(Archives of Internal Medicine [2002]: 1343–1348) examined possible causes for delayed diagnosis for women with breast cancer. The
6.33 The following graphical display is similar to one that appeared in USA Today (January 8, 2010).Use the information in this display to answer the following questions. Assume that the percentages in the graph are representative of adult Americans.a. What is the probability that a randomly
6.32 The accompanying data are from the article “Characteristics of Buyers of Hybrid Honda Civic IMA:Preferences, Decision Process, Vehicle Ownership, and Willingness-to-Pay” (Institute for Environmental Decisions, November 2006). Each of 311 people who purchased a Honda Civic was classified
6.31 The article “Chances Are You Know Someone with a Tattoo, and He’s Not a Sailor” (Associated Press, June 11, 2006) included results from a survey of adults aged 18 to 50. The accompanying data are consistent with summary values given in the article.At Least One Tattoo No Tattoo Age
6.30 Two different airlines have a flight from Los Angeles to New York that departs each weekday morning at a certain time. Let E denote the event that the first airline’s flight is fully booked on a particular day, and let F denote the event that the second airline’s flight is fully booked on
6.29 Suppose that a six-sided die is “loaded” so that any particular even-numbered face is twice as likely to land face up as any particular odd-numbered face.Consider the chance experiment that consists of rolling this die.a. What are the probabilities of the six simple events? (Hint: Denote
6.28 A student placement center has requests from five students for interviews regarding employment with a particular consulting firm. Three of these students are math majors, and the other two students are statistics majors.Unfortunately, the interviewer has time to talk to only two of the
6.27 The student council for a school of science and math has one representative from each of the five academic departments: biology (B), chemistry (C), mathematics(M), physics (P), and statistics (S). Two of these students are to be randomly selected for inclusion on a university-wide student
6.26 After all students have left the classroom, a statistics professor notices that four copies of the text were left under desks. At the beginning of the next lecture, the professor distributes the four books at random to the four students (1, 2, 3, and 4) who claim to have left books. One
6.25 A deck of 52 cards is mixed well, and 5 cards are dealt.a. It can be shown that (disregarding the order in which the cards are dealt) there are 2,598,960 possible five-card hands, of which only 1287 are hands consisting entirely of spades. What is the probability that a hand will consist
6.24 The same issue of The Chronicle for Higher Education referenced in the previous exercise also reported the following information for degrees awarded by U.S. colleges to Hispanic students in the 2008–2009 academic year:● A total of 274,515 degrees were awarded to Hispanic students.●
6.23 According to The Chronicle for Higher Education(Aug. 26, 2011), there were 787,325 associate degrees awarded by U.S. community colleges in the 2008–2009 academic year. A total of 488,142 of these degrees were awarded to women.a. If a person who received a degree in 2008–2009 was selected
6.21 Suppose you want to estimate the probability that a customer at a particular grocery store will pay by credit card. Over the past three months, 80,500 purchases were made, and 37,100 of them were paid for by credit card. What is the estimated probability that a customer will pay by credit card?
6.20 Refer to the following information on full-term births in the United States over a given period of time:Type of Birth Number of Births Single birth 41,500,000 Twins 500,000 Triplets 5,000 Quadruplets 100 Use this information to estimate the probability that a randomly selected pregnant woman
6.19 A professor assigns five problems to be completed as homework. At the next class meeting, two of the five problems will be selected at random and collected for grading. You only completed the first three problems.a. What is the probability that you will be able to turn in both of the problems
6.18 Phoenix is a hub for a large airline. Suppose that on a particular day, 8000 passengers arrived in Phoenix on this airline. Phoenix was the final destination for 1800 of these passengers. The others were all connecting to flights to other cities. On this particular day, several inbound flights
6.17 Roulette is a game of chance that involves spinning a wheel that is divided into 38 equal segments, as shown in the accompanying picture.A metal ball is tossed into the wheel as it is spinning, and the ball eventually lands in one of the 38 segments. Each segment has an associated color. Two
6.16 ▼ Medical insurance status—covered (C) or not covered (N)—is determined for each individual arriving for treatment at a hospital’s emergency room. Consider the chance experiment in which this determination is made for two randomly selected patients.The simple events are O1 5 (C, C),
6.15 A bookstore sells two types of books (fiction and nonfiction) in several formats (hardcover, paperback, digital, and audio). For the chance experiment that consists of observing the type and format of a singlebook purchase, two of the eight possible outcomes are a hardcover fiction book and an
6.14 The manager of a music store has kept records of the number of CDs bought in a single transaction by customers who make a purchase at the store. The accompanying table gives six possible outcomes and the estimated probability associated with each of these outcomes for the chance experiment
6.13 A large department store offers online ordering.When a purchase is made online, the customer can select one of four different delivery options: expedited overnight delivery, expedited second-business-day delivery, standard delivery, or delivery to the nearest store for customer pick-up.
6.12 Consider a Venn diagram picturing two events A and B that are not mutually exclusive.a. Shade the event sA ø BdC. On a separate Venn diagram shade the event AC > BC. How are these two events related?b. Shade the event sA > BdC. On a separate Venn diagram shade the event AC ø BC. How are
6.11 An engineering construction firm is currently working on power plants at three different sites. Define events E1, E2, and E3 as follows:E1 5 the plant at Site 1 is completed by the contract date E2 5 the plant at Site 2 is completed by the contract date E3 5 the plant at Site 3 is completed by
6.10 A family consisting of three people—P1, P2, and P3—belongs to a medical clinic that always has a physician at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic exactly once and is randomly assigned to a station. One experimental outcome is (1,
6.9 Refer to the previous exercise and now suppose that the chance experiment terminates only when two nondefective batteries have been obtained.a. Let A denote the event that at most three batteries must be examined before the chance experiment terminates. What outcomes are contained in A?b. Let B
6.7 A library has five copies of a certain textbook on reserve of which two copies (1 and 2) are hardcover books and the other three (3, 4, and 5) are softcover books. A student examines these books in random order, stopping only when a softcover book has been selected.a. Display the possible
6.6 A college library has four copies of a certain book;the copies are numbered 1, 2, 3, and 4. Two of these are selected at random. The first selected book is placed on 2-hour reserve, and the second book can be checked out overnight.a. Construct a tree diagram to display the 12 outcomes in the
6.4 A tennis shop sells five different brands of rackets, each of which comes in either a midsize version or an oversize version. Consider the chance experiment in which brand and size are noted for the next racket purchased. One possible outcome is Head midsize, and another is Prince
6.3 Consider the chance experiment in which the type of transmission—automatic (A) or manual (M)—is recorded for each of the next two cars purchased from a certain dealer.a. What is the set of all possible outcomes (the sample space)? (Hint: See Example 6.2.)b. Display the possible outcomes in
6.2 Define the term sample space, and then give the sample space for the chance experiment you described in Exercise 6.1.
6.1 Define the term chance experiment, and give an example of a chance experiment with four possible outcomes.
●● calculate the probability of events, including events that are the union of, the intersection of, or the complement of other events.v●● calculate conditional probabilities.●● estimate probabilities empirically and using simulation.
●● identify the sample space for a given chance experiment.
●● interpret a probability in context as a long-run relative frequency of occurrence.
●● the difference between an unconditional and a conditional probability.Students will be able to:
●● what it means for two events to be independent.
●● what it means for two events to be mutually exclusive.
●● basic properties of probabilities.
CR5.19 ● The paper “Population Pressure and Agricultural Intensity” (Annals of the Association of American Geographers[1977]: 384–396) reported a positive association between population density and agricultural intensity. The following data consist of measures of population density (x) and
CR5.18 ● A study, described in the paper “Prediction of Defibrillation Success from a Single Defibrillation Threshold Measurement” (Circulation [1988]: 1144–1149) investigated the relationship between defibrillation success and the energy of the defibrillation shock (expressed as a multiple
CR5.17 Exercise CR5.16 gave the least-squares regression line for predicting y 5 clutch size from x 5 snout-vent length(“Reproductive Biology of the Aquatic Salamander Amphiuma tridactylum in Louisiana,” Journal of Herpetology [1999]: 100–105). The paper also reported r2 5 .7664 and SSTo 5
CR5.16 In the article “Reproductive Biology of the Aquatic Salamander Amphiuma tridactylum in Louisiana” (Journal of Herpetology[1999]: 100–105), 14 female salamanders were studied.Using regression, the researchers predicted y 5 clutch size (number of salamander eggs) from x 5 snout-vent
CR5.15 The accompanying scatterplot shows observations on hemoglobin level, determined both by the standard spectrophotometric method (y) and by a new, simpler method based on a color scale (x) (“A Simple and Reliable Method for Estimating Hemoglobin,” Bulletin of the World Health
CR5.14 ● Cost-to-charge ratios (the percentage of the amount billed that represents the actual cost) for 11 Oregon hospitals of similar size were reported separately for inpatient and outpatient services. The data are shown in the following table.Cost-to-Charge Ratio Hospital Inpatient Outpatient
13.8 1.4 3.5 3.3 14.8 3.7a. Compute the values of the mean and the median for blood lead level for the sample of African Americans.b. Which of the mean or the median is larger? What characteristic of the data set explains the relative values of the mean and the median?c. Construct a comparative
CR5.13 ● ▼ The paper “Relationship Between Blood Lead and Blood Pressure Among Whites and African Americans” (a technical report published by Tulane University School of Public Health and Tropical Medicine, 2000) gave summary quantities for blood lead level (in micrograms per deciliter) for
CR5.12 ● ▼ A report from Texas Transportation Institute(Texas A&M University System, 2005) on congestion reduction strategies looked into the extra travel time (due to traffic congestion) for commute travel per traveler per year in hours for different urban areas. Below are the data for urban
CR5.11 ● The paper referenced in Exercise CR5.10 also gave data on sodium content (in milligrams per kilogram) of 10 chocolate puddings made from instant mix:3099 3112 2401 2824 2682 2510 2297 3959 3068 3700a. Compute the mean, the standard deviation, and the interquartile range for sodium
CR5.10 ● ▼ The paper “Total Diet Study Statistics on Element Results” (Food and Drug Administration, April 25, 2000) gave information on sodium content for various types of foods.Twenty-six tomato catsups were analyzed. Data consistent with summary quantities given in the paper were Sodium
CR5.8 ● ▼ Medicare’s medical plans offer a wide range of variations and choices for seniors when picking a drug plan (San Luis Obispo Tribune, November 25, 2005). The monthly cost for a stand-alone drug plan varied from a low of $1.87 in Montana, Wyoming, North Dakota, South Dakota, Nebraska,
CR5.7 ● Bidri is a popular and traditional art form in India. Bidri articles (bowls, vessels, and so on) are made by casting from an alloy containing primarily zinc along with some copper. Consider the following observations on copper content (%) for a sample of Bidri artifacts in London’s
CR5.5 ● Foal weight at birth is an indicator of health, so it is of interest to breeders of thoroughbred horses. Is foal weight related to the weight of the mare (mother)? The accompanying data are from the paper “Suckling Behaviour Does Not Measure Milk Intake in Horses” (Animal
CR5.2 Data from a survey of 1046 adults age 50 and older were summarized in the AARP Bulletin (November 2009). The following table gives relative frequency distributions of the responses to the question, “How much do you plan to spend for holiday gifts this year?” for respondents age 50 to 64
5.67 Consider the four (x, y) pairs (0, 0), (1, 1), 1, 21), and (2, 0).a. What is the value of the sample correlation coefficient r?b. If a fifth observation is made at the value x 5 6, find a value of y for which r . 0.5.c. If a fifth observation is made at the value x 5 6, find a value of y for
5.66 ● An accurate assessment of oxygen consumption provides important information for determining energy expenditure requirements for physically demanding tasks. The paper “Oxygen Consumption During Fire Suppression: Error of Heart Rate Estimation”(Ergonomics [1991]: 1469–1474) reported on
5.65 ● The article “Reduction in Soluble Protein and Chlorophyll Contents in a Few Plants as Indicators of Automobile Exhaust Pollution” (International Journal of Environmental Studies [1983]: 239–244) reported the following data on x 5 distance from a highway (in meters) and y 5 lead
5.64 No tortilla chip lover likes soggy chips, so it is important to find characteristics of the production process that produce chips with an appealing texture.The accompanying data on x 5 frying time (in seconds) and y 5 moisture content (%) appeared in the paper, “Thermal and Physical
5.62 ● The paper “Aspects of Food Finding by Wintering Bald Eagles” (The Auk [1983]: 477–484) examined therelationship between the time that eagles spend aerially searching for food (indicated by the percentage of eagles soaring) and relative food availability. The accompanying data were
5.61 The paper “Effects of Canine Parvovirus (CPV) on Gray Wolves in Minnesota” (Journal of Wildlife Management[1995]: 565–570) summarized a regression of y 5 percentage of pups in a capture on x 5 percentage of CPV prevalence among adults and pups. The equation of the least-squares line,
5.60 ● The following table gives the number of organ transplants performed in the United States each year from 1990 to 1999 (The Organ Procurement and Transplantation Network, 2003):Year Number of Transplants(in thousands)1 (1990) 15.0 2 15.7 3 16.1 4 17.6 5 18.3 6 19.4 7 20.0 8 20.3 9 21.4 10
5.59 ● Percentages of public school students in fourth grade in 1996 and in eighth grade in 2000 who were at or above the proficient level in mathematics were given in the article“Mixed Progress in Math” (USA Today, August 3, 2001) for eight western states:State 4th grade (1996) 8th grade
5.58 ● Researchers asked each child in a sample of 411 school-age children if they were more or less likely to purchase a lottery ticket at a store if lottery tickets were visible on the counter. The percentage that said that they were more likely to purchase a ticket by grade level are as
5.57 ● The following data on x 5 score on a measure of test anxiety and y 5 exam score for a sample of n 5 9 students are consistent with summary quantities given in the paper “Effects of Humor on Test Anxiety and Performance” (Psychological Reports [1999]:1203–1212):x 23 14 14 0 17 20 20
5.56 ● The paper “A Cross-National Relationship Between Sugar Consumption and Major Depression?” (Depression and Anxiety [2002]: 118–120) concluded that there was a correlation between refined sugar consumption(calories per person per day) and annual rate of major depression (cases per 100
5.55 ● The accompanying data represent x 5 amount of catalyst added to accelerate a chemical reaction and y 5 resulting reaction time:x 1 2 3 4 5 y 49 46 41 34 25a. Calculate r. Does the value of r suggest a strong linear relationship?b. Construct a scatterplot. From the plot, does the word
5. In the context of this activity, write a brief description of the danger of extrapolation.
4. If there appears to be a relationship between age and flexibility, fit a model that is appropriate for describing the relationship.

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