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Introduction To Statistics And Data Analysis 6th Edition Roxy Peck, Chris Olsen, Tom Short - Solutions
The paper “Examining Communication- and Media- Based Recreational Sedentary Behaviors Among Canadian Youth: Results from the COMPASS Study” (Preventive Medicine [2015]: 74–80) estimated that the time spent playing video or computer games by high school boys had a mean of 123.4 minutes per day
The events E and Ti are defined as E = the event that someone who is out of work and actively looking for work will find a job within the next month and Ti = 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 out
An author has written a book and submitted it to a publisher. The publisher offers to print the book and gives the author the choice between a flat payment of $10,000 and a royalty plan. Under the royalty plan the author would receive $1 for each copy of the book sold. The author thinks that the
Refer to the information given in Exercise 7.39. a. Calculate the mean and variance of z 5 total number of vehicles (cars and buses) on the ferry. b. Calculate the mean and variance of w 5 total amount of money collected in tolls. Exercise 7.39
Refer to the information given in Exercise 7.39. a. Calculate the mean and variance of the total amount of money collected in tolls from cars. b. Calculate the mean and variance of the total amount of money collected in tolls from buses. Exercise 7.39 x 0 1 2 3 p(x) 0.05 0.10 4 5 0.25 0.30 0.20
Exercise 7.8 gave the following probability distribution for x = the number of courses for which a randomly selected student at a certain university is registered: For this probability distribution, ? = 4.66 and ? = 1.20. a. Because ? - ? = 3.46, the x values 1, 2, and 3 are more than 1 standard
Referring to the previous exercise, use the result of Part (a) along with the fact that a carton contains 12 eggs to determine the mean value of z = the number of unbroken eggs. z can be written as a linear function of y; see Example 7.15. Previous exercise 3 4 y p(v) 0.65 0.01 0.04 0.20 0.10
Consider selecting a household in rural Thailand at random. Define the random variable x to bex = number of individuals living in the selected householdBased on information in an article that appeared in the Journal of Applied Probability (2011: 173–188), the probability distribution of x is
The density curve for the random variable w (the sum of two wait times) is given in the previous exercise. What is the probability that w is between 10 and 30? It might be easier first to find the probability that w is not between 10 and 30.
The article “Probabilistic Risk Assessment of Infrastructure Networks Subjected to Hurricanes” (12th International Conference on Applications of Statistics and Probability in Civil Engineering, 2015) suggests a uniform distribution as a model for the actual landfall position of the eye of a
The accompanying data on x = student-teacher ratio for a random sample of 25 high schools in Maine selected from a population of 85 high schools are consistent with summary values for the state of Maine that appeared in an article in the Bangor Daily News (September 22,2016,
Components coming off an assembly line are either free of defects (S, for success) or defective (F, for failure). Suppose that 70% of the components are defect-free. Components are independently selected and tested one by one. Let y denote the number of components that must be tested until a
Of all airline flight requests received by a certain discount ticket broker, 70% are for domestic travel (D) and 30% are for international flights (I). Define the random variable x to be the number of requests among the next three requests that are for domestic flights. Assuming independence of
Simulate the chance experiment described in the previous exercise using five slips of paper, with two marked defective and three marked not defective.Place the slips in a box, mix them well, and draw out two. Record the number of defective boards. Replace the slips and repeat until you have 50
Refer to the previous exercise. Suppose that because of the high rate of false-positives for the drug test, Mumble.com has instituted a mandatory independent second test for those who test positive on the first test.a. If one employee is selected at random, what is the probability that the selected
Suppose that a new Internet company Mumble .com requires all employees to take a drug test. Mumble .com can afford only the inexpensive drug test—the one with a 5% false-positive rate and a 10% false-negative rate. (That means that 5% of those who are not using drugs will incorrectly test
According to a study conducted by a risk assessment firm (Associated Press, December 8, 2005), drivers residing within 1 mile of a restaurant are 30% more likely to be in an accident in a given policy year. Consider the following two events: A = event that a driver has an accident during a policy
The Cedar Rapids Gazette (November 20, 1999) reported the following information on compliance with child restraint laws for cities in Iowa: a. Use the information provided to estimate the following probabilities: i. The probability that a randomly selected child is properly restrained given that
The article “Doctors Misdiagnose More Women, Blacks” (San Luis Obispo Tribune, April 20, 2000) gave the following information, which is based on a large study of more than 10,000 patients treated in emergency rooms in the eastern and midwestern United States:1. Doctors misdiagnosed heart
Two shipping services offer overnight delivery of parcels, and both promise delivery before 10 a.m. A mailorder catalog company ships 30% of its overnight packages using service 1 and 70% using service 2. Service 1 fails to meet the 10 a.m. delivery promise 10% of the time, whereas Service 2 fails
A person stands at the corner marked A of the square pictured in Exercise 7.4 and tosses a coin. If it lands heads up, the person moves one corner clockwise, to B. If the coin lands tails up, the person moves one corner counterclockwise, to D. This process is then repeated until the person arrives
Beverly is building a fireplace. She is using handmade decorative 8-inch bricks for the bottom row of the fireplace. Although the bricks are advertised as 8-inch bricks, the actual length of a brick is variable, and the brick lengths are approximately normally distributed with a mean of 8 inches
A point is randomly selected on the surface of a lake that has a maximum depth of 100 feet. Let y be the depth of the lake at the randomly chosen point.a. What are possible values of y?b. Is y discrete or continuous?
The following quote is from USA TODAY (January 21, 2010):Most Americans think the Census is important, and the majority say they will participate in the count this spring— although Hispanics, younger people and the less educated are not as enthusiastic, a Pew Research Center survey found.The poll
A point is randomly selected from the interior of the square pictured. Let x denote the distance from the lower left-hand corner A of the square to the selected point.? a. What are possible values of x? b. Is x a discrete or a continuous variable? See Example 7.3. B. 1 foot
Suppose that a box contains 25 light bulbs, of which 20 are good and the other 5 are defective. Consider randomly selecting three bulbs without replacement.Let E denote the event that the first bulb selected is good, F be the event that the second bulb is good, and G represent the event that the
Refer to Exercise 6.116, but now suppose that two viewers are randomly selected (without replacement). Let R1 and R2 denote the events that the first and second individuals, respectively, watched an R-rated movie. Are R1 and R2 independent events? Explain. From a practical point of view, can these
A theater complex is currently showing four R-rated movies, three PG-13 movies, two PG movies, and one G movie. The following table gives the number of people at the first showing of each movie on a certain Saturday: Suppose that one of these people is randomly selected. a. What is the
The general addition rule for three events states that A new magazine publishes columns entitled ?Art? (A), ?Books? (B), and ?Cinema? (C). Suppose that 14% of all subscribers read A23% read B 37% read C 8% read A and B 9% read A and C 13% read B and C 5% read all three columns What is the
In a school machine shop, 60% of all machine breakdowns occur on lathes and 15% occur on drill presses. Let E denote the event that the next machine breakdown is on a lathe, and let F denote the event that a drill press is the next machine to break down. With P(E) = 0.60 and P(F) = 0.15,
A study of the impact of seeking a second opinion about a medical condition is described in the paper “Evaluation of Outcomes from a National Patient-Initiated Second Opinion Program” (The American Journal of Medicine [2015], 1138e25– 1138e33). Based on a review of 6791 patientinitiated
The following table summarizing data on smoking status and age group is consistent with summary quantities obtained in a Gallup Poll published in the online article ?In U.S., Young Adults? Cigarette Use is Down Sharply? (gallup.com, December 10, 2015, retrieved April 25, 2017). Assume that it is
The article “Obesity, Smoking Damage U.S. Economy,” which appeared in the Gallup Online Business Journal (gallup.com, September 7, 2016, retrieved April 25, 2017), reported that based on a large representative sample of adult Americans, 52.7% claimed that they exercised at least 30 minutes on 3
False positive results are not uncommon with mammograms, a test used to screen for breast cancer. For a woman who has a positive mammogram, the probability that she actually has breast cancer is less than 0.05 if she is under 40 years old, and ranges from 0.05 to 0.109 if she is over 40 years old
Four students must work together on a group project. They decide that each will take responsibility for a particular part of the project, as follows: Because of the way the tasks have been divided, one student must finish before the next student can begin work. To ensure that the project is
On April 1, 2010, the Bureau of the Census in the United States attempted to count every U.S. resident. Suppose that the counts in the table given below are obtained for four counties in one region. a. If one person is selected at random from this region, what is the estimated probability that the
The report ?Airline Quality Rating 2016? (airlinequalityrating.com/reports/2016_AQR_Final .pdf, retrieved April 25, 2017) provides an overview of the complaints about airlines received by the U.S. Department of Transportation. The table below gives the number of complaints received by type of
The paper referenced in the previous exercise also included data for a second radiologist, Radiologist 2. Based on the data from the previous exercise for Radiologist 1 and the data in the accompanying table for Radiologist 2, write a paragraph comparing the accuracy of sex predictions made by
Radiologists are often asked to predict the sex of a baby from ultrasound images made during pregnancy. The authors of the paper ?The Use of Three Dimensional Ultrasound for Fetal Gender Determination in the First Trimester? (The British Journal of Radiology, [2003]: 448?451) followed up on 159
The article “U.S. Investors Split Between Digital and Traditional Banking” (gallup.com, August 5, 2016, retrieved April 25, 2017) summarized data from a Gallup survey of a random sample of 1019 U.S. adults with investments of $10,000 or more.Based on the survey data, it was estimated that 31%
Suppose that we define the following events:C = event that a randomly selected driver is observed to be using a cell phoneA = event that a randomly selected driver is observed driving a passenger automobileV = event that a randomly selected driver is observed driving a van or SUVT = event that a
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 = event that the first customer selected subscribes to cable TV and C2 = event that the second
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 P(F) = 0.10 and
A 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 at random from the 10 vehicles available.a. Let E denote the
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.Previous exerciseThe National Public Radio show Car Talk used to
The National Public Radio show Car Talk used to have a feature called “The Puzzler.” Listeners were 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
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. Suppose that any event involving
Consider the following events:T = event that a randomly selected adult trusts credit card companies to safeguard his or her personal dataM = event that a randomly selected adult is between the ages of 19 and 36O = event that a randomly selected adult is 37 or olderBased on a June 9, 2016, Gallup
In a January 2016 Harris Poll, each of 2252 American adults was asked the following question:If you had to choose, which ONE of the following sports would you say is your favorite?” (“Pro Football is Still America’s Favorite Sport,” theharrispoll.com/sports/Americas_Fav_Sport_2016 .html,
The report “Great Jobs, Great Lives. The Relationship Between Student Debt, Experiences and Perceptions of College Worth” (Gallup-Purdue Index 2015 Report) gave information on the percentage of recent college graduates (those graduating between 2006 and 2015, inclusive) who strongly agree with
The report “TV Drama/Comedy Viewers and Health Information” (cdc.gov/healthcommunication/pdf /healthstyles_2005.pdf, retrieved April 25, 2017) describes the results of a large survey that was conducted for the Centers for Disease Control and Prevention (CDC). The sample was selected in a way
The National Highway Traffic Safety Administration requires each U.S. state to carry out an observational study to assess the level of seat belt use in the state. The report ?2015 Utah Seat Belt Use Survey? (Utah Department of Public Safety, September 14, 2015) summarized data from the study done
The report ?2015 Utah Seat Belt Use Survey? (Utah Department of Public Safety?Highway Safety Office, September 14, 2015) stated that based on observing a large number of vehicle occupants, the estimated percentage of Utah drivers and passengers who wear seatbelts is 87.2%. The report also gave
The paper ?Accuracy and Reliability of Self-Reported Weight and Height in the Sister Study? (Public Health Nutrition [2012]: 989?999) investigates whether women accurately report their weight. The table below is based on comparing actual weight to self-reported weight for women participating in a
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
The article ?Americans Growing More Concerned About Head Injuries in Football? (theharrispoll.com, December 21, 2015) describes a survey of 2096 adult Americans. Survey participants were asked if they were football fans and also if they agreed or disagreed that the rules that the National Football
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
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. Assuming these data are representative of adult
Two different airlines have a flight from Los Angeles to New York that departs each weekday morning at a certain time. Suppose that E denotes the event that the first airline’s flight is fully booked on a particular day, and F denotes the event that the second airline’s flight is fully booked
The same issue of The Chronicle for Higher Education Almanac referenced in the previous exercise also reported the following information for Ph.D. degrees awarded by U.S. colleges in the 2013–2014 academic year:● A total of 54,070 Ph.D. degrees were awarded.● 12,504 of these degrees were in
According to The Chronicle for Higher Education Almanac (2016), there were 1,003,329 Associate degrees awarded by U.S. community colleges in the 2013–2014 academic year. A total of 613,034 of these degrees were awarded to women.a. If a person who received a degree in 2013–2014 was selected at
The report “Teens, Social Media & Technology Overview 2015” (Pew Research Center, April 9, 2015) summarized data from a large survey of teens age 13 to 17. Of those surveyed, 71% use Facebook and 52% use Instagram. Use these percentages to explain why the two events identified below cannot
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 for this chance experiment
Consider the chance experiment described in the previous exercise. a. For customers who purchase a single book, the estimated probabilities for the different possible outcomes are given in the cells of the accompanying table. What is the probability that a randomly selected single-book purchase
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 single-book purchase, two of the eight possible outcomes are a hardcover fiction book and an
Consider the chance experiment described in the previous exercise. a. What is the estimated probability that a randomly selected customer downloads five or more songs? b. What is the estimated probability that a randomly selected customer downloads one or two songs? c. What is the estimated
The manager of an online music store has kept records of the number of songs downloaded in a single transaction by customers who make a purchase at the store. Consider the chance experiment of observing the number of songs downloaded by a randomly selected customer. The accompanying table gives six
Consider the chance experiment described in the previous exercise. Suppose that the probability of an overnight delivery selection is 0.1, the probability of a second-day delivery selection is 0.3, and the probability of a standard-delivery selection is 0.4. Find the following probabilities.a. the
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-day delivery, standard delivery, or delivery to the nearest store for customer pick-up. Consider the chance
Consider a Venn diagram picturing two events A and B that are not mutually exclusive.a. Shade the event (A ⋃ B)C. On a separate Venn diagram shade the event AC ⋂ BC. How are these two events related?b. Shade the event (A ⋂ BC). On a separate Venn diagram shade the event AC ⋃ BC. How are
Using the outcomes for the chance experiment described in the previous exercise, identify outcomes in each of the following events:a. BCb. CCc. A ⋃ Bd. A ⋂ Be. A ⋂ CPrevious exerciseSuppose that, starting at a certain time, batteries coming off an assembly line are examined one by one to see
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 be
Suppose that, starting at a certain time, batteries coming off an assembly line are examined one by one to see whether they are defective (let D = defective and N = not defective). The chance experiment terminates as soon as a nondefective battery is obtained.a. Give five possible outcomes for this
A new model of laptop computer can be ordered with one of three screen sizes (10 inches, 12 inches, 15 inches) and one of four hard drive sizes (50 GB, 100 GB, 150 GB, and 200 GB). Consider the chance experiment in which a laptop order is selected and the screen size and hard drive size are
Refer to the chance experiment described in the previous exercise. a. Head, Prince, and Wilson are U.S. companies and the others are not. Let C denote the event that the racket purchased is made by a U.S. company. List the outcomes in the event B or C. b. List outcomes in B and C. c. Display the
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 oversize.
Refer to the chance experiment described in the previous exercise and the sample space for that experiment.a. List the outcomes in each of the following events. Which of these events are simple events? See Example 6.3i. the event that at least one car has an automatic transmissionii. the event that
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)?b. Display the possible outcomes in a tree diagram.
Define the term sample space, and then give the sample space for the chance experiment you described in Exercise 6.1.Exercise 6.1Define the term chance experiment, and give an example of a chance experiment with four possible outcomes.
Define the term chance experiment, and give an example of a chance experiment with four possible outcomes.
The following quote is from the paper “The Weight of the Bottle as a Possible Extrinsic Clue with Which to Estimate the Price (and Quality) of the Wine? Observed Correlations” (Food Quality and Preference [2012]: 41–45):The weight of the wine bottles was positively correlated (r = 0.12; p ,
The paper ?Depression, Body Mass Index, and Chronic Obstructive Pulmonary Disease?A Holistic Approach? (International Journal of COPD [2016]:239?249) gave data on change in body mass index (BMI in kilograms/meter2) and change in a measure of depression for patients suffering from depression who
Refer to the heart transplant data given in the previous exercise.a. Find a transformation of x and/or y that straightens the plot. Construct a scatterplot for your transformed variables.b. Using the transformed variables from Part (a), fit a least-squares line and use it to predict the number
The following table gives the number of heart transplants performed in the Unites States each year from 2006 to 2015 (U.S. Department of Health and Human Services,optn.transplant.hrsa.gov/data/view-data-reports /national-data/, retrieved April 22, 2017):Year ...................... Number of Heart
Food intake of grazing animals is limited by the rate grass can be chewed and swallowed, as well as the rate at which food can be digested. The authors of the paper “What Constrains Daily Intake in Thomson’s Gazelles?” (Ecology [1999]: 2338–2347) observed the grazing activity of captive
Use the information provided in the previous exercise to answer the following questions. a. Here are the values of x9 = log(x) and y9 = log(y): Construct a scatterplot of these transformed data, and comment on the pattern. b. Based on the accompanying MINITAB output, does the least-squares line
The accompanying data are a subset of data from the report “Great Jobs, Great Lives” (Gallup-Purdue Index2015 Report, gallup.com/reports/197144/gallup-purdue-index-report-2015.aspx, retrieved April 22, 2017). The values are approximate values read from a scatterplot. Students at a number of
The article ?$115K! The 13 Best Paying U.S. Companies? (USA TODAY, August 11, 2015) gave the following data on median worker pay (in thousands of dollars) and the 1-year percent change in stock price for the 13 highest paying companies in the United States. A scatterplot of these data is also
The first Batman movie was made over 50 years ago in 1966. Over the years, Batman has been played on screen by a number of actors and even by a Lego figure in the Lego Batman movies. In the original comic books, Batman was 188 centimeters tall (about 6'2") and weighed 95 kilograms (about 210
Acrylamide is a chemical that is sometimes found in cooked starchy foods and which is thought to increase the risk of certain kinds of cancer. The paper “A Statistical Regression Model for the Estimation of Acrylamide Concentrations in French Fries for Excess Lifetime Cancer Risk Assessment”
The report ?Airline Quality Rating 2016? (airlinequalityrating.com/reports/2016_AQR_Final.pdf, retrieved April 22, 2017) included the data for 13 U.S. airlines given in the table below. a. With x 5 Airline quality rating and y 5 On-time arrival percentage, construct a scatterplot. Does the
Does it pay to stay in school? The report Trends in Higher Education (The College Board, 2010) looked at the median hourly wage gain per additional year of schooling. The report states that workers with a high school diploma had a median hourly wage that was 10% higher than those who had only
The California State Park System Statistical Report for the 2014/2015 Fiscal Year (parks.ca.gov/pages/795/files/14-15%20Statistical%20 Report%20-%20INTERNET.pdf) gave the accompanying data on x 5 Amount of money collected in user fees (in thousands of dollars) and y = Operating cost (in thousands
The data given in the previous exercise on x = Callto-shock time (in minutes) and y = Survival rate (percent) were used to compute the equation of the least-squares line, which was ŷ = 101.33 - 9.30xThe newspaper article “FDA OKs Use of Home Defibrillators” (San Luis Obispo Tribune, November
Acrylamide is a chemical that is sometimes found in cooked starchy foods and which is thought to increase the risk of certain kinds of cancer. The paper “A Statistical Regression Model for the Estimation of Acrylamide Concentrations in French Fries for Excess Lifetime Cancer Risk Assessment”
The report ?Airline Quality Rating 2016? (airlinequalityrating.com/reports/2016_AQR_Final .pdf) included the accompanying data on the on-time arrival percentage and the number of complaints filed per 100,000 passengers for U.S. airlines. The report did not include data on the number of complaints
The accompanying data are a subset of data from the report “Great Jobs, Great Lives” (Gallup-PurdueIndex 2015 Report, gallup.com/reports/197144 /gallup-purdue index-report-2015.aspx). The values are approximate values read from a scatterplot.Students at a number of universities were asked if
The article ?$115K! The 13 Best Paying U.S. Companies? (USA TODAY, August 11, 2015) gave the following data on median worker pay (in thousands of dollars) and the 1-year percent change in stock price for the 13 highest paying companies in the United States. a. Construct a scatterplot for these
Data from the U.S. Federal Reserve Board (federalreserve.gov/releases/housedebt/, retrieved April 21, 2017) on consumer debt (as a percentage of personal income) and mortgage debt (also as a percentage of personal income) for the 10 years from 2006 to 2015 are shown in the following table:Consumer
Below are the data used to construct the time series plots in the previous exercise. Calculate the value of the correlation coefficient for the amount spent on science, space, and technology and the amount spent on pets. Explain how this value is consistent with your answer to the previous
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