Fundamentals of Statistics Plus MyLab Statistics with Pearson eText - Title-Specific Access Card Package (5th Edition)
5th Edition
ISBN: 9780134763729
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 5.6, Problem 19AYU
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To find: The number of different ways that three men and three women can be seated around a circular table.
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
4. Linear Regression - Model Assumptions and Interpretation
A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple
linear regression model is proposed:
The analyst fits the model and obtains:
•
Ŷ50,000+150X
YBoB₁X + €
•
R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
Questions:
a) Interpret the slope coefficient in context.
b) Explain what the R² value tells us about the model's performance.
c) Based on the residual pattern, what regression assumption is likely violated? What might be the
consequence?
d) Suggest at least two remedies to improve the model, based on the residual analysis.
Chapter 5 Solutions
Fundamentals of Statistics Plus MyLab Statistics with Pearson eText - Title-Specific Access Card Package (5th Edition)
Ch. 5.1 - What is the probability of an event that is...Ch. 5.1 - What does it mean for an event to be unusual? Why...Ch. 5.1 - True or False: In a probability model, the sum of...Ch. 5.1 - True or False: Probability is a measure of the...Ch. 5.1 - In probability, a(n) _____ is any process that can...Ch. 5.1 - NW 6. A(n) _____ is any collection of outcomes...Ch. 5.1 - Verify that the table in the next column is a...Ch. 5.1 - Verify that the following is a probability model....Ch. 5.1 - Why is the following not a probability model?...Ch. 5.1 - Why is the following not a probability model?...
Ch. 5.1 - Which of the following numbers could be the...Ch. 5.1 - Which of the following numbers could be the...Ch. 5.1 - According to Nate Silver, the probability of a...Ch. 5.1 - In seven-card stud poker, a player is dealt seven...Ch. 5.1 - Suppose that you toss a coin 100 times and get 95...Ch. 5.1 - Suppose that you roll a die 100 times and get six...Ch. 5.1 - Bob is asked to construct a probability model for...Ch. 5.1 - NW 18. Blood Types A person can have one of four...Ch. 5.1 - If a person rolls a six-sided die and then flips a...Ch. 5.1 - If a basketball player shoots three free throws,...Ch. 5.1 - According to the U.S. Department of Education,...Ch. 5.1 - According to the American Veterinary Medical...Ch. 5.1 - let the sample space be S =...Ch. 5.1 - let the sample space be S =...Ch. 5.1 - let the sample space be S =...Ch. 5.1 - let the sample space be S =...Ch. 5.1 - Play Sports? A survey of 500 randomly selected...Ch. 5.1 - Volunteer? In a survey of 1100 female adults (18...Ch. 5.1 - NW 29. Home Runs The Wall Street Journal regularly...Ch. 5.1 - Planting Tulips A bag of 100 tulip bulbs purchased...Ch. 5.1 - Roulette In the game of roulette, a wheel consists...Ch. 5.1 - Birthdays Exclude leap years from the following...Ch. 5.1 - Genetics A gene is composed of two alleles, either...Ch. 5.1 - More Genetics In Problem 33, we learned that for...Ch. 5.1 - NW 35. College Survey In a national survey...Ch. 5.1 - College Survey In a national survey conducted by...Ch. 5.1 - Larceny Theft A police officer randomly selected...Ch. 5.1 - Multiple Births The following data represent the...Ch. 5.1 - In Problems 3942, use the given table, which lists...Ch. 5.1 - Prob. 40AYUCh. 5.1 - In Problems 3942, use the given table, which lists...Ch. 5.1 - In Problems 3942, use the given table, which lists...Ch. 5.1 - Going to Disney World John, Roberto, Clarice,...Ch. 5.1 - Six Flags In 2011, Six Flags St. Louis had 10...Ch. 5.1 - Prob. 45AYUCh. 5.1 - Prob. 46AYUCh. 5.1 - NW 47. Simulation Use a graphing calculator or...Ch. 5.1 - Classifying Probability Determine whether the...Ch. 5.1 - Prob. 49AYUCh. 5.1 - Prob. 51AYUCh. 5.1 - The middle 50% of enrolled freshmen at Washington...Ch. 5.1 - NFL Combine Each year the National Football League...Ch. 5.1 - Putting It Together: Drug Side Effects In...Ch. 5.1 - Prob. 55AYUCh. 5.1 - In computing classical probabilities, all outcomes...Ch. 5.1 - Describe what an unusual event is. Should the same...Ch. 5.1 - Prob. 58AYUCh. 5.1 - Describe the difference between classical and...Ch. 5.1 - Prob. 60AYUCh. 5.1 - Suppose you live in a town with two hospitalsone...Ch. 5.2 - What does it mean when two events are disjoint?Ch. 5.2 - If E and F are disjoint events, then P(E or F) =...Ch. 5.2 - If E and F are not disjoint events, then P(E or F)...Ch. 5.2 - What does it mean when two events are complements?Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 512, a probability experiment is...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - In Problems 1318, find the probability of the...Ch. 5.2 - If P (E) = 0.60, P (E or F) = 0.85, and P (E and...Ch. 5.2 - Prob. 20AYUCh. 5.2 - In Problems 2124, a golf ball is selected at...Ch. 5.2 - In Problems 2124, a golf ball is selected at...Ch. 5.2 - In Problems 2124, a golf ball is selected at...Ch. 5.2 - In Problems 2124, a golf ball is selected at...Ch. 5.2 - Weapon of Choice The following probability model...Ch. 5.2 - Family Structure The following probability model...Ch. 5.2 - If events E and F are disjoint and the events F...Ch. 5.2 - Draw a Venn diagram like that in Figure 10 that...Ch. 5.2 - Medicare Fines In an effort to reduce the number...Ch. 5.2 - Housing The following data represents the number...Ch. 5.2 - A Deck of Cards A standard deck of cards contains...Ch. 5.2 - A Deck of Cards A standard deck of cards contains...Ch. 5.2 - Birthdays Exclude leap years from the following...Ch. 5.2 - Roulette In the game of roulette, a wheel consists...Ch. 5.2 - Health Problems According to the Centers for...Ch. 5.2 - Visits to the Doctor A National Ambulatory Medical...Ch. 5.2 - Language Spoken at Home According to the U.S....Ch. 5.2 - Getting to Work According to the U.S. Census...Ch. 5.2 - Cigar Smoking The data in the table in the next...Ch. 5.2 - Working Couples A guidance counselor at a middle...Ch. 5.2 - The Placebo Effect A company is testing a new...Ch. 5.2 - Social Media Harris Interactive conducted a survey...Ch. 5.2 - Driver Fatalities The following data represent the...Ch. 5.2 - Prob. 44AYUCh. 5.2 - Putting It Together: Red Light Cameras In a study...Ch. 5.2 - Exam Scores The following data represent the...Ch. 5.3 - Two events E and F are _____ if the occurrence of...Ch. 5.3 - The word and in probability implies that we use...Ch. 5.3 - The word or in probability implies that we use the...Ch. 5.3 - True or False: When two events are disjoint, they...Ch. 5.3 - If two events E and F are independent, P (E and F)...Ch. 5.3 - Suppose events E and F are disjoint. What is P(E...Ch. 5.3 - Determine whether the events E and F are...Ch. 5.3 - Determine whether the events E and F are...Ch. 5.3 - Suppose that events E and F are independent, P (E)...Ch. 5.3 - Suppose that events E and F are independent, P (E)...Ch. 5.3 - Flipping a Coin What is the probability of...Ch. 5.3 - Rolling a Die What is the probability of obtaining...Ch. 5.3 - Southpaws About 13% of the population is...Ch. 5.3 - Double Jackpot Shawn lives near the border of...Ch. 5.3 - False Positives The ELISA is a test to determine...Ch. 5.3 - Prob. 16AYUCh. 5.3 - Life Expectancy The probability that a randomly...Ch. 5.3 - Life Expectancy The probability that a randomly...Ch. 5.3 - Derivatives In finance, a derivative is a...Ch. 5.3 - Quality Control Suppose that a company selects two...Ch. 5.3 - Reliability and Redundancy In airline...Ch. 5.3 - Reliability For a parallel structure of identical...Ch. 5.3 - Prob. 23AYUCh. 5.3 - Cold Streaks Players in sports are said to have...Ch. 5.3 - Bowling Suppose that Ralph gets a strike when...Ch. 5.3 - Driving under the Influence Among 21- to...Ch. 5.3 - Prob. 27AYUCh. 5.3 - Audits and Pet Ownership According to Internal...Ch. 5.3 - Weight Gain and Gender According to the National...Ch. 5.3 - Stocks Suppose your financial advisor recommends...Ch. 5.3 - Betting on Sports According to a Gallup Poll,...Ch. 5.3 - Prob. 32AYUCh. 5.3 - Prob. 33AYUCh. 5.3 - Prob. 34AYUCh. 5.4 - The notation P(F|E) means the probability of event...Ch. 5.4 - If P (E) = 0,6 and P(E\F) = 0.34, are events E and...Ch. 5.4 - Prob. 3AYUCh. 5.4 - Suppose that E and F are two events and that P(E...Ch. 5.4 - Suppose that E and F are two events and that N(E...Ch. 5.4 - Suppose that E and F are two events and that N...Ch. 5.4 - Suppose that E and F are two events and that P (E)...Ch. 5.4 - Prob. 8AYUCh. 5.4 - According to the U.S. Census Bureau, the...Ch. 5.4 - Prob. 10AYUCh. 5.4 - Drawing a Card Suppose that a single card is...Ch. 5.4 - Prob. 12AYUCh. 5.4 - Rainy Days For the month of June in the city of...Ch. 5.4 - Cause of Death According to the U.S. National...Ch. 5.4 - High School Dropouts According to the U.S. Census...Ch. 5.4 - Income by Region According to the U.S. Census...Ch. 5.4 - Made in America In a recent Harris Poll, a random...Ch. 5.4 - Social Media Adult Americans (18 years or older)...Ch. 5.4 - Driver Fatalities The following data represent the...Ch. 5.4 - Speeding Tickets Use the results of Problem 44 in...Ch. 5.4 - Acceptance Sampling Suppose that you just received...Ch. 5.4 - Committee A committee consisting of four women and...Ch. 5.4 - Suppose that two cards are randomly selected from...Ch. 5.4 - Suppose that two cards are randomly selected from...Ch. 5.4 - Board Work This past semester, I had a small...Ch. 5.4 - Party My wife has organized a monthly neighborhood...Ch. 5.4 - Playing Music on Random Setting Suppose that a...Ch. 5.4 - Packaging Error Because of a manufacturing error,...Ch. 5.4 - Planting Tulips A bag of 30 tulip bulbs purchased...Ch. 5.4 - Golf Balls The local golf store sells an onion bag...Ch. 5.4 - Smokers According to the National Center for...Ch. 5.4 - Prob. 32AYUCh. 5.4 - The Birthday Problem Determine the probability...Ch. 5.4 - The Birthday Problem Using the procedure given in...Ch. 5.4 - Prob. 35AYUCh. 5.4 - Party Affiliation The following data represent...Ch. 5.4 - A Flush A flush in the card game of poker occurs...Ch. 5.4 - Prob. 38AYUCh. 5.4 - Independence in Small Samples from Large...Ch. 5.4 - Independence in Small Samples from Large...Ch. 5.4 - Prob. 41AYUCh. 5.4 - Prob. 42AYUCh. 5.5 - A _____ is an ordered arrangement of r objects...Ch. 5.5 - A _____ is an arrangement of r objects chosen from...Ch. 5.5 - True or False: In a combination problem, order is...Ch. 5.5 - The factorial symbol, n!, is defined as n! _____...Ch. 5.5 - In Problems 510, find the value of each factorial....Ch. 5.5 - In Problems 510, find the value of each factorial....Ch. 5.5 - In Problems 510, find the value of each factorial....Ch. 5.5 - In Problems 510, find the value of each factorial....Ch. 5.5 - Prob. 9AYUCh. 5.5 - Prob. 10AYUCh. 5.5 - In Problems 1118, find the value of each...Ch. 5.5 - Prob. 12AYUCh. 5.5 - In Problems 1118, find the value of each...Ch. 5.5 - In Problems 1118, find the value of each...Ch. 5.5 - Prob. 15AYUCh. 5.5 - Prob. 16AYUCh. 5.5 - Prob. 17AYUCh. 5.5 - In Problems 1118, find the value of each...Ch. 5.5 - In Problems 1926, find the value of each...Ch. 5.5 - In Problems 1926, find the value of each...Ch. 5.5 - Prob. 21AYUCh. 5.5 - Prob. 22AYUCh. 5.5 - Prob. 23AYUCh. 5.5 - Prob. 24AYUCh. 5.5 - Prob. 25AYUCh. 5.5 - In Problems 1926, find the value of each...Ch. 5.5 - List all the permutations of five objects a, b, c,...Ch. 5.5 - List all the permutations of four objects a, b, c,...Ch. 5.5 - List all the combinations of five objects a, b, c,...Ch. 5.5 - Prob. 30AYUCh. 5.5 - Clothing Options A man has six shirts and four...Ch. 5.5 - Prob. 32AYUCh. 5.5 - Prob. 33AYUCh. 5.5 - Arranging Students In how many ways can 15...Ch. 5.5 - Traveling Salesperson A salesperson must travel to...Ch. 5.5 - Prob. 36AYUCh. 5.5 - Prob. 37AYUCh. 5.5 - Stocks on the NASDAQ Companies whose stocks are...Ch. 5.5 - Garage Door Code Outside a home there is a keypad...Ch. 5.5 - Social Security Numbers A Social Security number...Ch. 5.5 - User Names Suppose that a local area network...Ch. 5.5 - User Names How many user names are possible in...Ch. 5.5 - Combination Locks A combination lock has 50...Ch. 5.5 - Forming License Plate Numbers How many different...Ch. 5.5 - INDY 500 Suppose 40 cars start at the Indianapolis...Ch. 5.5 - Betting on the Perfecta In how many ways can the...Ch. 5.5 - Forming a Committee Four members from a 20-person...Ch. 5.5 - Forming a Committee Four members from a 50-person...Ch. 5.5 - Lottery A lottery exists where balls numbered 125...Ch. 5.5 - Forming a Committee In the U.S. Senate, there are...Ch. 5.5 - Simple Random Sample How many different simple...Ch. 5.5 - Simple Random Sample How many different simple...Ch. 5.5 - Prob. 53AYUCh. 5.5 - Prob. 54AYUCh. 5.5 - DNA Sequences (See Example 10 on page 278.) How...Ch. 5.5 - Prob. 56AYUCh. 5.5 - Landscape Design A golf-course architect has four...Ch. 5.5 - Starting Lineup A baseball team consists of three...Ch. 5.5 - Prob. 59AYUCh. 5.5 - Mega Millions In Mega Millions, an urn contains...Ch. 5.5 - Selecting a Jury The grade appeal process at a...Ch. 5.5 - Selecting a Committee Suppose that there are 55...Ch. 5.5 - Acceptance Sampling Suppose that a shipment of 120...Ch. 5.5 - In the Dark A box containing twelve 40-watt light...Ch. 5.5 - Randomly Playing Songs Suppose a playlist you just...Ch. 5.5 - Packaging Error Through a manufacturing error,...Ch. 5.5 - Prob. 67AYUCh. 5.5 - Two of a Kind Follow the outline presented in...Ch. 5.5 - Prob. 69AYUCh. 5.5 - Acceptance Sampling Suppose that you have just...Ch. 5.5 - Password Policy According to the Sefton Council...Ch. 5.6 - What is the difference between a permutation and a...Ch. 5.6 - What method of assigning probabilities to a simple...Ch. 5.6 - Prob. 3AYUCh. 5.6 - Prob. 4AYUCh. 5.6 - Prob. 5AYUCh. 5.6 - Prob. 6AYUCh. 5.6 - Prob. 7AYUCh. 5.6 - Prob. 8AYUCh. 5.6 - Prob. 9AYUCh. 5.6 - Prob. 10AYUCh. 5.6 - In Problems 1012, evaluate each expression. 11....Ch. 5.6 - In Problems 1012, evaluate each expression. 12....Ch. 5.6 - Suppose that events E and F are independent. P (E)...Ch. 5.6 - Prob. 14AYUCh. 5.6 - Prob. 16AYUCh. 5.6 - Soccer? In a survey of 500 randomly selected...Ch. 5.6 - Apartment Vacancy A real estate agent conducted a...Ch. 5.6 - Prob. 19AYUCh. 5.6 - Starting Lineups Paytons futsal team consists of...Ch. 5.6 - Titanic Survivors The following data represent the...Ch. 5.6 - Marijuana Use According to the Statistical...Ch. 5.6 - Prob. 23AYUCh. 5.6 - National Honor Society The distribution of...Ch. 5.6 - Instant Winner In 2002, Valerie Wilson won 1...Ch. 5.6 - Text Twist In the game Text Twist, six letters are...Ch. 5.6 - Marriage and Education According to the U.S....Ch. 5.6 - Weather Forecast The weather forecast says there...Ch. 5.6 - Essay Test An essay test in European History has...Ch. 5.6 - Exercise Routines Todd is putting together an...Ch. 5.6 - New Cars If the 2015 Hyundai Genesis has 2 engine...Ch. 5.6 - Lingo In the gameshow Lingo, the team that...Ch. 5 - (a) a. Which among the following numbers could be...Ch. 5 - For Problems 25, let the sample space be S = {red,...Ch. 5 - For Problems 25, let the sample space be S = {red,...Ch. 5 - For Problems 25, let the sample space be S = {red,...Ch. 5 - For Problems 25, let the sample space be S = {red,...Ch. 5 - Suppose that P (E) = 0.76, P (F) = 0.45, and P (E...Ch. 5 - Suppose that P (E) = 0.36, P (F) = 0.12, and E and...Ch. 5 - Suppose that events E and F are independent. In...Ch. 5 - Suppose that P (E) = 0.8, P (F) = 0.5, and P (E...Ch. 5 - Suppose that P (E) = 0.59 and P(F|E) = 0.45. What...Ch. 5 - Suppose that P (E and F) = 0.35 and P (F) = 0.7....Ch. 5 - Determine the value of each of the following: a....Ch. 5 - Roulette In the game of roulette, a wheel consists...Ch. 5 - Traffic Fatalities In 2013, there were 32.719...Ch. 5 - Long Life? In a poll conducted by Genworth...Ch. 5 - Gestation Period versus Weight The following data...Ch. 5 - Who Do You Trust? According to the National...Ch. 5 - Pick 3 For the Illinois Lotterys PICK 3 game, a...Ch. 5 - Prob. 19RECh. 5 - Drawing Cards Suppose that you draw 3 cards...Ch. 5 - Forming License Plates A license plate is designed...Ch. 5 - Prob. 22RECh. 5 - Arranging Flags How many different vertical...Ch. 5 - Prob. 24RECh. 5 - Arizonas Pick 5 In one of Arizonas lotteries,...Ch. 5 - Packaging Error Because of a mistake in packaging,...Ch. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - Playing Five-Card Stud In the game of five-card...Ch. 5 - Prob. 30RECh. 5 - Lottery Luck In 1996, a New York couple won 2.5...Ch. 5 - Coffee Sales The following data represent the...Ch. 5 - Prob. 1CTCh. 5 - Prob. 2CTCh. 5 - For Problems 24, let the sample space be S =...Ch. 5 - For Problems 24, let the sample space be S =...Ch. 5 - Suppose that P (E) = 0.37 and P (F) = 0.22. a....Ch. 5 - Suppose that P (E) = 0.15, P (F) = 0.45, and...Ch. 5 - Determine the value of each of the following: a....Ch. 5 - Craps is a dice game in which two fair dice are...Ch. 5 - According to Gallup, 26% of adult Americans...Ch. 5 - The following probability model shows the...Ch. 5 - The following represent the results of a survey in...Ch. 5 - During the 2014 season, the Los Angeles Dodgers...Ch. 5 - You just received a shipment of 10 DVD players....Ch. 5 - Prob. 14CTCh. 5 - The U.S. Senate Appropriations Committee has 29...Ch. 5 - Prob. 16CTCh. 5 - Prob. 17CTCh. 5 - A survey distributed at the 28th Lunar and...Ch. 5 - How many distinguishable DNA sequences can be...Ch. 5 - A student is taking a 40-question multiple-choice...Ch. 5 - Offender is at least 18.Ch. 5 - Prob. 2CSCh. 5 - Prob. 3CSCh. 5 - Prob. 4CSCh. 5 - Prob. 5CSCh. 5 - Prob. 6CSCh. 5 - Prob. 7CSCh. 5 - Prob. 8CSCh. 5 - Prob. 9CSCh. 5 - Prob. 10CSCh. 5 - Prob. 11CSCh. 5 - Prob. 12CSCh. 5 - Prob. 13CSCh. 5 - Prob. 14CSCh. 5 - Prob. 15CSCh. 5 - Prob. 16CSCh. 5 - Prob. 17CSCh. 5 - Prob. 18CSCh. 5 - Prob. 19CSCh. 5 - Prob. 20CSCh. 5 - Prob. 21CSCh. 5 - Prob. 22CSCh. 5 - Prob. 23CSCh. 5 - Prob. 24CS
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