Statistics: The Art and Science of Learning from Data (4th Edition)
4th Edition
ISBN: 9780321997838
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
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Chapter 6, Problem 89CP
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A common way for two people to settle a frivolous dispute is to play a game of rock-paper-scissors. In this game, each person simultaneously displays a hand signal to indicate a rock, a piece of paper, or a pair of scissors. Rock beats scissors, scissors beats paper, and paper beats rock. If both players select the same hand signal, the game results in a tie.
Two roommates, roommate A and roommate B, are expecting company and are arguing over who should have to wash the dishes before the company arrives. Roommate A suggests a game of rock-paper-scissors to settle the dispute.
Consider the game of rock-paper-scissors to be an experiment. In the long run, roommate A chooses rock 21% of the time, and roommate B chooses rock 61% of the time; roommate A selects paper 39% of the time, and roommate B selects paper 21% of the time; roommate A chooses scissors 40% of the time, and roommate B chooses scissors 18% of the time. (These choices are made randomly and independently of each…
Chapter 6 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Ch. 6.1 - Rolling dice a. State in a table the probability...Ch. 6.1 - Dental Insurance You plan to purchase dental...Ch. 6.1 - San Francisco Giants hitting The table shows the...Ch. 6.1 - Best of three In a best out of three series played...Ch. 6.1 - Grade distribution An instructor always assigns...Ch. 6.1 - Selling houses Let X represent the number of homes...Ch. 6.1 - Playing the lottery The state of Ohio has several...Ch. 6.1 - Roulette A roulette wheel consists of 38 numbers,...Ch. 6.1 - More Roulette The previous exercise on roulette...Ch. 6.1 - Prob. 10PB
Ch. 6.1 - Profit and the weather From past experience, a...Ch. 6.1 - Buying on eBay You are watching two items posted...Ch. 6.1 - Selling at the right price Some companies, such as...Ch. 6.1 - Uniform distribution A random number generator is...Ch. 6.1 - TV watching A social scientist uses the General...Ch. 6.2 - Probabilities in tails For a normal distribution,...Ch. 6.2 - Probability in graph For the normal distributions...Ch. 6.2 - Empirical rule Verify the empirical rule by using...Ch. 6.2 - Central probabilities For a normal distribution,...Ch. 6.2 - z-score for given probability in tails For a...Ch. 6.2 - Probability in tails for given z-score For a...Ch. 6.2 - z-score for right-tail probability a. For the...Ch. 6.2 - Prob. 23PBCh. 6.2 - Prob. 24PBCh. 6.2 - Prob. 25PBCh. 6.2 - Coffee Machine Suppose your favorite coffee...Ch. 6.2 - Energy use An energy study in Gainesville,...Ch. 6.2 - Birth weight for boys In the United States, the...Ch. 6.2 - MDI The Mental Development Index (MDI) of the...Ch. 6.2 - Quartiles and outliers Refer to the previous...Ch. 6.2 - April precipitation Over roughly the past 100...Ch. 6.2 - Tall enough to ride? A new roller coaster at an...Ch. 6.2 - SAT versus ACT SAT math scores follow a normal...Ch. 6.2 - Relative height Refer to the normal distributions...Ch. 6.3 - Kidney transplants In kidney transplantations,...Ch. 6.3 - Compatible donors Refer to the previous exercise....Ch. 6.3 - Symmetric binomial Construct a graph similar to...Ch. 6.3 - Number of girls in a family Each newborn baby has...Ch. 6.3 - Prob. 39PBCh. 6.3 - Prob. 40PBCh. 6.3 - Passing by guessing A quiz in a statistics course...Ch. 6.3 - NBA shooting In the National Basketball...Ch. 6.3 - Season performance Refer to the previous exercise....Ch. 6.3 - Is the die balanced? A balanced die with six sides...Ch. 6.3 - Prob. 45PBCh. 6.3 - Prob. 46PBCh. 6.3 - Prob. 47PBCh. 6.3 - Checking guidelines For Example 13 on the gender...Ch. 6.3 - Class sample Four of the 20 students (20%) in a...Ch. 6.3 - Prob. 50PBCh. 6.3 - Binomial assumptions For the following random...Ch. 6 - Grandparents Let X = the number of living...Ch. 6 - Straight or boxed? Consider a Pick-3 lottery such...Ch. 6 - Auctioning paintings A collector is interested in...Ch. 6 - Prob. 55CPCh. 6 - Are you risk averse? You need to choose between...Ch. 6 - Flyers insurance An insurance company sells a...Ch. 6 - Normal probabilities For a normal distribution,...Ch. 6 - Prob. 59CPCh. 6 - Prob. 60CPCh. 6 - Quartiles If z is the positive number such that...Ch. 6 - Boys and girls birth weight Exercise 6.28...Ch. 6 - Cholesterol The American Heart Association reports...Ch. 6 - Female heights Female heights in North America...Ch. 6 - Cloning butterflies The wingspans of recently...Ch. 6 - Gestation times For 5459 pregnant women using...Ch. 6 - Used car prices Data from the Web site carmax.com...Ch. 6 - Used car deals Refer to the previous exercise....Ch. 6 - Global warming Suppose that weekly use of gasoline...Ch. 6 - Fast-food profits Macs fast-food restaurant finds...Ch. 6 - Metric height A Dutch researcher reads that male...Ch. 6 - Manufacturing tennis balls According to the rules...Ch. 6 - Brides choice of surname According to a study done...Ch. 6 - Prob. 74CPCh. 6 - Prob. 75CPCh. 6 - Prob. 76CPCh. 6 - Weather A weather forecaster states, The chance of...Ch. 6 - Dating success Based on past experience, Julio...Ch. 6 - Canadian lottery In one Canadian lottery option,...Ch. 6 - Likes on Facebook A large retail chain sends out...Ch. 6 - Likes with online credit The retail chain from the...Ch. 6 - Which distribution for sales? A salesperson uses...Ch. 6 - Best of five Example 2 gave the probability...Ch. 6 - Prob. 84CPCh. 6 - Prob. 85CPCh. 6 - Longest streak made In basketball, when the...Ch. 6 - Airline overbooking For the Boston to Chicago...Ch. 6 - Prob. 89CPCh. 6 - Prob. 90CPCh. 6 - Prob. 91CPCh. 6 - Prob. 92CPCh. 6 - Prob. 93CPCh. 6 - Prob. 94CPCh. 6 - Prob. 95CPCh. 6 - Prob. 96CPCh. 6 - Prob. 97CPCh. 6 - Prob. 98CPCh. 6 - Prob. 99CPCh. 6 - Prob. 100CPCh. 6 - Prob. 101CP
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- A qualifying exam for a graduate school program has a math section and a verbal section. Students receive a score of 1, 2, or 3 on each section. Define X as a student’s score on the math section and Y as a student’s score on the verbal section. Test scores vary according to the following bivariate probability distribution. y 1 2 3 1 0.22 0.33 0.05 x 2 0.00 0.08 0.20 3 0.07 0.05 0.00 μXX = , and μYY = σXX = , and σYY = The covariance of X and Y is . The coefficient of correlation is . The variables X and Y independent. The expected value of X + Y is , and the variance of X + Y is . To be accepted to a particular graduate school program, a student must have a combined score of 4 on the qualifying exam. What is the probability that a randomly selected exam taker qualifies for the program? 0.45 0.47 0.46 0.33 Chebysheff’s Theorem states that the…arrow_forwardwhat is the correct answer and why?arrow_forward(a) How many bit strings of length 10 both begin with a 1 and end with 2 zeroes? (b) How many permutations of the letters PQRSTUV contain PRS and QV?arrow_forward
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- A common way for two people to settle a frivolous dispute is to play a game of rock-paper-scissors. In this game, each person simultaneously displays a hand signal to indicate a rock, a piece of paper, or a pair of scissors. Rock beats scissors, scissors beats paper, and paper beats rock. If both players select the same hand signal, the game results in a tie. Two roommates, roommate A and roommate B, are expecting company and are arguing over who should have to wash the dishes before the company arrives. Roommate A suggests a game of rock-paper-scissors to settle the dispute. Consider the game of rock-paper-scissors to be an experiment. In the long run, roommate A chooses rock 24% of the time, and roommate B chooses rock 85% of the time; roommate A selects paper 12% of the time, and roommate B selects paper 14% of the time; roommate A chooses scissors 64% of the time, and roommate B chooses scissors 1% of the time. (These choices are made randomly and independently of each…arrow_forwardPerform the following hypothesis test: HO: µ = 6 H1: µ 6 The sample mean is 5.6, sample standard deviation of 1.5 and a sample size of 42. Use a 5% significance level. Need to answer the following questions: what is the value of the test statistic? what is the p-value for this test (round to 3 decimal places)? what is the decision (reject the null hypothesis or do not reject the null hypothesis)?arrow_forwardPerform the following hypothesis test of a proportion: HO: p = 0.125 HA: p 0.125 The sample proportion is 0.2 based on a sample size of 95. Use a 10% significance level. need to solve the following questions: what is the value of the test statistic? what is the p-value? what is the decision (reject the null hypothesis or do not reject the null hypothesis)?arrow_forward
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