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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Chapter 6.1, Problem 7PB

Playing the lottery The state of Ohio has several statewide lottery options. One is the Pick 3 game in which you pick one of the 1000 three-digit numbers between 000 and 999. The lottery selects a three-digit number at random. With a bet of $1, you win $500 if your number is selected and nothing ($0) otherwise. (Many states have a very similar type of lottery.) (Source: Background information from www.ohiolottery.com.)

a. With a single $1 bet, what is the probability that you win $500?
b. Let X denote your winnings for a $1 bet, so x = $0 or x = $500. Construct the probability distribution for X.
c. Show that the mean of the distribution equals 0.50, corresponding to an expected return of 50 cents for the dollar paid to play. Interpret the mean.
d. In Ohio’s Pick 4 lottery, you pick one of the 10,000 fourdigit numbers between 0000 and 9999 and (with a $1 bet) win $5000 if you get it correct. In terms of your expected winnings, with which game are you better off—playing Pick 4, or playing Pick 3? Justify your answer.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 6.1, Problem 6PB

Chapter 6.1, Problem 8PB

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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. 23PB Ch. 6.2 - Prob. 24PB Ch. 6.2 - Prob. 25PB Ch. 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. 39PB Ch. 6.3 - Prob. 40PB Ch. 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. 45PB Ch. 6.3 - Prob. 46PB Ch. 6.3 - Prob. 47PB Ch. 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. 50PB Ch. 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. 55CP Ch. 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. 59CP Ch. 6 - Prob. 60CP Ch. 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. 74CP Ch. 6 - Prob. 75CP Ch. 6 - Prob. 76CP Ch. 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. 84CP Ch. 6 - Prob. 85CP Ch. 6 - Longest streak made In basketball, when the...Ch. 6 - Airline overbooking For the Boston to Chicago...Ch. 6 - Prob. 89CP Ch. 6 - Prob. 90CP Ch. 6 - Prob. 91CP Ch. 6 - Prob. 92CP Ch. 6 - Prob. 93CP Ch. 6 - Prob. 94CP Ch. 6 - Prob. 95CP Ch. 6 - Prob. 96CP Ch. 6 - Prob. 97CP Ch. 6 - Prob. 98CP Ch. 6 - Prob. 99CP Ch. 6 - Prob. 100CP Ch. 6 - Prob. 101CP

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Solution Summary: The author calculates the probability of winning 500 by picking one of the 1,000 three-digit numbers between 000 and 999.

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