Elementary Statistics: Picturing the World (6th Edition)
6th Edition
ISBN: 9780321911216
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Chapter 1.1, Problem 27E
To determine
To identify: The population and sample.
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1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
In a town with 5000 adults, a sample of 50 is selected using SRSWOR and asked their opinion of a proposed municipal project; 30 are found to favor it and 20 oppose it. If, in fact, the adults of the town were equally divided on the proposal, what would be the probability of observing what has been observed? Approximate using the Binomial distribution. Compare this with the exact probability which is 0.0418.
Chapter 1 Solutions
Elementary Statistics: Picturing the World (6th Edition)
Ch. 1.1 - Prob. 1TYCh. 1.1 - Prob. 2TYCh. 1.1 - Prob. 3TYCh. 1.1 - How is a sample related to a population?Ch. 1.1 - Why is a sample used more often than a population?Ch. 1.1 - What is the difference between a parameter and a...Ch. 1.1 - What are the two main branches of statistics?Ch. 1.1 - True or False? In Exercises 510, determine whether...Ch. 1.1 - True or False? In Exercises 510, determine whether...Ch. 1.1 - True or False? In Exercises 510, determine whether...
Ch. 1.1 - True or False? In Exercises 510, determine whether...Ch. 1.1 - True or False? In Exercises 510, determine whether...Ch. 1.1 - True or False? In Exercises 510, determine whether...Ch. 1.1 - Prob. 11ECh. 1.1 - Prob. 12ECh. 1.1 - Prob. 13ECh. 1.1 - Prob. 14ECh. 1.1 - Prob. 15ECh. 1.1 - Prob. 16ECh. 1.1 - Prob. 17ECh. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - Graphical Analysis In Exercises 2124, use the Venn...Ch. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - Prob. 25ECh. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.1 - Prob. 28ECh. 1.1 - Prob. 29ECh. 1.1 - Prob. 30ECh. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - Prob. 34ECh. 1.1 - Prob. 35ECh. 1.1 - Prob. 36ECh. 1.1 - Distinguishing Between a Parameter and a Statistic...Ch. 1.1 - Prob. 38ECh. 1.1 - Prob. 39ECh. 1.1 - Prob. 40ECh. 1.1 - Prob. 41ECh. 1.1 - Prob. 42ECh. 1.1 - Prob. 43ECh. 1.1 - Prob. 44ECh. 1.1 - Prob. 47ECh. 1.1 - Prob. 48ECh. 1.2 - Prob. 1TYCh. 1.2 - Prob. 2TYCh. 1.2 - Prob. 3TYCh. 1.2 - Name each level of measurement for which data can...Ch. 1.2 - Name each level of measurement for which data can...Ch. 1.2 - True or False? In Exercises 36, determine whether...Ch. 1.2 - True or False? In Exercises 36, determine whether...Ch. 1.2 - True or False? In Exercises 36, determine whether...Ch. 1.2 - True or False? In Exercises 36, determine whether...Ch. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Classifying Data by Type In Exercises 714,...Ch. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Classifying Data By Level In Exercises 1520,...Ch. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - The items below appear on a physician's intake...Ch. 1.2 - Graphical Analysis In Exercises 2124, determine...Ch. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Classifying Data by Type and Level In Exercises...Ch. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - Prob. 33ECh. 1.2 - Prob. 34ECh. 1.2 - Prob. 1CSCh. 1.2 - Prob. 2CSCh. 1.2 - Prob. 3CSCh. 1.2 - Prob. 4CSCh. 1.2 - Prob. 5CSCh. 1.2 - Prob. 6CSCh. 1.2 - Prob. 7CSCh. 1.2 - Prob. 8CSCh. 1.3 - Prob. 1TYCh. 1.3 - Prob. 2TYCh. 1.3 - Prob. 3TYCh. 1.3 - Prob. 4TYCh. 1.3 - What is the difference between an observational...Ch. 1.3 - What is the difference between a census and a...Ch. 1.3 - What is the difference between a random sample and...Ch. 1.3 - What is replication in an experiment? Why is...Ch. 1.3 - True or False? In Exercises 510, determine whether...Ch. 1.3 - True or False? In Exercises 510, determine whether...Ch. 1.3 - True or False? In Exercises 510, determine whether...Ch. 1.3 - Prob. 8ECh. 1.3 - True or False? In Exercises 510, determine whether...Ch. 1.3 - True or False? In Exercises 510, determine whether...Ch. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Random Number Table Use the sixth row of Table 1...Ch. 1.3 - Random Number Table Use the tenth row of Table 1...Ch. 1.3 - Random Numbers In Exercises 17 and 18, use...Ch. 1.3 - Random Numbers In Exercises 17 and 18, use...Ch. 1.3 - Sleep Deprivation A researcher wants to study the...Ch. 1.3 - Using a Simple Random Sample Volunteers for an...Ch. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1.3 - Prob. 27ECh. 1.3 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1.3 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1.3 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1.3 - Choosing Between a Census and a Sampling In...Ch. 1.3 - Choosing Between a Census and a Sampling In...Ch. 1.3 - Recognizing a Biased Question In Exercises 3134,...Ch. 1.3 - Recognizing a Biased Question In Exercises 3134,...Ch. 1.3 - Recognizing a Biased Question In Exercises 3134,...Ch. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Natural Experiments Observational studies are...Ch. 1.3 - Open and Closed Questions Two types of survey...Ch. 1.3 - Prob. 40ECh. 1.3 - Prob. 1ACh. 1.3 - In Exercises 14, identify the population and the...Ch. 1 - Prob. 1.1.1RECh. 1 - Prob. 1.1.2RECh. 1 - Prob. 1.1.3RECh. 1 - Prob. 1.1.4RECh. 1 - Prob. 1.1.5RECh. 1 - Prob. 1.1.6RECh. 1 - Which part of the survey described in Exercise 3...Ch. 1 - Prob. 1.1.8RECh. 1 - Prob. 1.1.9RECh. 1 - Prob. 1.1.10RECh. 1 - In Exercises 1114, determine whether the data are...Ch. 1 - In Exercises 1114, determine whether the data are...Ch. 1 - In Exercises 1518, determine the level of...Ch. 1 - In Exercises 1518, determine the level of...Ch. 1 - Prob. 1.2.15RECh. 1 - In Exercises 1518, determine the level of...Ch. 1 - In Exercises 19 and 20, determine whether the...Ch. 1 - Prob. 1.2.18RECh. 1 - Prob. 1.3.19RECh. 1 - Prob. 1.3.20RECh. 1 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1 - Prob. 1.3.25RECh. 1 - Identifying Sampling Techniques In Exercises 2328,...Ch. 1 - You want to know the favorite spring break...Ch. 1 - A study of the dietary habits of 359,264 Korean...Ch. 1 - Prob. 1.3.29RECh. 1 - Determine whether each number describes a...Ch. 1 - Prob. 1CQCh. 1 - Prob. 2CQCh. 1 - Determine whether the study is an observational...Ch. 1 - An experiment is performed to test the effects of...Ch. 1 - Prob. 5CQCh. 1 - Which technique used in Exercise 7 could lead to a...Ch. 1 - Determine whether you would take a census or use a...Ch. 1 - Determine whether each number describes a...Ch. 1 - Prob. 1CTCh. 1 - Prob. 2CTCh. 1 - Identify the sampling technique used, and discuss...Ch. 1 - Prob. 4CTCh. 1 - Determine whether the survey question is biased....Ch. 1 - Prob. 6CTCh. 1 - Prob. 1RSRDCh. 1 - Prob. 2RSRDCh. 1 - Prob. 3RSRDCh. 1 - The SEC (Securities and Exchange Commission) is...Ch. 1 - A quality control department is testing 25...Ch. 1 - Consider the population of ten digits: 0, 1, 2, 3,...Ch. 1 - Consider the population of 41 whole numbers from 0...Ch. 1 - Use random numbers to simulate rolling a six-sided...Ch. 1 - Prob. 6TCh. 1 - Use random numbers to simulate tossing a coin 100...Ch. 1 - You tossed a coin 100 times and got 77 heads and...Ch. 1 - A political analyst would like to survey a sample...
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