Introductory Statistics (2nd Edition)
2nd Edition
ISBN: 9780321978271
Author: Robert Gould, Colleen N. Ryan
Publisher: PEARSON
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Chapter 10, Problem 20SE
Is the Random Number Table Really Random? We counted ones, twos, threes, fours, and fives from a few lines of a random number table, and we should expect to get equal numbers of each. (We ignored the sixes, sevens, eights, nines, and zeros.) There were 14 ones, 12 twos, 16 threes, 11 fours, and 8 fives, which is 61 numbers in the categories selected. First, find the expected counts, which should all be the same.
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Then test the hypothesis that the random number table does not generate equal proportions of ones, twos, threes, fours, and fives, using a significance level of
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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 10 Solutions
Introductory Statistics (2nd Edition)
Ch. 10 - Tests a. In Chapter 8, you learned some tests of...Ch. 10 - In Chapter 9, you learned some tests of means. Are...Ch. 10 - Crime and Gender A statistics student conducted a...Ch. 10 - Red Cars and Stop Signs The table shows the raw...Ch. 10 - The table summarizes the outcomes of a study that...Ch. 10 - Finger Length There is a theory that relative...Ch. 10 - Prob. 7SECh. 10 - Prob. 8SECh. 10 - Effects of Television Violence on Men (Example 1)...Ch. 10 - Prob. 10SE
Ch. 10 - Mummies with Heart Disease According to the...Ch. 10 - Prob. 12SECh. 10 - Violins Stradivarius violins, made in the 1700s by...Ch. 10 - Coin Flips You flip a coin 100 times and get 58...Ch. 10 - Prob. 15SECh. 10 - Prob. 16SECh. 10 - Prob. 17SECh. 10 - Prob. 18SECh. 10 - Are Humans Like Random Number Generators? (Example...Ch. 10 - Is the Random Number Table Really Random? We...Ch. 10 - Coin Spins A penny was spun on a hard, flat...Ch. 10 - Prob. 22SECh. 10 - Is the Six-Sided Die Fair? The table shows the...Ch. 10 - Is the Six-Sided Die Fair? Repeat the chi-square...Ch. 10 - Violins Professional musicians listened to five...Ch. 10 - Mummies with Heart Disease Exercise 10.11 on...Ch. 10 - Party and Right Direction (Example 4) Suppose a...Ch. 10 - Antibiotic or Placebo A large number of surgery...Ch. 10 - Prob. 29SECh. 10 - Prob. 30SECh. 10 - Prob. 31SECh. 10 - Unemployment Rates U.S. Unemployment rates for all...Ch. 10 - Prob. 33SECh. 10 - Weight Loss Overweight or obese adults from...Ch. 10 - Prob. 35SECh. 10 - Prob. 36SECh. 10 - Gender and Happiness of Marriage The table shows...Ch. 10 - Is Smiling Independent of Age? Randomly chosen...Ch. 10 - Preschool Attendance and High School Graduation...Ch. 10 - Preschool Attendance and High School Graduation...Ch. 10 - Preschool Attendance and High School Graduation...Ch. 10 - Prob. 42SECh. 10 - Prob. 43SECh. 10 - Antiretrovirals to Prevent HIV A study conducted...Ch. 10 - Confederates and Compliance A study was done to...Ch. 10 - Endocarditis Kang et al. reported on a randomized...Ch. 10 - Prob. 47SECh. 10 - Prob. 48SECh. 10 - Prob. 49SECh. 10 - Night Shifts A random sample of nurses working...Ch. 10 - Gender and Political Party Affiliation The data in...Ch. 10 - Children and Happiness The data in the table come...Ch. 10 - Prob. 53SECh. 10 - Nice Rats Rats had a choice of freeing another rat...Ch. 10 - Young Criminals and Violence A statistics student...Ch. 10 - Egg Allergy in Children In a randomized,...Ch. 10 - Suppose you have a random sample of students...Ch. 10 - In exercises 10.57 to 10.64, choose an appropriate...Ch. 10 - Suppose you take a survey of random students at a...Ch. 10 - Prob. 60CRECh. 10 - Prob. 61CRECh. 10 - In exercises 10.57 to 10.64, choose an appropriate...Ch. 10 - Prob. 63CRECh. 10 - In exercises 10.57 to 10.64, choose an appropriate...Ch. 10 - Perry Preschool Arrests The Perry Preschool...Ch. 10 - Parental Training and Criminal Behavior of...Ch. 10 - Prob. 67CRECh. 10 - Prob. 68CRECh. 10 - Prob. 69CRECh. 10 - Prob. 70CRECh. 10 - Robot Cockroaches Cockroaches tend to rest in...Ch. 10 - Robot Cockroaches Refer to the description in...Ch. 10 - Prob. 73CRECh. 10 - Conviction Rate with Opposite Race Here are the...
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