Introductory Statistics (2nd Edition)
2nd Edition
ISBN: 9780321978271
Author: Robert Gould, Colleen N. Ryan
Publisher: PEARSON
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Textbook Question
Chapter 8, Problem 73CRE
Choosing a Test and Giving the Hypotheses Give the null and alternative hypotheses for each test, and state whether a one-proportion
a. You test a person to see whether he can tell tap water from bottled water. You give him 20 sips selected randomly (half from tap water and half from bottled water) and record the proportion he gets correct to test the hypothesis.
b. You test a random sample of students at your college who stand on one foot with their eyes closed and determine who can stand for at least 10 seconds, comparing athletes and nonathletes.
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Chapter 8 Solutions
Introductory Statistics (2nd Edition)
Ch. 8 - Choose one of the answers given. The null...Ch. 8 - Choose one of the answers in each case. In...Ch. 8 - Boot Camp (Example 1) Suppose an experiment is...Ch. 8 - Scrubs A research hospital tries a new antibiotic...Ch. 8 - Magic A magician claims he can cause a coin to...Ch. 8 - Water A friend is tested to see whether he can...Ch. 8 - Heart Attack Prevention A new drug is being tested...Ch. 8 - Stroke Survival Rate The proportion of people who...Ch. 8 - Coin Flips (Example 2) A coin is flipped 30 times...Ch. 8 - Die Rolls You roll a six-sided die 30 times and...
Ch. 8 - Prob. 11SECh. 8 - Multiple-Choice Test A teacher is giving an exam...Ch. 8 - Dropouts According to Time magazine (June 11,...Ch. 8 - Prob. 14SECh. 8 - Boot Camp, Again (Example 4) Refer to Exercise...Ch. 8 - Prob. 16SECh. 8 - Coke versus Pepsi (Example 5) Suppose you are...Ch. 8 - St. Louis Jury Pool St. Louis County is 24 African...Ch. 8 - Coke vs. Pepsi (Example 6) Suppose you are testing...Ch. 8 - Prob. 20SECh. 8 - Cheating? A professor creates two versions of a 20...Ch. 8 - Guessing A 20-question multiple choice quiz has...Ch. 8 - Dreaming (Example 7) A 2003 study of dreaming...Ch. 8 - Age Discrimination About 30 of the population in...Ch. 8 - Marriage Obsolete (Example 8) When asked whether...Ch. 8 - Prob. 26SECh. 8 - Coke versus Pepsi A taste test is done to see...Ch. 8 - Seat Belts Suppose we are testing people to see...Ch. 8 - Sleep Walking (Example 9) According to Time...Ch. 8 - Prob. 30SECh. 8 - Sleep Walking, Again (Example 10) According to...Ch. 8 - Women CEOs, Again the percentage of female CEOs in...Ch. 8 - p-Values For each graph, indicate whether the...Ch. 8 - p-Values For each graph, state whether the shaded...Ch. 8 - Gun Control Historically, the percentage of U.S....Ch. 8 - Death Penalty A Pew Poll in November 2011 showed...Ch. 8 - Prob. 37SECh. 8 - Plane Crashes According to one source, 50 of plane...Ch. 8 - Mercury in Freshwater Fish Some experts believe...Ch. 8 - Prob. 40SECh. 8 - Morse’s Proportion of ts Samuel Morse determined...Ch. 8 - Morse’s Proportion of as Samuel Morse determined...Ch. 8 - p-Values (Example 11) A researcher carried out a...Ch. 8 - Coin Flips A test is conducted in which a coin is...Ch. 8 - Errors with Pennies (Example 12) Suppose you are...Ch. 8 - Errors with Toast Suppose you are testing someone...Ch. 8 - Blackstone on Errors in Trials Sir William...Ch. 8 - Alpha By establishing a small value for the...Ch. 8 - Flaws (Example 13) A person spinning a 1962 penny...Ch. 8 - Flaws The null hypothesis on true/false tests is...Ch. 8 - Which Method? A proponent of a new proposition on...Ch. 8 - Which Method? A proponent of a new proposition on...Ch. 8 - Effectiveness of Financial Incentives A...Ch. 8 - Is it acceptable practice to look at your research...Ch. 8 - If we reject the null hypothesis, can we claim to...Ch. 8 - If we do not reject the null hypothesis, is it...Ch. 8 - When a person stands trial for murder, the jury is...Ch. 8 - When, in a criminal court, a defendant is found...Ch. 8 - Arthritis A magazine advertisement claims that...Ch. 8 - No-Carb Diet A weight-loss diet claims that it...Ch. 8 - When comparing two sample proportions with a...Ch. 8 - When comparing two sample proportions with a...Ch. 8 - Prob. 63SECh. 8 - Prob. 64SECh. 8 - Prob. 65SECh. 8 - Prob. 66SECh. 8 - Prob. 67SECh. 8 - Prob. 68SECh. 8 - Smiling and Gender (Example 15) In a 1997 study,...Ch. 8 - Prob. 70SECh. 8 - Prob. 71CRECh. 8 - Prob. 72CRECh. 8 - Choosing a Test and Giving the Hypotheses Give the...Ch. 8 - Choosing a Test and Naming the Population(s) In...Ch. 8 - Prob. 75CRECh. 8 - Butter Taste Test A man is tested to determine...Ch. 8 - Biased Coin? A study is done to see whether a coin...Ch. 8 - Biased Coin? A study is done to see whether a coin...Ch. 8 - Prob. 79CRECh. 8 - Coin Flips Suppose you tested 50 coins by flipping...Ch. 8 - Prob. 81CRECh. 8 - Prob. 82CRECh. 8 - Prob. 83CRECh. 8 - Weight Loss in Men Many polls have asked people...Ch. 8 - Prob. 85CRECh. 8 - Prob. 86CRECh. 8 - Prob. 87CRECh. 8 - Prob. 88CRECh. 8 - Wording of Polls A poll in California (done by the...Ch. 8 - Prob. 90CRECh. 8 - Three-Strikes Law California’s controversial...Ch. 8 - Prob. 92CRECh. 8 - Prob. 93CRECh. 8 - Prob. 94CRECh. 8 - A friend claims he can predict the suit of a card...Ch. 8 - A friend claims he can predict how a six-sided die...Ch. 8 - Votes for Independents Judging on the basis of...Ch. 8 - Votes for Independents Refer to Exercise 8.97....Ch. 8 - Texting While Driving The mother of a teenager has...Ch. 8 - True/False Test A teacher giving a true/false test...Ch. 8 - ESP Suppose a friend says he can predict whether a...Ch. 8 - ESP Again Suppose a friend says he can predict...Ch. 8 - Does Hand Washing Save Lives? In the mid-1800s,...Ch. 8 - Prob. 104CRECh. 8 - Guessing on a True/False Test A true/false test...Ch. 8 - Guessing on a Multiple-Choice Test A...
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- 8- 6. Show that, for any random variable, X, and a > 0, 8 心 P(xarrow_forward15. This problem extends Problem 20.6. Let X, Y be random variables with finite mean. Show that 00 (P(X ≤ x ≤ Y) - P(X ≤ x ≤ X))dx = E Y — E X.arrow_forward(b) Define a simple random variable. Provide an example.arrow_forward17. (a) Define the distribution of a random variable X. (b) Define the distribution function of a random variable X. (c) State the properties of a distribution function. (d) Explain the difference between the distribution and the distribution function of X.arrow_forward16. (a) Show that IA(w) is a random variable if and only if A E Farrow_forward15. Let 2 {1, 2,..., 6} and Fo({1, 2, 3, 4), (3, 4, 5, 6}). (a) Is the function X (w) = 21(3, 4) (w)+711.2,5,6) (w) a random variable? Explain. (b) Provide a function from 2 to R that is not a random variable with respect to (N, F). (c) Write the distribution of X. (d) Write and plot the distribution function of X.arrow_forward20. Define the o-field R2. Explain its relation to the o-field R.arrow_forward7. Show that An → A as n→∞ I{An} - → I{A} as n→ ∞.arrow_forward7. (a) Show that if A,, is an increasing sequence of measurable sets with limit A = Un An, then P(A) is an increasing sequence converging to P(A). (b) Repeat the same for a decreasing sequence. (c) Show that the following inequalities hold: P (lim inf An) lim inf P(A) ≤ lim sup P(A) ≤ P(lim sup A). (d) Using the above inequalities, show that if A, A, then P(A) + P(A).arrow_forward19. (a) Define the joint distribution and joint distribution function of a bivariate ran- dom variable. (b) Define its marginal distributions and marginal distribution functions. (c) Explain how to compute the marginal distribution functions from the joint distribution function.arrow_forward18. Define a bivariate random variable. Provide an example.arrow_forward6. (a) Let (, F, P) be a probability space. Explain when a subset of ?? is measurable and why. (b) Define a probability measure. (c) Using the probability axioms, show that if AC B, then P(A) < P(B). (d) Show that P(AUB) + P(A) + P(B) in general. Write down and prove the formula for the probability of the union of two sets.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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