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 5.4, Problem 60PB
Convicted by mistake In criminal trials (e.g., murder, robbery, driving while impaired, etc.) in the United States, it must be proven that a defendant is guilty beyond a reasonable doubt. This can be thought of as a very strong unwillingness to convict defendants who are actually innocent. In civil trials (e.g., breach of contract, divorce hearings for alimony, etc.), it must only be proven by a preponderance of the evidence that a defendant is guilty. This makes it easier to prove a defendant guilty in a civil case than in a murder case. In a high-profile pair of cases in the mid 1990s, O. J. Simpson was found to be not guilty of murder in a criminal case against him. Shortly thereafter, however, he was found guilty in a civil case and ordered to pay damages to the families of the victims.
- a. In a criminal trial by jury, suppose the
probability the defendant is convicted, given guilt, is 0.95, and the probability the defendant is acquitted, given innocence, is 0.95. Suppose that 90% of all defendants truly are guilty. Given that a defendant is convicted, find the probability he or she was actually innocent. Draw a tree diagram or construct acontingency table to help you answer. - b. Repeat part a, but under the assumption that 50% of all defendants truly are guilty.
- c. In a civil trial, suppose the probability the defendant is convicted, given guilt is 0.99, and the probability the defendant is acquitted, given innocence, is 0.75. Suppose that 90% of all defendants truly are guilty. Given that a defendant is convicted, find the probability he or she was actually innocent. Draw a tree diagram or construct a contingency table to help you answer.
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Convicted by mistake In criminal trials (e.g., murder,
robbery, driving while impaired, etc.) in the United States,
it must be proven that a defendant is guilty beyond
reasonable doubt. This can be thought of as a very strong
unwillingness to convict defendants who are
innocent. In civil trials (e.g., breach of contract, divorce
hearings for alimony, etc.), it must only be proven by a
preponderance of the evidence that a defendant is guilty.
This makes it easier to prove a defendant guilty in a civil
case than in a murder case. In a high-profile pair of cases
in the mid 1990s, O. J. Simpson was found to be not guilty
of murder ina criminal case against him. Shortly there-
after, however, he was found guilty in a civil case and
ordered to pay damages to the families of the victims.
a. In a criminal trial by jury, suppose the probability the
defendant is convicted, given guilt, is 0.95, and the
probability the defendant is acquitted, given innocence,
is 0.95. Suppose that 90% of all…
Although tea is the world's most widely consumed beverage after water, little is known about its nutritional value. Folacin is the only B vitamin present in any significant amount in tea, and recent
advances in assay methods have made accurate determination of folacin content feasible. Consider the accompanying data on folacin content for randomly selected specimens of the four leading brands
of green tea.
1:
2: 5.6 7.4 9.7 6.0 8.3
3: 6.7 7.4 5. 7.3 5.4 6.2
4: 6.3 7.2 7.8 4.4 4.9 3.9
7.8 6.1 6.7 8.5 9.0 10.0 9.5
USE SALT
Does this data suggest that true average folacin content is the same for all brands?
(a) Carry out a test using a = 0.05. State the appropriate hypotheses.
о но на = H2=H3=на
H₂: all four μ's are unequal
ної ні #Mz #μз + H4
H₂: all four μ's are equal
о но ну=H2=μз =На
H: at least two μ's are unequal
ної Ні #Hz #μз #На
Ha: at least two μ's are equal
Find the value of the test statistic in this test. (Round your answer to two decimal places.)
f =
What can be said about…
Three people are suspected of robbery of a hardware store: Alex, Ben, and Saleh. Preliminaryinvestigation by the police has led to the following conclusions:
(i) If Saleh is involved in the crime, then Ben is also involved.(ii) If Alex is guilty, then Ben is also guilty.
The first conclusion of the preliminary investigation turned out to be true, and the second turnedout to be false. Who committed the robbery?
Chapter 5 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Ch. 5.1 - Probability Explain what is meant by the long-run...Ch. 5.1 - Testing a coin Your friend decides to flip a coin...Ch. 5.1 - Vegetarianism You randomly sample 10 people in...Ch. 5.1 - Airline accident deaths Airplane safety has been...Ch. 5.1 - World Cup 2014 The powerrank.com website...Ch. 5.1 - Random digits Consider a random number generator...Ch. 5.1 - Polls and sample size A pollster agency wants to...Ch. 5.1 - Heart transplant Before the first human heart...Ch. 5.1 - Nuclear war You are asked to use your best...Ch. 5.1 - Simulate coin flips Use the web app Random Numbers...
Ch. 5.1 - Unannounced pop quiz A teacher announces a pop...Ch. 5.2 - Student union poll Part of a student opinion poll...Ch. 5.2 - Random digit A single random digit (from 09) is...Ch. 5.2 - Pop quiz A teacher gives a four-question...Ch. 5.2 - More true-false questions Your teacher gives a...Ch. 5.2 - Rolling two dice Some friends are playing a game...Ch. 5.2 - Two girls A couple plans to have two children....Ch. 5.2 - Three children A couple plans to have three...Ch. 5.2 - Wrong sample space A couple plans to have four...Ch. 5.2 - Insurance Every year the insurance industry spends...Ch. 5.2 - Cell phone and case At the local cell phone store,...Ch. 5.2 - Seat belt use and auto accidents Based on records...Ch. 5.2 - Protecting the environment When the General Social...Ch. 5.2 - Prob. 25PBCh. 5.2 - Newspaper sales You are the director of newspaper...Ch. 5.2 - Prob. 27PBCh. 5.3 - Recidivism rates A 2014 article from Business...Ch. 5.3 - Prob. 29PBCh. 5.3 - Audit and low income Table 5.3 on audit status and...Ch. 5.3 - Religious affiliation The 2012 Statistical...Ch. 5.3 - Prob. 32PBCh. 5.3 - Prob. 33PBCh. 5.3 - Go Celtics! Larry Bird, who played pro basketball...Ch. 5.3 - Prob. 35PBCh. 5.3 - Homeland security According to an article in The...Ch. 5.3 - Down syndrome again Example 8 discussed the Triple...Ch. 5.3 - Prob. 38PBCh. 5.3 - Happiness in relationship Are people happy in...Ch. 5.3 - Prob. 40PBCh. 5.3 - Prob. 41PBCh. 5.3 - Prob. 42PBCh. 5.3 - Prob. 43PBCh. 5.3 - Prob. 44PBCh. 5.3 - Family with two children For a family with two...Ch. 5.3 - Prob. 46PBCh. 5.4 - Birthdays of presidents Of the first 44 presidents...Ch. 5.4 - Prob. 48PBCh. 5.4 - Lots of pairs Show that with 25 students, there...Ch. 5.4 - Prob. 50PBCh. 5.4 - Prob. 51PBCh. 5.4 - Prob. 52PBCh. 5.4 - Coincidence in your life State an event that has...Ch. 5.4 - Monkeys typing Shakespeare Since events of low...Ch. 5.4 - A true coincidence at DisneyWorld Wisconsin has...Ch. 5.4 - Prob. 56PBCh. 5.4 - Mammogram diagnostics Breast cancer is the most...Ch. 5.4 - Prob. 58PBCh. 5.4 - Prob. 59PBCh. 5.4 - Convicted by mistake In criminal trials (e.g.,...Ch. 5.4 - DNA evidence compelling? DNA evidence can be...Ch. 5.4 - Prob. 62PBCh. 5.4 - Simulating donations to local blood bank The...Ch. 5.4 - Probability of winning In Example 16, we estimated...Ch. 5 - Peyton Manning completions As of the end of the...Ch. 5 - Due for a boy? A couple has five children, all...Ch. 5 - Prob. 68CPCh. 5 - Choices for lunch For the set lunch at Amelias...Ch. 5 - Caught doctoring the books After the major...Ch. 5 - Life after death In a General Social Survey, in...Ch. 5 - Death penalty jury In arguing against the death...Ch. 5 - Drivers exam Three 15-year-old friends with no...Ch. 5 - Prob. 74CPCh. 5 - Health insurance According to a 2006 census bureau...Ch. 5 - Prob. 76CPCh. 5 - Prob. 77CPCh. 5 - Prob. 78CPCh. 5 - Prob. 79CPCh. 5 - Roll two more dice Refer to the previous exercise....Ch. 5 - Prob. 81CPCh. 5 - Waste dump sites A federal agency is deciding...Ch. 5 - Prob. 83CPCh. 5 - Prob. 84CPCh. 5 - Prob. 85CPCh. 5 - Death penalty and false positives For the decision...Ch. 5 - Prob. 87CPCh. 5 - Screening for heart attacks Biochemical markers...Ch. 5 - Prob. 89CPCh. 5 - Color blindness For genetic reasons, color...Ch. 5 - Prob. 91CPCh. 5 - Prostate cancer A study of the PSA blood test for...Ch. 5 - Prob. 95CPCh. 5 - Illustrate probability terms with scenarios a....Ch. 5 - Short term versus long run Short-term aberrations...Ch. 5 - Prob. 98CPCh. 5 - Mrs. Test Mrs. Test (see www.mrstest.com) sells...Ch. 5 - Prob. 100CPCh. 5 - Prob. 101CPCh. 5 - Prob. 102CPCh. 5 - Protective bomb Before the days of high security...Ch. 5 - Streak shooter Sportscaster Maria Coselli claims...Ch. 5 - Multiple choice Choose ALL correct responses. For...Ch. 5 - Prob. 106CPCh. 5 - Prob. 107CPCh. 5 - Multiple choice: Dream come true You have a dream...Ch. 5 - Prob. 109CPCh. 5 - True or false Answer true of false for each part....Ch. 5 - True or false When you flip a balanced coin twice,...Ch. 5 - Prob. 112CPCh. 5 - Prob. 113CPCh. 5 - Prob. 114CPCh. 5 - Prob. 115CPCh. 5 - Prob. 116CP
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- (b) Given the results from the local school, do you think the Education Department's claims are false? (Justify your answer.)arrow_forwardWhat is the final conclusion? O A. There is not sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed. O B. There is sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed. O c. There is sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed. O D. There is not sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed.arrow_forwardMaking an informed decision – Should we convict? A woman who was shopping in Los Angeles had her purse stolen by a young, blonde female who was wearing a ponytail. The blonde female got into a yellow car that was driven by a man with a mustache and a beard. The police located a blonde female named Janet who wore her hair in a ponytail and had a male friend who had a mustache and beard and also drove a yellow car. Based on this evidence the police arrested the two suspects. Because there were no eyewitnesses and no real evidence, the prosecution used probability to make its case against the defendants. The probabilities listed below were presented by the prosecution for the known characteristics of the thieves. Characteristic Probability Yellow car 1/10 Man with mustache 1/4 Woman with ponytail 1/10 Woman with blonde hair 1/3 Man with beard Interracial couple in a car 1/10 1/1000 (a) Assuming that the characteristics listed above are independent of each other, what is the probability…arrow_forward
- Yogurt. Consumer Reports tested 14 brands of vanilla yogurt and found these numbers of calories per serving: 160 200 220 230 120 180 140 130 170 190 80 120 100 170 a) Check the assumptions and conditions for inference. b) A diet guide claims that you will get 120 calories from a serving of vanilla yogurt. What does this evidence indicate? Test an appropriate hypothesis and state your conclusion.arrow_forwardWhat relevant conclusion(s) can be drawn from the following hypotheses. "Every student has an Internet account." "Homer does not have an Internet account." "Maggie has an Internet account." Type your answer in the space providedarrow_forwardhelp neededarrow_forward
- The research group asked the following question of individuals who earned in excess of $100,000 per year and those who earned less than $100,000 per year: "Do you believe that it is morally wrong for unwed women to have children?" Of the 1,205 individuals who earned in excess of $100,000 per year, 712 said yes; of the 1,310 individuals who earned less than $100,000 per year, 693 said yes. Construct a 95% confidence interval to determine if there is a difference in the proportion of individuals who believe it is morally wrong for unwed women to have children.The lower bound is _______The upper bound is________. (Round to three decimal places as needed.)arrow_forwardIn a large University, a group of students is being charged with dishonesty in taking the final examination. What hypothesis is being tested if the discipline committee commits a Type 1 Error? A. The students are innocent B. The students are guilty C. The students will apologize D. The students ignore the casearrow_forward2. In a 2009 nonscientific poll on the Web site of the Daily Gazette of Schenectady, NewYork, readers were asked the following question: “Are you less inclined to buy a GeneralMotors or Chrysler vehicle now that they have filed for bankruptcy?” Of the respondents,56.1% answered “Yes” . In a recent survey of 1200 adult Americans who were asked thesame question, 615 answered “Yes.” Can you reject the null hypothesis at the 1%significance level in favor of the alternative that the percentage of all adult Americanswho are less inclined to buy a General Motors or Chrysler vehicle since the companiesfiled for bankruptcy is different from 56.1%? Use both the p-value and the critical-valueapproaches.arrow_forward
- In hypothesis testing, the hypothesis that we are trying to prove is a. either the null or alternative hypothesis B. the alternative hypothesis C. the null hypothesisarrow_forwardA researcher observes that more acts of vandalism are committed by same-sexgangs than by mixed-sex gangs. She theorizes that competition for recognitionamong equal-status peers increases the tendency to commit publicly deviant acts.What type(s) of reasoning is this?A. inductive reasoningB. deductive reasoningC. neither inductive nor deductive reasoningD. both inductive and deductive reasoningarrow_forwardTest Conduct a hypothesis test for the following problem: A medical researcher says that at least 20% of US adults are smokers. In a random sample of 200 uS adults, 18.5% say that they are smokers. At a =0.01 significance level, is there enough evidence to reject the researcher's claim? Ho: 0.20 p> 0.20 p 0.20 Claim: Select an answer What is the level of significance given in this problem? What is the critical value for this sample? What is the test statistic for this sample? What is the rejection region for this sample?arrow_forward
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