Introduction To Statistics And Data Analysis
Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 10.2, Problem 12E

Researchers at Boston’s Children’s Hospital and Harvard Medical School analyzed records of breast cancer screening and diagnostic evaluations (National Expenditure for False-Positive Mammograms and Breast Cancer Overdiagnoses Estimated at $4 Billion a Year,” Health Affairs [2015]: 576–583). Discussing the downsides of the screening process, the article states that the rate of false-positives is higher than previously thought, and that false-positives lead to unnecessary medical follow-up that can be costly.

Suppose that screening is used to decide between a null hypothesis of

H0: no cancer is present

and an alternative hypothesis of

Ha: cancer is present.

(Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.) (Hint: See Example 10.6.)

  1. a. Would a false-positive (thinking that cancer is present when in fact it is not) be a Type I error or a Type II error?
  2. b. Describe a Type I error in the context of this problem, and discuss the possible consequences of making a Type I error.
  3. c. Describe a Type II error in the context of this problem, and discuss the possible consequences of making a Type II error.
  4. d. Which type of error are the researchers concerned about when they say that false-positives lead to unnecessary medical follow-up? Explain why it would be reasonable to use a small significance level.
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Chapter 10 Solutions

Introduction To Statistics And Data Analysis

Ch. 10.1 - The article Facebook Use and Academic Performance...Ch. 10.2 - Researchers at Bostons Childrens Hospital and...Ch. 10.2 - The paper Breast MRI as an Adjunct to Mammography...Ch. 10.2 - Medical personnel are required to report suspected...Ch. 10.2 - How accurate are DNA paternity tests? By comparing...Ch. 10.2 - A television manufacturer claims that (at least)...Ch. 10.2 - A manufacturer of hand-held calculators receives...Ch. 10.2 - Water specimens are taken from water used for...Ch. 10.2 - Suppose that for a particular hypothesis test, the...Ch. 10.2 - Suppose that you arc an inspector for the Fish and...Ch. 10.2 - The paper Living Near Nuclear Power Plants and...Ch. 10.2 - An automobile manufacturer is considering using...Ch. 10.3 - Use the definition of the P-value to explain the...Ch. 10.3 - For which of the following P-values will the null...Ch. 10.3 - Pairs of P-values and significance levels, , are...Ch. 10.3 - Pairs of P-values and significance levels are...Ch. 10.3 - Let p denote the proportion of students at a...Ch. 10.3 - Assuming a random sample from a large population,...Ch. 10.3 - In a survey conducted by CareerBuilder.com,...Ch. 10.3 - In a survey of 1000 women age 22 to 35 who work...Ch. 10.3 - The paper Debt Literacy, Financial Experiences and...Ch. 10.3 - Most Like it Hot is the title of a press release...Ch. 10.3 - In a survey of 1005 adult Americans, 46% indicated...Ch. 10.3 - The article Euthanasia Still Acceptable to Solid...Ch. 10.3 - The report Digital Democracy Survey (Deloitte...Ch. 10.3 - The article How to Block Nuisance Calls (The...Ch. 10.3 - The article Facebook Use and Academic Performance...Ch. 10.3 - The article Public Acceptability in the UK and the...Ch. 10.3 - The article Cops Get Screened for Digital Dirt...Ch. 10.3 - Refer back to the previous exercise. The actual...Ch. 10.3 - The report 2007 Electronic Monitoring ...Ch. 10.3 - The United States Elections Project...Ch. 10.4 - Give as much information as you can about the...Ch. 10.4 - Give as much information as you can about the...Ch. 10.4 - Give as much information as you can about the...Ch. 10.4 - Paint used to paint lines on roads must reflect...Ch. 10.4 - A certain pen has been designed so that actual...Ch. 10.4 - Prob. 48ECh. 10.4 - The paper Playing Active Video Games Increases...Ch. 10.4 - A study of fast-food intake is described in the...Ch. 10.4 - Refer to the study and hypothesis test of the...Ch. 10.4 - The report 2016 Salary Survey Executive Summary...Ch. 10.4 - The Economist collects data each year on the price...Ch. 10.4 - The report Majoring in Money: How American College...Ch. 10.4 - The authors of the paper Changes in Quantity,...Ch. 10.4 - Medical research has shown that repeated wrist...Ch. 10.4 - A comprehensive study conducted by the National...Ch. 10.4 - In a study of media use, each person in a large...Ch. 10.4 - Refer to the study description and sample...Ch. 10.4 - The paper titled Music for Pain Relief (The...Ch. 10.4 - Many consumers pay careful attention to stated...Ch. 10.4 - Much concern has been expressed regarding the...Ch. 10.5 - The power of a test is influenced by the sample...Ch. 10.5 - Water specimens are taken from water used for...Ch. 10.5 - Prob. 65ECh. 10.5 - Let denote the mean lifetime (in hours) for a...Ch. 10.5 - The city council in a large city has become...Ch. 10.5 - The amount of shaft wear after a fixed mileage was...Ch. 10.5 - Optical fibers are used in telecommunications to...Ch. 10.5 - Let denote the mean diameter for bearings of a...Ch. 10.5 - Use the information given in the previous exercise...Ch. 10.6 - In 2006, Boston Scientific sought approval for a...Ch. 10.6 - The article Boy or Girl: Which Gender Baby Would...Ch. 10.7 - We are only beginning to learn about the long-term...Ch. 10.7 - A study of hospitalized patients who develop...Ch. 10.7 - Prob. 76ECh. 10.7 - Prob. 77ECh. 10.7 - Prob. 78ECh. 10.7 - Prob. 79ECh. 10.8 - Prob. 80ECh. 10.8 - Prob. 81ECh. 10.8 - Prob. 83ECh. 10.8 - Prob. 84ECh. 10 - The report A Crisis in Civic Education (American...Ch. 10 - In a national survey of 2013 adults, 1590...Ch. 10 - Students at the Akademia Podlaka conducted an...Ch. 10 - Prob. 89CRCh. 10 - People in a random sample of 236 students enrolled...Ch. 10 - According to a large national survey conducted by...Ch. 10 - In a representative sample of adult Americans age...Ch. 10 - The article Facebook Use and Academic Performance...Ch. 10 - A number of initiatives on the topic of legalized...Ch. 10 - Duck hunting in populated areas faces opposition...Ch. 10 - Past experience has indicated that the response...Ch. 10 - An automobile manufacturer who wishes to advertise...Ch. 10 - A student organization uses the proceeds from a...Ch. 10 - A hot tub manufacturer advertises that with its...Ch. 10 - Prob. 1CRECh. 10 - Prob. 2CRECh. 10 - Prob. 3CRECh. 10 - Prob. 4CRECh. 10 - Prob. 5CRECh. 10 - The article Should Canada Allow Direct-to-Consumer...Ch. 10 - Prob. 7CRECh. 10 - It probably wouldnt surprise you to know that...Ch. 10 - The article Doctors Cite Burnout in Mistakes (San...Ch. 10 - The National Geographic Society conducted a study...Ch. 10 - Heinz Plays Catch-up After Under-Filling Ketchup...Ch. 10 - In a survey conducted by Yahoo Small Business,...Ch. 10 - In an AP-AOL sports poll (Associated Press,...Ch. 10 - The article titled 13% of Americans Dont Use the...Ch. 10 - A survey of teenagers and parents in Canada...Ch. 10 - The same survey referenced in the previous...
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