PART I REVIEW EXERCISES

Review exercises are short and straightforward exercises that help you solidify the basic ideas and skills in each part of this book. We have provided “hints’’ that indicate where you can find the relevant material for the odd-numbered problems.

Question

I.1 Know these terms. A friend who knows no statistics has encountered some statistical terms in reading for her psychology course. Explain each of the following terms in one or two simple sentences.

  1. (a) Simple random sample. (Hint: See pages 2426.)

  2. (b) 95% confidence. (Hint: See pages 4749.)

  3. (c) Statistically significant. (Hint: See page 103.)

  4. (d) Informed consent. (Hint: See pages 144145.)

I.1 (a) Every subset of n individuals from the population has the same probability of selection. (b) 95% of all possible samples will produce a confidence interval that captures the population parameter. (c) The difference between the treatment groups is large enough that it would rarely occur by chance. (d) Subjects are informed in advance about the nature of the study as well as any risk or harm it may bring, and consent to participate.

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I.2 Know these terms. A friend who knows no statistics has encountered some statistical terms in her biology course. Explain each of the following terms in one or two simple sentences.

  1. (a) Observational study.

  2. (b) Double-blind.

  3. (c) Nonsampling error.

  4. (d) Matched pairs.

Question

I.3 A biased sample. A student plans to collect student opinions for a class assignment. He decides to post on his Facebook page a request for people to text him their opinions. Explain why this sampling method is almost certainly biased. (Hint: See pages 2124.)

I.3 This is an example of a voluntary response sample. Voluntary response samples are typically biased as they tend to attract the strongest opinions and do not represent the population as a whole.

Question

I.4 Select an SRS. A student at a large university wants to study the responses that students receive when calling an academic department for information. She selects an SRS of four departments from the following list for her study. Use software or Table A at line 115 to do this.

Accounting

Architecture

Art

Biology

Business Administration

Chemistry

Communication

Computer Science

Dance

Economics

Electrical Engineering

Elementary Education

English

Foreign Languages

History

Horticulture

International Studies

Marketing

Mathematics

Music

Natural Resources

Nursing

Pharmacy

Philosophy

Physics

Political Science

Pre-med

Psychology

Sociology

Veterinary Science

Question

I.5 Select an SRS. The faculty grievance system at a university specifies that a five-member hearing panel shall be drawn at random from the 25-member grievance committee. Use software or Table A at line 128 to draw an SRS of size four from the following committee members.

Anis

Atlas

Bailey

Banks

Edwards

Frazier

Gardner

Guthrie

Kowalski

Kupka

Lehman

Leonard

Mee

Michelson

Morgan

Murphy

Pagolu

Ramsey

Ray

Sall

Utlaut

Valente

Weese

Wendelberger

Woodall

(Hint: See pages 2629.)

I.5 Answers will vary with technology. Using line 128: Frazier, Mee, Morgan, Wendelberger.

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Question

I.6 Errors in surveys. Give an example of a source of nonsampling error in a sample survey. Then give an example of a source of sampling error.

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I.7 Errors in surveys. An overnight opinion poll calls randomly selected telephone numbers. This polling method misses all people without a phone. Is this a source of nonsampling error or of sampling error? Does the poll’s announced margin of error take this source of error into account? (Hint: See pages 6470.)

I.7 Sampling error. No.

Question

I.8 Errors in surveys. A college chooses an SRS of 100 students from the registrar’s list of all undergraduates to interview about student life. If it selected two SRSs of 100 students at the same time, the two samples would give somewhat different results. Is this variation a source of sampling error or of nonsampling error? Does the survey’s announced margin of error take this source of error into account?

Question

I.9 Errors in surveys. Exercises I.7 and I.8 each mention a source of error in a sample survey. Would each kind of error be reduced by doubling the size of the sample with no other changes in the survey procedures? Explain your answers. (Hint: See pages 4347 and pages 6570.)

I.9 Only the error in Exercise I.8 would be reduced. Increasing the sample size reduces the variation from sample to sample.

Question

I.10 Errors in surveys. A Gallup Poll found that 46% of American smartphone users agree with the statement, “I can’t imagine my life without my smartphone.” The Gallup press release says:

Results of attitudes and behaviors of smartphone usage are based on 15,747 members of the Gallup Panel who have smartphones. . . . For results based on this sample, one can say that the margin of sampling error is ±1 percentage point at the 95% confidence level.

The release also points out that this margin of error is due only to sampling error. Give one example of a source of error in the poll result that is not included in this margin of error.

Question

image I.11 Find the margin of error. On April 24, 2015, “Bruce Jenner—The Interview” was aired. The interview was between Diane Sawyer and Bruce Jenner and discussed Jenner’s experience as a transgender person. Jenner came out to the public as Caitlyn Jenner on June 1, 2015. An NBC News Online Survey asked a national sample of 2153 adults aged 18 and over, “Caitlyn Jenner, the transgender Olympic champion formerly known as Bruce Jenner, recently revealed her transition on the cover of Vanity Fair. Do you think Caitlyn Jenner’s public transition will help society become more accepting of transgender people?” Twenty percent of those surveyed replied that Jenner’s public transition “will help a lot,” while 46% responded “will help a little.”

  1. (a) What is the population for this 2015 survey? (Hint: See pages 810.)

  2. (b) Assuming the 2015 survey used random sampling, use the quick and approximate method to find a margin of error. Then give a complete confidence statement for a conclusion about the population. (Hint: See pages 4547.)

I.11 (a) American adults. (b) Approximate margin of error is 2.2%. We are 95% confident the percent of American adults who think Caitlyn Jenner’s public transition will help society be a lot more accepting of transgender people lies between 17.8% and 22.2%.

Question

I.12 Find the margin of error. A May 2015 Quinnipiac University Poll asked 2105 American adults (18 years and over), “As you may know, David Letterman has retired. Thinking about other late-night television talk show hosts who are currently on TV, who is your favorite?” Jimmy Fallon came out on top, with 20% of Americans favoring him over others.

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  1. (a) What is the population for this sample survey?

  2. (b) Assuming the sample was a random sample, use the quick and approximate method to find a margin of error. Make a confidence statement about the opinion of the population.

Question

I.13 What kind of sample? At a party, there are 30 students over age 21 and 20 students under age 21. You choose at random six of those over 21 and separately choose at random four of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed: what is that chance? Why is your sample not an SRS? What is this kind of sample called? (Hint: See pages 2427 and pages 7375.)

I.13 Each student has a one-in-five (20%) chance of being interviewed. To be an SRS, every sample of size 10 from the population must have the same probability of selection. However, a sample of 10 students over age 21 is not even possible in this sampling plan. This is a stratified sample.

Question

I.14 Design an experiment. A university’s Department of Statistics wants to attract more majors. It prepares two advertising brochures. Brochure A stresses the intellectual excitement of statistics. Brochure B stresses how much money statisticians make. Which will be more attractive to first-year students? You have a questionnaire to measure interest in majoring in statistics, and you have 50 first-year students to work with. Outline the design of an experiment to decide which brochure works better.

Question

I.15 Design an experiment. Gary and Greg share an apartment 10 miles from campus. Gary thinks that the fastest way to get to campus is to take the shortest route, which involves taking several side streets. Greg thinks the fastest way is to take the route with the highest speed limits, which involves taking the highway most of the way but is two miles longer than Gary’s route. You recruit 20 friends who are willing to try either method and time how long it takes them to arrive on campus. Outline the design of an experiment to decide which method takes less time. (Hint: See pages 98101.)

Exercises I.16 to I.19 are based on an article in the Journal of the American Medical Association that compares the use of antibiotics to treat uncomplicated acute appendicitis instead of surgery with an appendectomy. Here is information from the article’s summary:

  • Design Randomized clinical trial conducted in Finland between 2009 and 2012.

  • Participants A total of 530 patients aged 18 to 60 years with uncomplicated appendicitis.

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  • Intervention Participants were randomized to receive either an antibiotic therapy (n = 257) or a standard appendectomy (n = 273).

  • Results For all but one of the patients receiving surgery, the appendectomy was successful, resulting in a success rate of 99.6%. In the antibiotic group, 70 patients required an appendectomy within 1 year of initial presentation of appendicitis, resulting in a success rate (no recurrent symptoms after 1 year) of 72.7%.

I.15 Randomly assign 10 friends to Gary’s route and 10 friends to Greg’s route. Compare the amount of time it takes to arrive on campus for the two routes. This experiment could also be done as matched pairs where all 20 friends drive both routes, and the order of the two routes in randomly assigned to each friend. One important lurking variable that would need to be controlled for is time of day the route is driven.

Question

I.16 Know these terms. Explain in one sentence each what “randomized’’ and “clinical trial’’ mean in the description of the design of the study.

Question

I.17 Experiment basics. Identify the subjects, the explanatory variable, and several response variables for this study. (Hint: See pages 9395.)

I.17 Subjects: 530 patients aged 18 to 60 years with uncomplicated appendicitis. Explanatory variable: Antibiotic therapy or standard appendectomy. Response variables: whether the appendectomy was successful, whether the patient had no recurrent symptoms after 1 year.

Question

I.18 Design an experiment. Use a diagram to outline the design of the experiment in this medical study.

Question

I.19 Ethics. What are the three first principles of data ethics? Explain briefly what the medical study must do to apply each of these principles. (Hint: See pages 141143.)

I.19 Institutional Review Board, informed consent, confidentiality of data. IRB reviews the study in advance to protect the subjects from possible harm. All individuals must be informed about the nature of the study, as well any risk of harm it may bring, and consent to participate (typically in writing). Finally, each individual’s data must be kept confidential once the study is completed. Only summary statistics for groups of subjects are made public.

Question

I.20 Measuring. Joni wants to measure the degree to which male college students belong to the political left. She decides simply to measure the length of their hair–longer hair will mean more left-wing.

  1. (a) Is this method likely to be reliable? Why?

  2. (b) This measurement appears to be invalid. Why?

  3. (c) Nevertheless, it is possible that measuring politics by hair length might have some predictive validity. Explain how this could happen.

Question

I.21 Reliability. You are laboring through a chemistry laboratory assignment in which you measure the conductivity of a solution. What does it mean for your measurement to be reliable? How can you improve the reliability of your final result? (Hint: See pages 172176.)

I.21 Reliability means similar results in repeated measurements. Reliability can be improved by taking many measurements and averaging them.

Question

I.22 Observation or experiment? The Nurses’ Health Study has queried a sample of more than 100,000 female registered nurses every two years since 1976. Beginning in 1980, the study asked questions about diet, including alcohol consumption. The researchers concluded that “light-to-moderate drinkers had a significantly lower risk of death’’ than either nondrinkers or heavy drinkers.

  1. (a) Is the Nurses’ Health Study an observational study or an experiment? Why?

  2. (b) What does “significant’’ mean in a statistical report?

  3. (c) Suggest some lurking variables that might explain why moderate drinkers have lower death rates than nondrinkers. (The study did adjust for these variables.)

Question

I.23 Observation or experiment? In a study of the relationship between physical fitness and personality, middle-aged college faculty who have volunteered for an exercise program are divided into low-fitness and high-fitness groups on the basis of a physical examination. All subjects then take a personality test. The high-fitness group has a higher average score for “self-confidence.’’

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  1. (a) Is this an observational study or an experiment? Why? (Hint: See pages 78 and 1214.)

  2. (b) We cannot conclude that higher fitness causes higher self-confidence. Suggest other relationships among these variables and perhaps lurking variables that might explain the higher self-confidence of the high-fitness group. (Hint: See pages 1214 and 9598.)

I.23 (a) This is an observational study because treatments were not assigned. (b) The high-fitness group might be younger or healthier; alternatively, confident people may be more likely to exercise.

Question

I.24 Percents up and down. Between January 14, 2015, and July 14, 2015, the average price of regular gasoline increased from $2.08 per gallon to $2.78 per gallon.

  1. (a) Verify that this is a 34% increase in price.

  2. (b) If the price of gasoline decreases by 34% from its July 14, 2015, level of $2.78 per gallon, what would be the new price? Notice that a 34% increase followed by a 34% decrease does not take us back to the starting point.

Question

I.25 Percentage decrease. On Monday, September 10, 2001 (the day before the September 11 attacks), the NASDAQ stock index closed the day at 1695. By the end of Monday, September 17, 2001 (the first full day of trading after the attacks), the NASDAQ stock index had dropped to 1580. By what percentage did the index drop? (Hint: See pages 191194.)

I.25 The index dropped by 115/1695 (or 0.0678), a 6.8% drop.

Question

I.26 An implausible number? Newsweek once said in a story that a woman who is not currently married at age 40 has a better chance of being killed by a terrorist than of getting married. Do you think this is plausible? What kind of data would help you check this claim?

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