1-1 Basic Skills and Concepts Statistical Literacy and Critical Thinking 1. Online Medical Info USA Today posted this question on its website: "How often do you seek medical information online?" Of 1072 Internet users who chose to respond, 38% of them responded with "frequently." What term is used to describe this type of survey in which the people surveyed consist of those who decided to respond? What is wrong with this type of sampling method? 2. Reported Versus Measured In a survey of 1046 adults conducted by Bradley Corporation, subjects were asked how often they wash their hands when using a public restroom, and 70% of the respondents said "always." a. Identify the sample and the population. b. Why would better results be obtained by observing the hand washing instead of asking about it? 3. Statistical Significance Versus Practical Significance When testing a new treatment, what is the difference between statistical significance and practical significance? Can a treat- ment have statistical significance, but not practical significance? 4. Correlation One study showed that for a recent period of 11 years, there was a strong cor- relation (or association) between the numbers of people who drowned in swimming pools and the amounts of power generated by nuclear power plants (based on data from the Centers for Disease Control and Prevention and the Department of Energy). Does this imply that increase ing power from nuclear power plants is the cause of more deaths in swimming pools? Why or why not? Consider the Source. In Exercises 5-8, determine whether the given source has the potential to create a bias in a statistical study. 5. Physicians Committee for Responsible Medicine The Physicians Committee for Responsible Medicine tends to oppose the use of meat and dairy products in our diets, and that organization has received hundreds of thousands of dollars in funding from the Foundation to Support Animal Protection. 6. Arsenic in Rice Amounts of arsenic in samples of rice grown in Texas were measured by the Food and Drug Administration (FDA). 7. Brain Size A data set in Appendix B includes brain volumes from 10 pairs of monozygotic (identical) twins. The data were collected by researchers at Harvard University, Massachusetts General Hospital, Dartmouth College, and the University of California at Davis.8. Chocolate An article in Journal of Nutrition (Vol. 130, No. 8) noted that chocolate is rich in flavonoids. The article notes "regular consumption of foods rich in flavonoids may reduce the risk of coronary heart disease." The study received funding from Mars, Inc.. the candy company. 17. C and the Chocolate Manufacturers Association. ingfu temp Sampling Method. In Exercises 9-12, determine whether the sampling method appears 18. S Mac to be sound or is flawed. sour 9. Nuclear Power Plants In a survey of 1368 subjects, the following question was posted on 19. the USA Today website: "In your view, are nuclear plants safe?" The survey subjects were Inter- cond net users who chose to respond to the question posted on the electronic edition of USA Today. 20 10. Clinical Trials Researchers at Yale University conduct a wide variety of clinical trials by we using subjects who volunteer after reading advertisements soliciting paid volunteers. 12 don 11. Credit Card Payments In an AARP, Inc. survey of 1019 randomly selected adults, each WH was asked how much credit card debt he or she pays off each month. 12. Smartphone Usage In a survey of smartphone ownership, the Pew Research Center ran- domly selected 1006 adults in the United States. In 8 Statistical Significance and Practical Significance. In Exercises 13-16, determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance. 13. Diet and Exercise Program In a study of the Kingman diet and exercise program, 40 subjects lost an average of 22 pounds. There is about a 1% chance of getting such results with a program that has no effect. 14. MCAT The Medical College Admissions Test (MCAT) is commonly used as part of the decision-making process for determining which students to accept into medical schools. To test the effectiveness of the Siena MCAT preparation course, 16 students take the MCAT test, then they complete the preparatory course, and then they retake the MCAT test, with the result that the aver- age (mean) score for this group rises from 25 to 30. There is a 0.3% chance of getting those results by chance. Does the course appear to be effective? 15. Gender Selection In a study of the Gender Aide method of gender selection used to increase the likelihood of a baby being born a girl, 2000 users of the method gave birth to 980 boys and 1020 girls. There is about a 19% chance of getting that many girls if the method had no effect. 16. IQ Scores Most people have IQ scores between 70 and 130. For $39.99, you can pur- chase a PC or Mac program from HighIQPro that is claimed to increase your IQ score by 10 to 20 points. The program claims to be "the only proven IQ increasing software in the brain training market," but the author of your text could find no data supporting that claim, so let's suppose that these results were obtained: In a study of 12 subjects using the program, the average increase in IQ score is 3 IQ points. There is a 25% chance of getting such results if the program has no effect. In Exercises 17-20, refer to the sample of body temperatures (degrees Fahrenheit) in the table below. (The body temperatures are from a data set in Appendix B.) Subject 2 3 5 8 AM 97.0 98.5 97.6 97.7 12 AM 98.7 97.6 97.8 98.0 98.4 98.4duction to Statistics 24. Blood Pressure A medical researcher tested for a difference in systolic blood pressure levels between male and female students who are 12 years of age. She randomly selected four males and four females for her study. 25. Driver Aggression In testing a treatment designed to reduce driver aggression in the United States, the original plan was to use a sample of 500 drivers randomly selected throughout the country. The program managers know that they would get a biased sample if they limit their study to drivers in New York City, so they planned to compensate for that bias by using a larger sample of 3000 drivers in New York City. 26. Atkins Weight Loss Program An independent researcher tested the effectiveness of the Atkins weight loss program by randomly selecting 1000 subjects using that program. Each of the subjects was called to report their weight before the diet and after the diet. 27. Crime Research A sociologist has created a brief survey to be given to 2000 adults ran- domly selected from the U.S. population. Here are her first two questions: (1) Have you ever been the victim of a felony crime? (2) Have you ever been convicted of a felony? 28. Medications The Pharmaceutical Research and Manufacturers of America wants infor- mation about the consumption of various medications. An independent researcher conducts a survey by mailing 10,000 questionnaires to randomly selected adults in the United States, and she receives 152 responses. 1-3 Beyond the Basics In Exercises 29-32, indicate whether the observational study used is cross-sectional, retro- spective, or prospective. 29. Nurses' Health Study II Phase II of the Nurses' Health Study was started in 1989 with 1 16,000 female registered nurses. The study is ongoing. 30. Heart Health Study Samples of subjects with and without heart disease were selected, then researchers looked back in time to determine whether they took aspirin on a regular basis. 31. Marijuana Study Researchers from the National Institutes of Health want to determine the current rates of marijuana consumption among adults living in states that have legalized the use of marijuana. They conduct a survey of 500 adults in those states.ing values as being representative of the population at there are missing values that are missing not at random (that is, their values are related to the reasons why they are missing), know that the remaining data may well be biased and any conclusions based on those remaining values may well be misleading. 1-2 Basic Skills and Concepts Statistical Literacy and Critical Thinking 1. Parameter and Statistic In a Harris Interactive survey of 2276 adults in the United States, it was found that 33% of those surveyed never travel using commercial airlines. Identify the population and sample. Is the value of 33% a statistic or a parameter? 2. Quantitative / Categorical Data Identify each of the following as quantitative data or categorical data. a. The platelet counts in Data Set 1 "Body Data" in Appendix B b. The cigarette brands in Data Set 13 "Cigarette Contents" in Appendix B1-3 Basic Skills and Concepts Statistical Literacy and Critical Thinking 10. Sex and Love 1. Back Pain Treatment In a study designed to test the effectiveness of paracetamol (or acer 4500 ma aminophen) as a treatment for lower back pain. 1643 patients were randomly assigned to one of three groups: (1) the 547 subjects in the placebo group were given pills containing no medical 11. UF tion; (2) 550 subjects were in a group given pills with paracetamol taken at regular intervals after the dents s (3) 546 subjects were in a group given pills with paracetamol to be taken when needed for pain relief. (See "Efficacy of Paracetamol for Acute Low-Back Pain." by Williams, et al., Lancer 12. C doi: 10.1016/50140-6736( 14)60805-9.) Is this study an experiment or an observational study? identif those Explain. 2. Blinding What does it mean when we say that the study cited in Exercise I was "double. 13. D three blind"? 14. 3. Replication In what specific way was replication applied in the study cited in Exercise 1? assig 4. Sampling Method The patients included in the study cited in Exercise I were those "who pun sought care for low-back pain directly or in response to a community advertisement." What type Con of sampling best describes the way in which the 1643 subjects were chosen: simple random by sample, systematic sample, convenience sample, stratified sample, cluster sample? Does the 15 . method of sampling appear to adversely affect the quality of the results? of Exercises 5-8 refer to the study of an association between which ear is used for cell phone calls and whether the subject is left-handed or right-handed. The study is reported in "Hemispheric Dominance and Cell Phone Use," by Seidman et al., JAMA Otolaryngology- Head & Neck Surgery, Vol. 139, No. 5. The study began with a survey e-mailed to 5000 people belonging to an otology online group, and 717 surveys were returned. (Otology relates to the ear and hearing.) 5. Sampling Method What type of sampling best describes the way in which the 717 sub- jects were chosen: simple random sample, systematic sample, convenience sample, stratified sample, cluster sample? Does the method of sampling appear to adversely affect the quality of the results? 6. Experiment or Observational Study Is the study an experiment or an observational study? Explain. 7. Response Rate What percentage of the 5000 surveys were returned? Does that response rate appear to be low? In general, what is a problem with a very low response rate? 8. Sampling Method Assume that the population consists of all students currently in your the given type. statistics class. Describe how to obtain a sample of six students so that the result is a sample of a. Simple random sample b. Systematic sample c. Stratified sample d. Cluster sample In Exercises 9-20, identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. 9. Cormorant Density Cormorant bird population densities were studied by using the "line transect method" with aircraft observers flying along the shoreline of Lake Huron and col- Research). lecting sample data at intervals of every 20 km (based on data from Journal of Great Lakes1-2 Types of Data c. The colors of the M&M candies in Data Set 27 "M&M Weights" in Appendix B d. The weights of the M&M candies in Data Set 27 "M&M Weights" in Appendix B 3. Discrete / Continuous Data Which of the following describe discrete data? a. The numbers of people surveyed in each of the next several years for the National Health and Nutrition Examination Surveys b. The exact foot lengths (measured in cm) of a random sample of statistics students c. The exact times that randomly selected drivers spend texting while driving during the past 7 days 4. Health Survey In a survey of 1020 adults in the United States, 44% said that they wash their hands after riding public transportation (based on data from KRC Research). a. Identify the sample and population. b. Is the value of 44% a statistic or parameter? c. What is the level of measurement of the value of 44%? (nominal, ordinal, interval, ratio) d. Are the numbers of subjects in such surveys discrete or continuous? In Exercises 5-12, identify whether the given value is a statistic or a parameter. 5. On-time Flights In a study of American Airlines flights from JFK in New York to LAX in Los Angeles, 48 flights are randomly selected and the average (mean) arrival time is 8.9 minutes late. 6. CHIS A recent California Health Interview Survey (CHIS) included 2799 adolescent resi- dents of California. 7. Housing Units According to the Census Bureau, the total number of housing units in the United States is 132,802,859. 8. Triangle Fire Fatalities A deadly disaster in the United States was the Triangle Shirtwaist Factory Fire in New York City. A population of 146 garment workers died in that fire. 9. Birth Weight In a study of 400 babies born at four different hospitals in New York State, it was found that the average (mean) weight at birth was 3152.0 grams. 10. Birth Genders In the same study cited in the preceding exercise, 51% of the babies were girls. 11. Titanic A study was conducted of all 2223 passengers aboard the Titanic when it sank. 12. Periodic Table The average (mean) atomic weight of all elements in the periodic table is 134.355 unified atomic mass units. In Exercises 13-20, determine whether the data are from a discrete or continuous data set. 13. Freshman 15 In a study of weight gains by college students in their freshman year, re- searchers record the amounts of weight gained by randomly selected students (as in Data Set 6 "Freshman 15" in Appendix B). 14. CHIS Among the subjects surveyed as part of the California Health Interview Survey (CHIS), several subjects are randomly selected and their heights are recorded. 15. Mcdonald's In a study of service times at a Mcdonald's drive-up window, the numbers of cars serviced each hour of several days are recorded. 16. House Attendance The Clerk of the U.S. House of Representatives records the number of representatives present at each session. 17. Corvettes A shift manager records the numbers of Corvettes manufactured during each day of production.1-3 Collecting Sample Data 10. Sexuality of Women The sexuality of women was discussed in Shere Hite's book Women and Love: A Cultural Revolution. Her conclusions were based on sample data that consisted of 4500 mailed responses from 100,000 questionnaires that were sent to women. 11. UFO Poll In a Kelton Research poll, 1114 Americans 18 years of age or older were called after their telephone numbers were randomly generated by a computer, and 36% of the respon dents said that they believe in the existence of UFOs. 12. Class Survey The author surveyed a sample from the population of his statistics class by identifying groups of males and females, then randomly selecting five students from each of those two groups. 13. Driving A student of the author conducted a survey on driving habits by randomly selecting three different classes and surveying all of the students as they left those classes. 14. Acupuncture Study In a study of treatments for back pain, 641 subjects were randomly assigned to the four different treatment groups of individualized acupuncture, standardized acu- puncture, simulated acupuncture, and usual care (based on data from "A Randomized Trial Comparing Acupuncture, Simulated Acupuncture, and Usual Care for Chronic Low Back Pain," by Cherkin et al., Archives of Internal Medicine, Vol. 169, No. 9). 15. Dictionary The author collected sample data by randomly selecting five books from each of the categories of science, fiction, and history. The numbers of pages in the books were then identified. 16. Deforestation Rates Satellites are used to collect sample data for estimating deforestation rates. The Forest Resources Assessment of the United Nations (UN) Food and Agriculture Or- ganization uses a method of selecting a sample of a 10-km-wide square at every 10 intersection of latitude and longitude. 17. Testing Lipitor In a clinical trial of the cholesterol drug Lipitor (atorvastatin), subjects were partitioned into groups given a placebo or Lipitor doses of 10 mg, 20 mg, 40 mg, or 80 mg. The subjects were randomly assigned to the different treatment groups (based on data from Pfizer, Inc.). 18. Exit Polls During the last presidential election, CNN conducted an exit poll in which specif- ic polling stations were randomly selected and all voters were surveyed as they left the premises. 19. Literary Digest Poll In 1936, Literary Digest magazine mailed questionnaires to 10 million people and obtained 2,266,566 responses. The responses indicated that Alf Landon would win the presidential election. He didn't. 20. Highway Strength The New York State Department of Transportation evaluated the quality of the New York State Thruway by testing core samples collected at regular intervals of 1 mile. Critical Thinking: What's Wrong? In Exercises 21-28, determine whether the study is an experiment or an observational study, and then identify a major problem with the study. 21. Online News In a survey conducted by USA Today, 1465 Internet users chose to respond to this question posted on the USA Today electronic edition: "Is news online as satisfying as print and TV news?" 52% of the respondents said "yes." 22. Physicians' Health Study The Physicians' Health Study involved 22,071 male physi- cians. Based on random selections, 11,037 of them were treated with aspirin and the other 1 1,034 were given placebos. The study was stopped early because it became clear that aspirin reduced the risk of myocardial infarctions by a substantial amount. 23. Drinking and Driving A researcher for a consortium of insurance companies plans to test for the effects of drinking on driving ability by randomly selecting 1000 drivers and then randomly assigning them to two groups: One group of 500 will drive in New York City after no alcohol consumption, and the second group will drive in New York City after consuming three shots of Jim Beam bourbon whiskey.2-1 Frequency Distributions for Organizing and Sun Constructing Frequency Distributions. In Exercises 11-18, use the indicated data to construct the frequency distribution. (The data for Exercises 13-16 can be downloaded at TriolaStats.com.) 11. Old Faithful Listed below are sorted duration times (seconds) of eruptions of the Old Faithful geyser in Yellowstone National Park. Use these times to construct a frequency distribu- tion. Use a class width of 25 seconds and begin with a lower class limit of 125 seconds. 125 203 205 221 225 229 233 233 235 236 236 237 238 238 239 240 240 240 240 241 241 242 242 242 243 243 244 245 245 245 245 246 246 248 248 248 249 249 250 251 252 253 253 255 255 256 257 258 262 264 12. Tornadoes Listed below are the F-scale intensities of recent tornadoes in the United States. Construct a frequency distribution. Do the intensities appear to have a normal distribution? 0 4001110 0 01201 101011110 10010011130 0 02030000 0 1- 13. Burger King Lunch Service Times Refer to Data Set 25 "Fast Food" and use the drive- through service times for Burger King lunches. Begin with a lower class limit of 70 seconds and use a class width of 40 seconds. Burger King Dinner Service Times Refer to Data Set 25 "Fast Food" and use the drive-ER 1 introduction to Statistics 18. Criminal Forensics When studying the relationship between lengths of feet and height so that footprint evidence at a crime scene can be used to estimate the height of the suspect,'s researcher records the exact lengths of feet from a large sample of random subjects. 19. Smartphones Students in a statistics class record the exact lengths of times that they sur 1-2 reptitiously use their smartphones during class. 33. Cou 20. Texting Fatalities The Insurance Institute for Highway Safety collects data consisting of three de the numbers of motor vehicle fatalities caused by driving while texting. because number a. Exac In Exercises 21-28, determine which of the four levels of measurement (nominal, ordinal, b. Sho interval, ratio) is most appropriate. c. The 21. College Rankings U.S. News & World Report periodically provides its rankings of na- tional universities, and in a recent year the ranks for Princeton, Harvard, and Yale were 1, 2, and d. Th for th 3. respectively. 22. Exit Poll For the presidential election of 2016, ABC News conducts an exit poll in which voters are asked to identify the political party (Democratic, Republican, and so on) that they registered with. 23. M&Ms Colors of M&Ms (red, orange, yellow, brown, blue, green) listed in Data Set 27 "M&M Weights" in Appendix B 24. Fast Food Service Times In a study of fast food service times, a researcher records the time intervals of drive-up customers beginning when they place their order and ending when they receive their order. 25. Baseball Baseball statistician Bill James records the years in which the baseball World Series is won by a team from the National League. 26. Movie Ratings The author rated the movie Star Wars: The Force Awakens with 5 stars on a scale of 5 stars. 27. Lead in Blood Blood lead levels of low, medium, and high used to describe the subjects in Data Set 7 "IQ and Lead" in Appendix B 28. Body Temperatures Body temperatures (in degrees Fahrenheit) listed in Data Set 3 "Body Temperatures" in Appendix B In Exercises 29-32, identify the level of measurement of the data as nominal, ordinal, inter- val, or ratio. Also, explain what is wrong with the given calculation. 29. Super Bowl The first Super Bowl attended by the author was Super Bowl XLVIII. On the first play of the game, the Seattle defense scored on a safety. The defensive players wore jerseys is 49.6. numbered 31, 28, 41, 56, 25, 54, 69, 50, 91, 72, 29, and the average (mean) of those numbers 30. Social Security Numbers As part of a project in a statistics class, students report the last to be 4.7. four digits of their Social Security numbers, and the average (mean) of those digits is computed2-1 Basic Skills and Concepts Statistical Literacy and Critical Thinking 1. Mcdonald's Dinner Service Times Refer to the accompanying table summarizing ser for Exercise 1 times (seconds) of Mcdonald's dinners. How many individuals are included in the summaice Dinner Service Times Is it possible to identify the exact values of all of the original service times? Frequency 2. Mcdonald's Dinner Service Times Refer to the accompanying frequency distribution What problem would be created by using classes of 60-120. 120-180, . .. . 300-360? 22 3. Relative Frequency Distribution Use percentages to construct the relative frequency di 14 tribution corresponding to the accompanying frequency distribution for Mcdonald's ding 2 service times. 5 4. What's Wrong? Heights of adult males are known to have a normal distribution, as de scribed in this section. A researcher claims to have randomly selected adult males and mea or Exercise 4 sured their heights with the resulting relative frequency distribution as shown here. Identify two Relative major flaws with these results. Frequency 23% 25% In Exercises 5-8, identify the class width, class midpoints, and class boundaries for the 22% given frequency distribution. Also identify the number of individuals included in the sum. mary. The frequency distributions are based on real data from Appendix B. 27% 28% 5. 6. Age (yr) of Best Actress Age (yr) of Best Actor When Oscar Was Won Frequency When Oscar Was Won Frequency 20-29 29 20-29 30-39 34 30-39 28 40-49 14 40-49 36 50-59 3 50-59 15 60-69 60-69 6 70-79 1 70-79 80-89 7. 8. Blood Platelet Count Blood Platelet Count of Males Frequency of Females Frequency 0-99 100-199 25 100-199 51 200-299 92 200-299 90 300-399 28 300-399 10 400-499 400-499 0 0 500-599 500-599 2 0 600-699 Normal Distributions. In Exercises 9 and 10, using a loose interpretation of the criteria for determining whether a frequency distribution is approximately a normal distribution, determine whether the given frequency distribution is approximately a normal distribution Give a brief explanation. 9. Best Actresses Refer to the frequency distribution from Exercise 5. 10. Best Actors Refer to the frequency distribution