chapters 1-2 questions
In Exercises 15 and 16, construct the frequency polygons. 2.3.15 Old Faithful Use the frequency distribution from Exercise 11 in Section 2-1 on page 49 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?
The distribution appears to be skewed to the left (or negatively skewed). Image pg 714
1.3.3. Replication In what specific way was replication applied in the study cited in Exercise 1?
The group sample sizes of 547, 550, and 546 are all large so that the researchers could see the effects of the paracetamol treatment.
In Exercises 29-32, identify the level of measurement of the data as nominal, ordinal, interval, or ratio. Also, explain what is wrong with the given calculation. 1.2.29. 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 numbered 31, 28, 41, 56, 25, 54, 69, 50, 91, 72, 29, and the average (mean) of those numbers is 49.6.
The numbers are not counts or measures of anything. They are at the nominal level of measurement, and it makes no sense to compute the average (mean) of them.
1.2.1 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?
The population consists of all adults in the United States, and the sample is the 2276 adults who were surveyed. Because the value of 33% refers to the sample, it is a statistic.
In Exercises 5 and 6, construct the dotplot. 2.3.5 Pulse Rates Listed below are pulse rates (beats per minute) of females selected from Data Set 1 "Body Data" in Appendix B. All of those pulse rates are even numbers. Is there a pulse rate that appears to be an outlier? What is its value?
The pulse rate of 36 beats per minute appears to be an outlier Image pg 713
1.1.1 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 consis
The respondents are a voluntary response sample or a self-selected sample. Because those with strong interests in the topic are more likely to respond, it is very possible that their responses do not reflect the opinions or behavior of the general population.
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.) 1.3.5. Sampling Method What type of sampling best describes the way in which the 717 subjects were chosen: simple random sample, systematic sample, convenience sample, stratified sample, cluster sample? Does the method of sampling appear to adversely a¥ect the quality of the results?
The sample appears to be a convenience sample. By e-mailing the survey to a readily available group of Internet users, it was easy to obtain results. Although there is a real potential for getting a sample group that is not representative of the population, indications of which ear is used for cell phone calls and which hand is dominant do not appear to be factors that would be distorted much by a sample bias.
Sampling Method. In Exercises 9-12, determine whether the sampling method appears to be sound or is flawed. 1.1.9 Nuclear Power Plants In a survey of 1368 subjects, the following question was posted on the USA Today website: "In your view, are nuclear plants safe?" The survey subjects were Internet users who chose to respond to the question posted on the electronic edition of USA Today.
The sample is a voluntary response sample and has strong potential to be flawed.
1.1.11 Credit Card Payments In an AARP, Inc. survey of 1019 randomly selected adults, each was asked how much credit card debt he or she pays of each month.
The sampling method appears to be sound.
2.2.7 Relative Frequency Histogram How would the shape of the histogram change if the vertical scale uses relative frequencies expressed in percentages instead of the actual frequency counts as shown here?
The shape of the graph would not change. The vertical scale would be different, but the relative heights of the bars would be the same.
1.3.1 Back Pain Treatment In a study designed to test the e¥ectiveness of paracetamol (or acetaminophen) 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 medication; (2) 550 subjects were in a group given pills with paracetamol taken at regular intervals; (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., Lancet, doi:10.1016>S0140-6736(14)60805-9.) Is this study an experiment or an observational study? Explain.
The study is an experiment because subjects were given treatments.
2.1.1. McDonald's Dinner Service Times Refer to the accompanying table summarizing service times (seconds) of McDonald's dinners. How many individuals are included in
The table summarizes 50 service times. It is not possible to identify the exact values of all of the original times.
1.2.31. Temperatures As this exercise is being written, it is 80 degrees F at the author's home and it is 40 degree F in Auckland, New Zealand, so it is twice as warm at the author's home as it is in Auckland, New Zealand.
The temperatures are at the interval level of measurement. Because there is no natural starting point with 0oF representing "no heat," ratios such as "twice" make no sense, so it is wrong to say that it is twice as warm at the author's home as it is in Auckland, New Zealand
Time-Series Graphs. In Exercises 9 and 10, construct the time-series graph 2.3.9 Gender Pay Gap Listed below are women's median earnings as a percentage of men's median earnings for recent years beginning with 1990. Is there a trend? How does it appear to affect women? Image pg 65
There is a gradual upward trend that appears to be leveling off in recent years. An upward trend would be helpful to women so that their earnings become equal to those of men. Image pg 714
1.3.7. 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?
With 717 responses, the response rate is 14%, which does appear to be quite low. In general, a very low response rate creates a serious potential for getting a biased sample that consists of those with a special interest in the topic.
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. 1.1.13. 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.
With only a 1% chance of getting such results with a program that has no effect, the program appears to have statistical significance. Also, because the average loss of 22 pounds does seem substantial, the program appears to also have practical significance.
Consider the Source. In Exercises 5-8, determine whether the given source has the potential to create a bias in a statistical study. 1.1.5 [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
Yes, there does appear to be a potential to create a bias.
Interpreting a Histogram. In Exercises 5-8, answer the questions by referring to the following Minitab-generated histogram, which depicts the weights (grams) of all quarters listed in Data Set 29 "Coin Weights" in Appendix B. (Grams are actually units of mass and the values shown on the horizontal scale are rounded.) 2.2.5 Sample Size What is the approximate number of quarters depicted in the three bars farthest to the left? Image pg 55
40
In Exercises 7 and 8, construct the stemplot. 2.3.7 Refer to the data listed in Exercise 5. How are the data sorted in the stemplot?
7. The data are arranged in order from lowest to highest, as 36, 56, 56, and so on. Image pg 714
Constructing Histograms. In Exercises 9-16, construct the histograms and answer the given questions. 2.2.9 Old Faithful Use the frequency distribution from Exercise 11 in Section 2-1 on page 49 to construct a histogram. Does it appear to be the graph of data from a population with a normal distribution?
Because it is far from being bell-shaped, the histogram does not appear to depict data from a population with a normal distribution. Image pg 713
In Exercises 17-20, identify how the graph is deceptive. 2.3.17 Self-Driving Vehicles In a survey of adults, subjects were asked if they felt comfortable being in a self-driving vehicle. The accompanying graph depicts the results (based on data from TE Connectivity).
Because the vertical scale starts with a frequency of 200 instead of 0, the difference between the "no" and "yes" responses is greatly exaggerated. The graph makes it appear that about five times as many respondents said "no," when the ratio is actually a little less than 2.5 to 1.
1.1.15. 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.
Because there is a 19% chance of getting that many girls by chance, the method appears to lack statistical significance. The result of 1020 girls in 2000 births (51% girls) is above the approximately 50% rate expected by chance, but it does not appear to be high enough to have practical significance. Not many couples would bother with a procedure that raises the likelihood of a girl from 50% to 51%
In Exercises 11 and 12 construct the Pareto chart. 2.3.11 Journal Retractions In a study of retractions in biomedical journals, 436 were due to error, 201 were due to plagiarism, 888 were due to fraud, 291 were duplications of publications, and 287 had other causes (based on data from "Misconduct Accounts for the Majority of Retracted Scientific Publications," by Fang, Steen, Casadevall, Proceedings of the National Academy of Sciences of the United States of America, Vol. 110, No. 3). Among such retractions, does misconduct (fraud, duplication, plagiarism) appear to be a major factor?
Misconduct includes fraud, duplication, and plagiarism, so it does appear to be a major factor. Image pg 714
1.1.7 [Brain Size] from Data Set 8 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
No, there does not appear to be a potential to create a bias.
1.2.23. M&Ms Colors of M&Ms (red, orange, yellow, brown, blue, green) listed in Data Set 27 "M&M Weights" in Appendix B
Nominal
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. 1.3.21. 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."
Observational study. The sample is a convenience sample consisting of subjects who decided themselves to respond. Such voluntary response samples have a high chance of not being representative of the larger population, so the sample may well be biased. The question was posted in an electronic edition of a newspaper, so the sample is biased from the beginning.
1.2.3 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
Only part (a) describes discrete data.
1.2.27. 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
Ordinal
In Exercises 21-28, determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. 1.2.21. College Rankings U.S. News & World Report periodically provides its rankings of national universities, and in a recent year the ranks for Princeton, Harvard, and Yale were 1, 2, and 3, respectively
Ordinal
1.2.11. 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.
Parameter
1.2.7. Housing Units According to the Census Bureau, the total number of housing units in the United States is 132,802,859.
Parameter
Relative Frequencies for Comparisons. In Exercises 19 and 20, construct the relative frequency distributions and answer the given questions. 2.1.19 Oscar Winners Construct one table (similar to Table 2-9 on page 47) that includes relative frequencies based on the frequency distributions from Exercises 5 and 6, and then compare the ages of Oscar-winning actresses and actors. Are there notable differences?
Image pg 712
In Exercises 13 and 14, construct the pie chart. 2.3.13 Journal Retractions Use the data from Exercise 11 "Journal Retractions."
Image pg 714
2.1.5 In Exercises 5-8, identify the class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. The frequency distributions are based on real data from Appendix B. Image pg 48
Class width: 10. Class midpoints: 24.5, 34.5, 44.5, 54.5, 64.5, 74.5, 84.5. Class boundaries: 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, 89.5. Number: 87.
2.1.7 Image pg 48
Class width: 100. Class midpoints: 49.5, 149.5, 249.5, 349.5, 449.5, 549.5, 649.5. Class boundaries: -0.5, 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5. Number: 153.
1.3.13. 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.
Cluster
1.2.19. Smartphones Students in a statistics class record the exact lengths of times that they surreptitiously use their smartphones during class
Continuous
In Exercises 13-20, determine whether the data are from a discrete or continuous data set. 1.2.13. Freshman 15 In a study of weight gains by college students in their freshman year, researchers record the amounts of weight gained by randomly selected students (as in Data Set 6 "Freshman 15" in Appendix B).
Continuous
1.3.19. 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
Convenience
1.2.15. 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
Discrete
1.2.17. Corvettes A shift manager records the numbers of Corvettes manufactured during each day of production.
Discrete
2.1.3 Relative Frequency Distribution Use percentages to construct the relative frequency distribution corresponding to the accompanying frequency distribution for McDonald's dinner service times.
Image pg 711
2.1.17 Analysis of Last Digits Heights of statistics students were obtained by the author as part of an experiment conducted for class. The last digits of those heights are listed below. Construct a frequency distribution with 10 classes. Based on the distribution, do the heights appear to be reported or actually measured? What do you know about the accuracy of the results? Image pg.49
Image pg 712
2.1.25 Systolic Blood Pressure Use the systolic blood pressures of the 300 subjects included in Data Set 1 "Body Data." Use a class width of 20 mm Hg and begin with a lower class limit of 80 mm Hg. Does the frequency distribution appear to be a normal distribution?
Image pg 712
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.) 2.1.11 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 distribution. Use a class width of 25 seconds and begin with a lower class limit of 125 seconds. Image pg 49
Image pg 712
1.2.25. Baseball Baseball statistician Bill James records the years in which the baseball World Series is won by a team from the National League.
Interval
1.1.3 [Statistical Significance Versus Practical Significance] When testing a new treatment, what is the difference between statistical significance and practical significance? Can a treatment have statistical significance, but not practical significance?
Statistical significance is indicated when methods of statistics are used to reach a conclusion that a treatment is effective, but common sense might suggest that the treatment does not make enough of a difference to justify its use or to be practical. Yes, it is possible for a study to have statistical significance, but not practical significance.
1.3.11. 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 respondents said that they believe in the existence of UFOs.
Random
1.3.17. 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 di¥erent treatment groups (based on data from Pfizer, Inc.).
Random
1.2.9. 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.
Statistic
In Exercises 5-12, identify whether the given value is a statistic or a parameter. 1.2.5 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.
Statistic
1.3.15. 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.
Stratified
In Exercises 9-20, identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. 1.3.9. 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 collecting sample data at intervals of every 20 km (based on data from Journal of Great Lakes Research).
Systematic
