Section 5B – Quiz Me: 5.B-4
Identify flaws and bias in studies.
Question 1 – 5B 9
Based solely on the information given, do you have reason to question the results of the following hypothetical study? Explain your reasoning.
A study of the academic preparation of high school language arts teachers used the teachers’ mathematics scores on a standardized test for data.
Is there reason to question the results? Select all that apply.
A. Yes, there is reason. It makes sense that all teachers would do well on the standardized test regardless of their academic preparation.
B. Yes, there is reason. The variables that were measured are not identified.
C. No, there is not reason. There is no bias in the study.
D. Yes, there is reason. The study was about the preparation of language arts teachers, but uses the teachers’ mathematics scores.
E. No, there is not reason. The goal of the study is clear.
F. Yes, there is reason. Scores on standardized tests do not necessarily predict preparation.
Question 2 – 5B 11
Based solely on the information given, do you have reason to question the results of the following hypothetical study? Explain your reasoning.
A study by a conservative foundation is designed to assess a new Democratic spending plan.
Is there reason to question the results? Select all that apply.
A. No, there is not reason. The goal of the study is clear.
B. Yes, there is reason. There is a possibility of bias in the study.
C. No, there is not reason. There is no bias in the study.
D. No, there is not reason. It is unlikely that there are any confounding variables in the study.
E. Yes, there is reason. It makes sense that a Democratic spending plan would be studied by a conservative foundation.
F. Yes, there is reason. The variables that were measured are not identified.
Question 3 – 5B 13
Consider the hypothetical study described below. Based solely on the information given, do you have reason to question the results of the study? Explain your reasoning.
A TV talk show host asks the TV audience, “Do you support new national mileage standards for automobiles?” and asks people to vote by telephone at a toll-free number.
Is there reason to question the results? Select all that apply.
A. No, there is not reason. There is no bias in the study.
B. No, there is not reason. It is unlikely that there are any confounding variables in the study.
C. Yes, there is reason. The TV audience might not be representative of the population.
D. Yes, there is reason. The wording of the question might produce inaccurate or dishonest responses.
E. Yes, there is reason. Call-in polls tend to be biased.
F. No, there is not reason. The goal of the study is clear.
Question 4 – 5B 15
Consider the hypothetical study described below. Based solely on the information given, do you have reason to question the results of the study? Explain your reasoning.
Researchers design five survey questions to determine whether Norwegian citizens are happier than American citizens.
Is there reason to question the results? Select all that apply.
A. No, there is not reason. It is unlikely that there are any confounding variables in the study.
B. Yes, there is reason. It is not clear how the variable of interest is measured.
C. No, there is not reason. The goal of the study is clear.
D. No, there is not reason. There is no bias in the study.
E. Yes, there is reason. It is not clear how the variable of interest is defined.
F. Yes, there is reason. The people being surveyed will likely not be representative of the population.
Question 5 – 5B 17
Based solely on the information given, do you have reason to question the results of the following hypothetical study? Explain your reasoning.
In a study designed to determine whether bicyclists who wear helmets have fewer accidents, researchers tracked 500 riders with helmets for one month.
Is there reason to question the results? Select all that apply.
A. No, there is not reason. The goal of the study is clear.
B. No, there is not reason. It is unlikely that there are any confounding variables in the study.
C. No, there is not reason. There is no bias in the study.
D. Yes, there is reason. It makes sense that riders who do not use helmets get into more accidents.
E. Yes, there is reason. The variables that were measured are not identified.
F. Yes, there is reason. The sample is biased; riders who do not use helmets should also be included.
Question 6 – 5B 19
Consider the hypothetical study described below. Based solely on the information given, do you have reason to question the results of the study? Explain your reasoning.
Sociologists studying domestic violence circulate a questionnaire asking each respondent if she or he has ever abused a spouse or partner.
Is there reason to question the results? Select all that apply.
A. No, there is not reason. It is unlikely that there are any confounding variables in the study.
B. Yes, there is reason. Self-reporting is often not accurate.
C. No, there is not reason. The goal of the study is clear.
D. Yes, there is reason. The people receiving the questionnaire might not be representative of the population.
E. Yes, there is reason. The wording of the question might produce inaccurate or dishonest responses.
F. No, there is not reason. There is no bias in the study.
Question 7 – 5B 21
Consider the study described below. Based solely on the information given, decide whether you would believe the stated claim. Justify your conclusion.
A research group that tracks tuition rates at colleges and universities compares the tuition at a small college today and 10 years ago and claims that tuition has increased 150% during that period.
Would you believe the claim? Select all that apply.
A. No, since there is no reliable way to determine whether tuitition actually increased.
B. No, since it is not clear whether inflation was taken into account.
C. Yes, since there is no bias in the study.
D. Yes, since the goal of the study is clear.
E. No, since the research group was trying to show that tuition had increased, introducing bias into the results.
F. Yes, since it is unlikely that there are any confounding variables in the study.
Question 8 – 5B 23
Consider the study described below. Based solely on the information given, decide whether you would believe the stated claim. Justify your conclusion.
Citing a higher incidence of cell-phone-related accidents among teens, the governor’s office claims that banning the use of hand-held cell phones among drivers under 20 years of age will save lives.
Would you believe the claim? Select all that apply.
A. Yes, since banning distractions for drivers makes sense.
B. No, since many other factors can lead to accidents.
C. Yes, since the sample was representative of the population.
D. No, since it is not explained how such a ban would be implemented.
E. No, since the relationship between cell phone use and traffic fatalities is not described.
F. Yes, since the goal of the study is clear.
Question 9 – 5B 25
Based solely on the information given about the following hypothetical study, decide whether you would believe the stated claim. Justify your conclusion.
The local Chamber of Commerce claims that the average number of employees among all businesses in town is 12.5.
Is there reason to question the claim? Select all that apply.
A. No, there is not reason. The Chamber of Commerce would have no reason to distort its data.
B. No, there is not reason. The number is believable for a town.
C. Yes, there is reason. The Chamber of Commerce is a biased office.
D. Yes, there is reason. The sample of businesses was too small.
Question 10 – 5B 27
Identify any potential sources of bias in the following study.
From a poll of people who recently bought cold medicine at all stores of a large drugstore chain, investigators concluded that the mean time between colds for all Americans is 5.6 months.
What sources of bias, if any, might this study have?
A. Participation bias only
B. Both selection and participation bias
C. Selection bias only
D. There is probably no bias in the study.
Question 11 – 5B 29
Identify any potential sources of bias in the following study.
An exit poll designed to predict the winner of a local election uses voluntary surveys with every Republican who votes between 8:00 and 9:45 a.m.
What sources of bias, if any, might this study have?
A. Participation bias only
B. Both selection and participation bias
C. Selection bias only
D. There is probably no bias in the study.
Question 12 – 5B 30
An article noted that chocolate is rich in flavonoids. The article reports that “regular consumption of foods rich in flavonoids may reduce the risk of coronary heart disease.” The study received funding from a candy company and a chocolate manufacturers association. Identify and explain at least one source of bias in the study described. Then suggest how the bias might have been avoided.
Choose the correct answer below.
A. Since the sample is self-selected, there is a definite participation bias in this study. The researchers should randomly select the subjects of the study.
B. The researchers may have been more inclined to provide favorable results because funding was provided by a party with a definite interest. The bias could have been avoided if the researchers were not paid by the candy company and the chocolate manufacturers.
C. The data do not seem to support the claims being made by the article. The article’s author should consult an expert to make sure that he or she is correctly interpreting the study’s results.
D. The questions used in the study might have caused the respondents to give inaccurate or dishonest responses. The question wording should be changed to be more neutral.
Question 13 – 5B 31
Identify any potential sources of bias in the following study.
In order to determine the opinions of people in the 19- to 25- year age group on controlling illegal immigration, researchers survey 2000 National Guard members in this age group.
What sources of bias, if any, might this study have?
A. Selection bias only
B. Selection and participation bias
C. Participation bias only
D. There is probably no bias in the study.
Question 14 – 5B 33
Identify any potential sources of bias in the following study.
Members of a reproductive health service are surveyed to determine whether American adults prefer abstinence, counseling and education, or morning-after pills for high school students.
What sources of bias, if any, might this study have?
A. Both selection and participation bias
B. Participation bias only
C. Selection bias only
D. There is probably no bias in the study.
5.B Should You Believe a Statistical Study?
Identify flaws in reporting on studies.
Question 1 – 5B 43
The headline “Drugs shown in 98 percent of movies” accompanied a news story that described a “government study” claiming that drug use, drinking, or smoking was depicted in 98% of the top movie rentals. Discuss whether the headline accurately represents the story.
Choose the correct answer below.
A. The headline appears to accurately represent the news story.
B. The headline refers to drugs whereas the story refers to “drug use, drinking, or smoking.” The headline is very misleading because the term “drugs” is generally considered to consist of drugs other than cigarettes or alcohol. Also, all movies consist of more than just the top movie rentals.
C. The headline is exaggerating the results given in the story. The headline uses a bigger figure for the amount of drugs in movies than the figure given in the story.
D. The headline is downplaying the results presented in the story, because the government produced the study.
Question 2 – 5B 45
Discuss the differences between the following questions, each of which could be the basis for a statistical study.
• What percentage of Internet dates lead to marriage?
• What percentage of marriages begin with Internet dates?
Choose the correct answer below.
A. The percentage of marriages beginning with Internet dates would be an observation while the percentage of Internet dates that lead to marriage would be an experiment.
B. The percentage of marriages beginning with Internet dates can be accurately measured while the percentage of Internet dates that lead to marriage cannot be accurately measured.
C. The questions are too different to compare.
D. The questions have different populations.
5.D Graphics in the Media
Decide if a statement involving statistical graphics makes sense.
Question 1 – 5D 9
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.
My bar chart contains more information than yours, because I made my bars three-dimensional.
Choose the correct answer below.
A. The statement does not make sense because making the bars three-dimenional does not necessarily mean that information was added. It could mean that only the appearance of the graph was changed.
B. The statement does not make sense because making the bars three-dimensional makes the graph harder to read and reduced the amount of information that can be read from it.
C. The statement makes sense because making the bars three-dimensional means that more information was used to create a third dimension in the graph.
D. The statement makes sense because making the bars three-dimensional makes the graph easier to read and increases the amount of information that can be read from it.
Question 2 – 5D 11
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.
There’s been only a very slight rise in our stock price over the past few months, but I wanted to make it look dramatic so I started the vertical scale from the lowest price rather than from zero.
Choose the correct answer below.
A. The statement does not make sense because reducing the range of the vertical axis to just fit the data will decrease the relative size of the variation in the data.
B. The statement makes sense because reducing the range of the vertical axis to just fit the data will increase the relative size of the variation in the data.
C. The statement makes sense because increasing the range of the vertical axis to contain all of the data will increase the relative size of the variation in the data.
D. The statement does not make sense because changing the axis cannot change the data that is being displayed.
5.D Graphics in the Media
Interpret multiple bar graphs, stack plots, contour maps, and other media graphs
Question 1 – 5D 13
Net grain production is the difference between the amount of grain a country produces and the amount of grain its citizens consume. It is positive if the country produces more than it consumes, and negative if the country consumes more than it produces. The figure shows the net grain production of four countries in 1990 and projected for 2030. Complete parts a through c.
a. Which of the four countries had to import grain to meet its needs in 1990?
A. China
B. India
C. Russia
D. U.S.
b. Which of the four countries are expected to need to import grain to meet needs in 2030?
A. India
B. U.S.
C. Russia
D. China
c. Given that India and China are the world’s two most populous countries, what does this graph tell you about how world agriculture will have to change between now and 2030?
A. It will need to decrease.
B. It can stay about the same.
C. It will need to increase.
A bar graph titled “Net Grain Production, 1990 and 2030 (projected)” has four countries labeled on the horizontal axis and a vertical axis labeled “Millions of tons” from negative 250 to 100 in increments of 50. T the horizontal axis crosses the vertical axis at vertical coordinate 0. Two vertical bars are at each of the horizontal axis labels, where the left bar represents 1990 and the right bar represents 2030. The bars extend up and down from the horizontal axis. The bars have heights as follows, with the horizontal axis label listed first and the bar height listed second: U.S., 75, 80; China, negative 5, negative 225; India, negative 4, negative 45; Russia, negative 40, negative 25. All heights are approximate.
Question 2 – 5D 15
In this figure, the graphs from top to bottom represent individuals who are not high school graduates, who are high school graduates, who have some college experience or an associate’s degree, and who have a bachelor’s degree or higher, in that order. Complete parts (a) and (b) below.
A multiple line chart titled Unemployment Rate by Education Level has a horizontal axis labeled Year and a vertical axis labeled Unemployment Rate. The horizontal axis has tick marks from 1992 to 2006 in increments of 2 as well as tick marks at 2009 and 2012. The vertical axis has tick marks from 0 percent to 16 percent in increments of 2 percent. From left to right, the four plotted lines rise and fall multiples times around the following average values, where the lines are listed from top to bottom: first line, 9 percent; second line, 6 percent; third line, 4.5 percent; fourth line, 2.5 percent.
a. Briefly describe how unemployment varies with educational attainment. Choose the correct answer below.
A. Unemployment stays approximately constant regardless of level of education.
B. As the level of education increases, pay rate decreases.
C. As the level of education increases, pay rate increases.
D. As the level of education increases, unemployment rates tend to decrease.
E. As the level of education increases, unemployment rates tend to increase.
b. How much more likely is a high school dropout to be unemployed than a worker with a bachelor’s degree?
A. About 10 times as likely
B. About 5 times as likely
C. About 2 to 3 times as likely
D. Just as likely
Question 3 – 5D 17
a. The bar for girls from country Upper E is more than twice as long as the bar for girls from country Upper C. Can it be concluded that test scores for girls from country Upper E were more than twice as high as test scores for girls from country Upper C? Explain.
A. Yes, because the bar is more than twice as long.
B. No, because the scale on the vertical axis does not start at 0.
C. Yes, because country Upper E does far better than country Upper C.
D. No, because the data is only a sample of the entire population.
b. Assume that the data in the figure represent overall regional differences in performances. Suppose that country G is in the same region as countries Upper B and Upper F. How can the test scores for boys and girls in country G compare?
A. Girls will probably score higher than boys.
B. Boys and girls will probably score the same.
C. Boys will probably score higher than girls.
D. Nothing can be predicted from the data.
Question 4 – 5D 19
Use the data in the graph to answer parts (a) through (c).
LOADING… Click the icon to view the graph.
a. Which category varies the most among the different types of institutions? By how much?
▼
Tuition and fees
Books and supplies
Other expenses
Room and board
Transportation
______________ varies the most. It has a variation of $______
(Type an integer or a decimal.)
Answers – Tuition and fees & 22,908
b. Excluding “other expenses” which cost category varies the least among the different types of institutions? Can you explain why this category varies so little?
A. Room and board varies the least because it costs all types of colleges the same amount of money to have a student live on campus.
B. Transportation varies the least because students at all types of colleges have the same mode of transportation.
C. Books and supplies varies the least because students at all types of colleges need approximately the same number of books and supplies and these don’t vary much in cost.
D. Tuition and fees varies the least because the operational costs for all types of colleges are the same.
c. Ignoring the “other expenses” category, the general trend is for all categories to cost more as you look down the chart from two-year public colleges to four-year private colleges. However, one category is an exception to this trend. Which category? Can you explain why? (Hint: If more than one category appears to have a downward trend, focus on the category with the largest downward trend.)
A. Books and supplies because two-year public colleges require more books and supplies than four-year private colleges
B. Room and board because it costs less to live on-campus than to live-off campus
C. Transportation because commuters must spend more money to get to school than students living on-campus
D. Tuition and fees because two-year public colleges need to charge more to attend due to smaller enrollment numbers
Question 5 – 5D 20
a. Estimate the numbers of college degrees awarded to men and to women (separately) in 1930 and in 1990.
The number of college degrees awarded to men in 1930 was.
▼
25,000
50,000
100,000
75,000
The number of college degrees awarded to women in 1930 was
▼
50,000
75,000
25,000
100,000
The number of college degrees awarded to men in 1990 was.
▼
562,000
674,400
786,800
449,600
The number of college degrees awarded to women in 1990 was
▼
585,500
468,400
702,600
819,700
b. Compare the numbers of degrees awarded to men and to women (separately) in 1980 and 2000. Choose the correct answer below.
A. In 1980 and in 2000, the number of men and women who received degrees were the same.
B. In 1980, more women than men received degrees; in 2000, more men than women received degrees.
C. In 1980, more men than women received degrees; in 2000, more women than men received degrees.
c. During what decade did the total number of degrees awarded increase the most?
A. 1990s
B. 1960s
C. 1940s
D. 1920s
d. Compare the total numbers of degrees awarded in 1950 and 2000.
The total number of degrees awarded in 1950 was
▼
1,245,000
622,500
223,500
447,000
The total number of degrees awarded in 2000 was
▼
1,245,000
447,000
223,500
622,500
Question 6 – 5D 21
The accompanying line chart shows the major spending categories of the federal budget over the last 50 years. (Payments to individuals includes Social Security and Medicare; net interest represents interest payments on the national debt; all other represents non-defense discretionary spending.) Complete parts (a) through (c) below.
a. Find the percentage of the budget that went to net interest in 1990 and 2012.
The percentage of the budget that went to net interest in 1990 is approximately
_______%. Answer – 10 %
(Round to the nearest integer as needed.)
The percentage of the budget that went to net interest 2012 is approximately
_______%. Answer – 5%
(Round to the nearest integer as needed.)
b. Find the percentage of the budget that went to defense in 1960 and 2012.
The percentage of the budget that went to national defense in 1960 is approximately
_______%. Answer – 55%
(Round to the nearest integer as needed.)
The percentage of the budget that went to national defense in 2012 is approximately
_______%. Answer – 20%
(Round to the nearest integer as needed.)
c. Find the percentage of the budget that went to payments to individuals in 1970 and 2012.
The percentage of the budget that went to payments to individuals in 1970 is approximately
________%. Answer – 30%
(Round to the nearest integer as needed.)
The percentage of the budget that went to payments to individuals in 2012 is approximately
_______%. Answer – 55%
(Round to the nearest integer as needed.)
Question 7 – 5D 23
Consider the contour map in the figure, which has six points marked on it. Assume that points A and B correspond to summits, and that the contour lines have 40-foot intervals. Complete parts a through d.
a. If you walk from A to C, do you walk uphill or downhill?
downhill
uphill
b. Does your elevation change more in walking from B to D or from D to F?
D to F
B to D
c. If you walk directly from E to F does your elevation increase, decrease, or remain the same?
A. Your elevation increases.
B. Your elevation remains the same.
C. Your elevation decreases.
d. What is your net elevation change if you walk from A to C to D to A?
_______feet. Answer – 0
Question 8 – 5D 25
The figure shows projections of the age distribution of the U.S. population from 2010 through 2050. Use this graph to answer the following questions. Complete parts a through d.
A three-dimensional bar graph uses bars to show data about the percentages of the U S population in different age groups for each decade from 2010 to 2050. The bars are arranged in a grid with rows corresponding to age groups and columns corresponding to years from 2010 to 2050 in increments of 10. The age groups are as follows from front to back: Less than 5, 5 to 14, 15 to 24, 25 to 34, 35 to 44, 45 to 54, 55 to 64, greater than 64. The bars for each year have the following heights from front to back: 2010, 7, 14, 15, 14, 14, 15, 13, 13; 2020, 7, 14, 14, 14, 13, 13, 14, 17; 2030, 7, 13, 14, 12, 13, 12, 12, 20; 2040, 7, 13, 13, 13, 12, 13, 12, 21; 2050, 7, 12, 13, 13, 13, 12, 13, 21. All heights are approximate.
a. What percentage of the population was over age 65 in 2010?
Answer – 13% (Round to the nearest integer as needed.)
What percentage of the population is projected to be over age 65 in 2050?
Answer – 20%
b. Describe the change in the 45-54 age group between 2010 and 2050.
A. The group stays about the same as a percentage of the population.
B. The group decreases as a percentage of the population.
C. The group increases as a percentage of the population.
c. Does the under-25 segment of the population increase or decrease in size between 2010 and 2050?
A. The group decreases as a percentage of the population.
B. The group increases as a percentage of the population.
C. The group stays about the same as a percentage of the population.
d. In what year did (will) 45- to 54-year-olds comprise the largest percentage of the population?
45- to 54-year-olds comprise the largest percentage in
▼
2050.
2030.
2010.
2040.
2020.
Question 9 – 5D 27
Figure 5.31 uses television sets to represent the number of homes with cable in 1970 and 2012. Note that the heights of the TVs represent the number of homes. Briefly explain how the graph creates a perceptual distortion that exaggerates the true change in the number of homes with cable.
Choose the correct answer below.
A. A perceptual distortion is created because the volumes of the TVs represent the number of homes, but the human eye tends to focus on the areas of the TV screens, exaggerating the true change to appear too large.
B. A perceptual distortion is created because the areas of the TV screens represent the number of homes, but the human eye tends to focus on the volumes of the TVs, exaggerating the true change to appear too small.
C. A perceptual distortion is created by the scale of the graphs. Since the scales vary between the two images, it exaggerates the true change in the number of homes.
D. A perceptual distortion is created because the heights of the TVs represent the number of homes, but the human eye tends to focus on the volumes of the TVs, exaggerating the true change to appear too large.
Question 10 – 5D 29
The graph to the right compares teaching salaries of women and men at private colleges and universities. What impression does the graph create? Does the graph depict the data fairly? If not, construct a graph that depicts the data fairly.
A bar graph titled “Salaries (dollars)” has a vertical axis labeled from 50000 to 80000 in increments of 10000 and a horizontal axis with the labels “Women” and “Men” from left to right. The graph contains two vertical bars of equal width that do not touch each other. The bars over the horizontal axis labels extend over vertical ranges as follows: Women, 50000 to 59000; Men, 50000 to 70000. All values are approximate.
What impression does the graph create?
A. The graph creates the impression that men and women have approximately the same salaries.
B. The graph creates the impression that men have salaries that are more than twice the salaries of women.
C. The graph creates the impression that women have salaries that are slightly higher than that of men.
D. The graph creates the impression that men have salaries that are slightly higher than that of women.
Does the graph depict the data fairly?
A. Yes, because the bars accurately represent each average.
B. No, because the vertical scale does not start at zero.
C. No, because the data are two-dimensional measurements.
D. Yes, because the vertical scale is appropriate for the data.
If the graph does not depict the data fairly, which graph below does?
A.
B.
C.
D. The graph depicts the data fairly
Question 11 – 5D 31
The table shows the numbers of cell phone subscriptions. Display the data using an ordinary vertical scale and an exponential vertical scale. Which graph is more useful? Why?
Choose the correct graph of the data with an ordinary vertical scale below.
A.
B.
C.
D.
Choose the correct graph of the data with an exponential vertical scale below.
A.
B.
C.
D.
Which graph is more useful? Why?
A. The graph in part a gives a worse picture of the true nature of the rate of change. The graph in part b makes it easier to see the changes in the early years.
B. The graph in part a gives a better picture of the true nature of the rate of change. The graph in part b makes it easier to see the changes in the early years.
C. The graph in part a gives a better picture of the true nature of the rate of change. The graph in part b makes it easier to see the changes in the late years.
D. The graph in part a gives a worse picture of the true nature of the rate of change. The graph in part b makes it easier to see the changes in the late years.
Question 12 – 5D 33
Recast the population data in the figure with a proper horizontal axis. What trends are clear in your new graph that are not clear in the original? Explain.
LOADING… Click the icon to view the figure of world population data.
Choose the correct graph below.
A.
1750
1850
1950
2050
0
2
4
6
8
10
Year
Population (billions)
A coordinate system has a horizontal axis labeled Year from 1750 to 2050 in increments of 50 and a vertical axis labeled Population (billions) from 0 to 10 in increments of 1. Line segments connect the following points from left to right: (1800, 1); (1830, 2); (1890, 3); (1930, 4); (1960, 5); (2000, 6); (2010, 7); (2020, 8); (2040, 9). All coordinates are approximate.
B.
1750
1850
1950
2050
0
2
4
6
8
10
Year
Population (billions)
A coordinate system has a horizontal axis labeled Year from 1750 to 2050 in increments of 50 and a vertical axis labeled Population (billions) from 0 to 10 in increments of 1. Line segments connect the following points from left to right: (1800, 1); (1930, 2); (1960, 3); (1970, 4); (1990, 5); (2000, 6); (2010, 7); (2020, 8); (2040, 9). All coordinates are approximate.
C.
1000
1400
1800
2200
2600
0
2
4
6
8
10
Year
Population (billions)
A coordinate system has a horizontal axis labeled Year from 1000 to 2600 in increments of 50 and a vertical axis labeled Population (billions) from 0 to 10 in increments of 1. Line segments connect the following points from left to right: (1800, 1); (1925, 2); (1950, 3); (1975, 4); (1975, 5); (2000, 6); (2000, 7); (2025, 8); (2050, 9). All coordinates are approximate.
Observe the graph with a proper horizontal axis found in the previous step. What trends are clear in the new graph that are not clear in the original figure? Explain. Choose the correct answer below.
A. Most of the growth occurred after 1850. It is not clear in the original figure because the horizontal axis is not linear.
B. Most of the growth occurred after 1950. It is not clear in the original figure because the horizontal axis is not linear.
C. Most of the growth occurred after 1950. It is not clear in the original figure because it has lots of visual impacts.
D. The population grows linearly. It is not clear in the original figure because it has lots of visual impacts.
Question 13 – 5D 33
The graph in the figure show data on the relative risk of schizophrenia among people born in different months. Complete parts a and b.
A line graph has a vertical axis labeled “Relative risk” from less than 0.6 to 1.4 in increments of 0.1 and a horizontal axis labeled “Month of birth” with 12 tick marks. Above each horizontal axis tick mark, a dot and vertical bar are plotted. From left to right, starting with the first tick and in increments of 1 tick, the data can be summarized as follows, where the vertical coordinate of the dot is listed first and the error bar range is listed second: 1.02 and 0.82 through 1.22; 1.07 and 0.92 through 1.32; 1.09 and 0.94 through 1.32; 1.02 and 0.83 through 1.22; 1.03 and 0.87 through 1.24; 0.99 and 0.82 through 1.2; 0.97 and 0.78 through 1.14; 0.89 and 0.74 through 1.06; 0.88 and 0.73 through 1.05; 0.9 and 0.76 through 1.1; 0.95 and 0.79 through 1.14, 0.99 and 0.82 through 1.2. A curve passes close to all of the points. All values are approximate.
a. Note that the scale of the vertical axis does not include zero. Sketch the same risk curve using an axis that includes zero.
A. A line graph has a vertical axis labeled from 0 to 1.4 in increments of 0.2 and a horizontal axis with 12 tick marks. Above each horizontal axis tick mark, a dot and vertical bar are plotted. From left to right, starting with the first tick and in increments of 1 tick, the data can be summarized as follows, where the vertical coordinate of the dot is listed first and the error bar range is listed second: 1.02 and 0.82 through 1.22; 1.2 and 1 through 1.39; 1.2 and 1.01 through 1.4; 1 and 0.82 through 1.2; 1.03 and 0.84 through 1.24; 0.96 and 0.78 through 1.15; 0.9 and 0.72 through 1.14; 0.85 and 0.62 through 0.98; 0.84 and 0.6 through 0.96; 0.82 and 0.68 through 1; 0.9 and 0.76 through 1.06; 1 and 0.82 through 1.2. All values are approximate.
B. A line graph has a vertical axis labeled from 0 to 1.4 in increments of 0.2 and a horizontal axis with 12 tick marks. Above each horizontal axis tick mark, a dot and vertical bar are plotted. From left to right, starting with the first tick and in increments of 1 tick, the data can be summarized as follows, where the vertical coordinate of the dot is listed first and the error bar range is listed second: 1.02 and 0.82 through 1.22; 1.07 and 0.92 through 1.32; 1.09 and 0.94 through 1.32; 1.02 and 0.83 through 1.22; 1.03 and 0.87 through 1.24; 0.99 and 0.82 through 1.2; 0.97 and 0.78 through 1.14; 0.89 and 0.74 through 1.06; 0.88 and 0.73 through 1.05; 0.9 and 0.76 through 1.1; 0.95 and 0.79 through 1.14, 0.99 and 0.82 through 1.2. All values are approximate.
C. A line graph has a vertical axis labeled from 0 to 1.4 in increments of 0.2 and a horizontal axis with 12 tick marks. Above each horizontal axis tick mark, a dot and vertical bar are plotted. From left to right, starting with the first tick and in increments of 1 tick, the data can be summarized as follows, where the vertical coordinate of the dot is listed first and the error bar range is listed second: 0.82 and 0.62 through 1.02; 1.18 and 0.98 through 1.38; 1.2 and 1 through 1.4; 0.8 and 0.6 through 1; 0.88 and 0.68 through 1.08; 0.68 and 0.48 through 0.88; 0.56 and 0.36 through 0.76; 0.26 and 0.06 through 0.46; 0.2 and 0 through 0.4; 0.35 and 0.15 through 0.55; 0.55 and 0.35 through 0.75; 0.75 and 0.55 through 0.95. All values are approximate.
Comment on the effect of this change.
A. The changes look bigger on the new graph.
B. The changes look about the same on the new graph.
C. The changes look smaller on the new graph.
b. Each value of the relative risk is shown with a dot at its most likely value and with an “error bar” indicating the range in which the data value probably lies. The study concludes that “the risk was also significantly associated with the month of birth.” Given the size of the error bars, does this claim appear justified? (Is it possible to draw a flat line that passes through all of the error bars?)
The claim does not appear justified.
The claim appears justified.
Question 14 – 5D 35
The Gapminder HIV Chart 2009 displays the wealth of various countries (per capita income) and the percentage of adults infected with HIV in the same countries. The size of the bubble is proportional to the actual number of HIV-infected adults. Complete parts (a) through (e) below.
a. How is the location of countries indicated on the display? Choose the correct answer below.
A. Colors indicate the continents.
B. The sizes of the bubbles indicate the locations.
C. Names indicate the countries.
D. The vertical axis indicates the locations.
On what continent is Benin located? Choose the correct answer below.
A. Asia
B. Africa
C. Europe
D. The Americas
b. Approximately how many people in Chad live with HIV? What is the per capita income in that country? Choose the correct answers below.
A. Approximately 1 million people; $3000
B. Approximately 10 thousand people; $10,000
C. Approximately 0.5 million people; $1000
D. Approximately 1 million people; $2000
c. Approximately how many people in India live with HIV? What is the per capita income in that country? Choose the correct answers below.
A. Approximately 0.5 million people; $1000
B. Approximately 1 million people; $2000
C. Approximately 10 thousand people; $10,000
D. Approximately 1 million people; $3000
d. Discuss how incidence of HIV appears to be related to the wealth of a country.
With some exceptions, HIV incidence
▼
increases
decreases
with the wealth of the country.
e. What country is the most notable exception to the conclusion in part (d)? Choose the correct answer below.
A. Russia
B. South Africa
C. Thailand
D. Brazil
5.E Correlation and Causality
Interpret scatterplots.
Question 1 – 5E 13
Consider the scatterplot to the right.
a. State whether the diagram shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, is it strong or weak?
b. Summarize any conclusions that can be drawn from the diagram.
A scatterplot titled “2014 Model Cars” with a horizontal axis labeled “Weight of cars (pounds)” from 1500 to 4500 in increments of 1000 and a vertical axis labeled “City gas mileage (miles per gallon)” from 10 to 35 in increments of 5 contains 16 points. The coordinates of the points are as follows: (2500, 27); (2500, 32); (2500, 28); (2500, 23); (3000, 23); (3000, 20); (3000, 22); (3000, 19); (3000, 19); (3000, 19); (3500, 20); (3500, 19); (3500, 19); (4000, 16); (4000, 16); (4000, 16). All coordinates are approximate.
a. Select the correct answer below.
A. There is a strong negative correlation.
B. There is a weak positive correlation.
C. There is a weak negative correlation.
D. There is a strong positive correlation.
E. There is no correlation.
b. Select the correct answer below.
A. Heavier cars get the same gas mileage as lighter cars.
B. Heavier cars generally get lower gas mileage.
C. Heavier cars generally get higher gas mileage.
D. No conclusion can be drawn.
Question 2 – 5E 15
Consider the scatterplot to the right.
a. State whether the diagram shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, is it strong or weak?
b. Summarize any conclusions that can be drawn from the diagram.
Charitable Giving (11 States) as Percentage of Adjusted Gross Income (AGI)
A scatterplot with a horizontal axis labeled Average A G I from 0 to 100000 in increments of 20000 and a vertical axis labeled Percent of A G I from 0 to 4 in increments of 0.5 contains 11 points. The coordinates of the points are as follows: (39000, 1.25); (43000, 3); (44000, 2.5); (46000, 2); (52000, 1.5); (50000, 3); (61000, 1.25); (62000, 2.25); (71000, 2.5); (78000, 3.5); (82000, 1.75). All coordinates are approximate.
a. Select the correct answer below.
A. There is a weak positive correlation.
B. There is a strong negative correlation.
C. There is a weak negative correlation.
D. There is a strong positive correlation.
E. There is no correlation.
b. Select the correct answer below.
A. Higher AGI may imply slightly lower charitable giving as a percentage of AGI.
B. Higher AGI implies much higher charitable giving as a percentage of AGI.
C. Higher AGI may imply slightly higher charitable giving as a percentage of AGI.
D. No conclusion can be drawn.
Determine whether variables are correlated.
Question 1 – 5E 17
For the following pair of variables, state the units that might be used to measure each variable. Then state whether you believe that they are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.
Latitude south of the equator and the average length of daylight in June
To measure latitude, the unit
▼
degrees of latitude
degrees Fahrenheit
hours
miles per gallon
might be used.
To measure length of daylight, the unit
▼
degrees of latitude
degrees Fahrenheit
hours
miles per gallon
might be used.
What correlation, if any, is there between the variables?
A. There is a positive correlation because the average length of daylight tends to increase when latitude increases.
B. There is a negative correlation because the average length of daylight tends to increase when latitude decreases.
C. The variables are not correlated.
Question 2 – 5E 19
For the following pair of variables, state the units that might be used to measure each variable. Then state whether you believe that the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.
Latitude south of the equator and the average high temperature in December
To measure latitude, the unit
▼
pounds per square inch
degrees of latitude
degrees Fahrenheit
square inches
might be used.
To measure temperature, the unit degrees Fahrenheit might be used.
What correlation, if any, is there between the variables?
A. There is a negative correlation because the average high temperature in December tends to increase when latitude decreases.
B. There is a positive correlation because the average high temperature in December tends to increase when latitude increases.
C. There is a positive correlation because the average high temperature in December tends to increase when latitude decreases.
D. There is a negative correlation because the average high temperature in December tends to increase when latitude increases.
E. The variables are not correlated.
Question 3 – 5E 21
For the following pair of variables, state the units that might be used to measure each variable. Then state whether you believe that the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.
Latitude north of the equator and the average high temperature in December
To measure latitude, the unit
▼
degrees of latitude
square inches
degrees Fahrenheit
pounds
might be used.
To measure temperature, the unit
▼
pounds
degrees Fahrenheit
square inches
degrees of latitude
might be used.
What correlation, if any, is there between the variables?
A. There is a negative correlation because the average high temperature in December tends to increase when latitude increases.
B. There is a negative correlation because the average high temperature in December tends to increase when latitude decreases.
C. There is a positive correlation because the average high temperature in December tends to increase when latitude decreases.
D. There is a positive correlation because the average high temperature in December tends to increase when latitude increases.
E. The variables are not correlated
Question 4 – 5E 23
For the following pair of variables, state the units that might be used to measure each variable. Then state whether you believe that the two variables are correlated. If you believe they are correlated, state whether the correlation is positive or negative. Explain your reasoning.
Latitude north of the equator and the average high temperature in December
To measure latitude, the unit
▼
degrees Fahrenheit
degrees of latitude
pounds
hours
might be used.
What correlation, if any, is there between the variables?
A. There is a positive correlation because the average high temperature in December tends to increase when latitude increases.
B. There is a positive correlation because the average high temperature in December tends to increase when latitude decreases.
C. There is a negative correlation because the average high temperature in December tends to increase when latitude increases.
D. There is a negative correlation because the average high temperature in December tends to increase when latitude decreases.
E. The variables are not correlated.
Question 5 – 5E 32
Consider the following statement about a correlation. State the correlation clearly (for example, there is a positive correlation between variable A and variable B). Then state whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. Explain your answer.
In a large resort city, the crime rate increased as the number of taxi cabs increased.
There is
▼
a negative
no
a positive
correlation between the crime rate and the number of taxi cabs.
Determine the possible explanation for the correlation. Choose the correct answer below.
A. This correlation is due to coincidence because no link exists between crime and cabs.
B. This correlation is due to a possible direct cause because criminals need cabs.
C. This correlation is due to a common underlying cause because it is possible that, with an increase in tourism, both the crime rate and the number of cabs increase.
D. This correlation is due to a common underlying cause because there is no link between crime and cabs.
E. This correlation is due to a coincidence because criminals need cabs.
F. There is no correlation because there is no link between crime and cabs.
Question 6 – 5E 33
Consider the following statement about a correlation. State the correlation clearly. Then state whether the correlation is most likely due to a coincidence, a common underlying cause, or a direct cause. Explain your answer.
Over the past three decades, the number of miles of freeways in Los Angeles has grown, and traffic congestion has worsened.
Select the correct answer below.
A. There is a positive correlation between the number of miles of freeways and the traffic congestion in Los Angeles.
B. There is no correlation between the number of miles of freeways and the traffic congestion in Los Angeles.
C. There is a negative correlation between the number of miles of freeways and the traffic congestion in Los Angeles.
Is the correlation most likely due to a coincidence, a common underlying cause, or a direct cause? Explain.
A. The correlation is most likely due to a coincidence because the number of miles of freeways and the traffic congestion is not related.
B. The correlation is most likely due to a direct cause because increasing the number of miles of freeways made the traffic congestion worse.
C. The correlation is most likely due to the common underlying cause of Los Angeles having a very large population.
D. There is no correlation between the number of miles of freeways and the traffic congestion in Los Angeles.
Question 7 – 5E 34
Consider the following statement about a correlation. State the correlation clearly (for example, there is a positive correlation between variable A and variable B). Then state whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. Explain your answer.
When gasoline prices rise, sales of sport utility vehicles decline.
There is
▼
a negative
a positive
no
correlation between gasoline prices and sport utility vehicle sales.
Determine the possible explanation for the correlation. Choose the correct answer below.
A. This correlation is due to coincidence because there is no link between gas prices and sales of sport utility vehicles.
B. This correlation is due to a possible direct cause because sport utility vehicles require more gasoline than a smaller type of vehicle.
C. This correlation is due to a common underlying cause because sport utility vehicles require more gasoline than a smaller type of vehicle.
D. This correlation is due to a possible direct cause because there is no link between gas prices and sales of sport utility vehicles.
E. This correlation is due to a common underlying cause because the price of gas increases the purchase price of only sports utility vehicles.
F. There is no correlation because there is no link between gas prices and sales of sport utility vehicles.
Question 8 – 5E 35
Consider the following statement about a correlation. State the correlation clearly. Then state whether the correlation is most likely due to a coincidence, a common underlying cause, or a direct cause. Explain your answer.
Sales of ice cream increase whenever the sales of swimming suits increase.
Select the correct answer below.
A. There is a negative correlation between the sales of ice cream and the sales of swimming suits.
B. There is a positive correlation between the sales of ice cream and the sales of swimming suits.
C. There is no correlation between the number of sales of ice cream and the sales of swimming suits.
Is the correlation most likely due to a coincidence, a common underlying cause, or a direct cause? Explain.
A. The correlation is most likely due to the common underlying cause that people eat more ice cream and people do more swimming in the summer time.
B. There is no correlation between the number of sales of ice cream and the sales of swimming suits.
C. The correlation is most likely due to a coincidence because ice cream sales and swimming suit sales share nothing in common.
D. The correlation is most likely due to a direct cause because increasing the sales ice cream increased the sales of swimming suits.
Question 9 – 5E 36
Automobile gas mileage decreases with tire pressure.
There is
▼
a positive
no
a negative
correlation between gas mileage and tire pressure.
Determine the possible explanation for the correlation. Choose the correct answer below.
A. This correlation is due to a direct cause because more gasoline is needed to roll a tire with lower pressure.
B. This correlation is due to a common underlying cause because as temperature decreases, both gas mileage and tire pressure decrease.
C. This correlation is due to coincidence because there is no link between gas mileage and tire pressure.
D. This correlation is due to a direct cause because there is no link between gas mileage and tire pressure.
E. This correlation is due to a common underlying cause because more gasoline is needed to roll a tire with lower pressure.
F. There is no correlation because there is no link between gas mileage and tire pressure.
Question 10 – 5E 37
Over a period of twenty years, the number of ministers and priests in a city increased, as did attendance at movies.
Select the correct answer below.
A. There is a negative correlation between the number of ministers and priests and the attendance at movies.
B. There is a positive correlation between the number of ministers and priests and the attendance at movies.
C. There is no correlation between the number of ministers and priests and the attendance at movies.
Is the correlation most likely due to a coincidence, a common underlying cause, or a direct cause? Explain.
A. There is no correlation between the number of ministers and priests and the attendance at movies.
B. The correlation is most likely due to the common underlying cause that the city’s entire population grew over twenty years.
C. The correlation is most likely due to a coincidence because the number of ministers and priests and the attendance at movies are not related.
D. The correlation is most likely due to a direct cause because increasing the number of ministers and priests increased the attendance at movies.
Question 11 – 5E 39
There is a strong correlation between tobacco smoking and incidence of lung cancer, and most physicians believe that tobacco smoking causes lung cancer. However, not everyone who smokes gets lung cancer. Briefly describe how smoking could cause cancer when not all smokers get cancer.
Select the correct answer below.
A. Smoking can cause cancer even though not all smokers get cancer because most smokers stop smoking before they get cancer.
B. Not all smokers get cancer because smoking only makes cancer worse and many smokers did not have cancer before they started smoking.
C. Not all smokers get cancer because cancer is caused by cell mutation, and while smoking increases the chances of such a mutation occurring, the mutation does not occur in every smoker.
D. Not all smokers get cancer because many people smoke tobacco products that do not cause cancer.
Question 12 – 5E 41
Suppose that people living near a particular high-voltage power line have a higher incidence of cancer than people living farther from the power line. Can you conclude that the high-voltage power line is the cause of the elevated cancer rate? If not, what other explanations might there be for it? What other types of research would you like to see before you conclude that high-voltage power lines cause cancer?
Select the correct answer below.
A. You can conclude that the power line is the cause of the elevated cancer rate because a correlation is enough to establish cause.
B. You cannot conclude that the power line is the cause of the elevated cancer rate because cause cannot be established until a mechanism is confirmed.
C. You cannot conclude that the power line is the cause of the elevated cancer rate because it is not known if the correlation is strong or weak.
D. You can conclude that the power line is the cause of the elevated cancer rate because elevated cancer rates are correlated with the cause even though other factors vary.
What other types of research would you like to see before you conclude that high-voltage power lines cause cancer?
A. No further research is needed.
B. A study that determines the genetic background of the people living close to the power line.
C. A study that determines the overall health of the city where the power line is located.
D. A study that determines the effect of electricity on a cell’s growth mechanism.
Create scatterplots.
Question 1 – 5E 25
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