Deck 14: Statistical Reasoning

Question 1

What sort of statistic does the following most clearly exemplify? There are 88 counties in the state of Ohio.

A)average
B)median
C)relative frequency
D)total
E)ratio

Answer 1

D

Question 2

What sort of statistic does the following most clearly exemplify? There are currently 128 species of maple trees.

A)total
B)ratio
C)distribution
D)average
E)median

Answer 2

A

Question 3

What sort of statistic does the following most clearly exemplify? Seventy-six percent of the fish in this stream are infected with parasites.

A)absolute frequency
B)relative frequency
C)distribution
D)average
E)median

Answer 3

B

Question 4

What sort of statistic does the following most clearly exemplify? I wasn't always driving at the same speed on my trip, but when I divided the total distance that I drove by the time it took, I got 38 miles per hour.

A)average
B)distribution
C)absolute frequency
D)total
E)median

Question 5

What sort of statistic does the following most clearly exemplify? At the weddings performed in this chapel in the last five years, 18% of the bridesmaids wore blue, 21% red, 7% yellow, 9% purple, 19% green, 23% pink, and 3% other colors.

A)distribution
B)average
C)median
D)relative frequency
E)absolute frequency

Question 6

All statistics deal with _____ and _____.

A)science; nature
B)science; culture
C)politics; religion
D)classes of things; their properties
E)classes of things; their lengths

Question 7

What sort of statistic does the following most clearly exemplify? In 2011, half of American households had an income greater than $50,502, while the other half had a lower income.

A)absolute frequency
B)relative frequency
C)distribution
D)average
E)median

Question 8

What sort of statistic does the following most clearly exemplify? Thirteen of the dog breeds recognized by the American Kennel Club are available at our pet store.

A)average
B)median
C)ratio
D)relative frequency
E)absolute frequency

Question 9

Which of the following statistics is a total?

A)Seventy-three percent of the graduates of our high school go on to college.
B)There are 218 homeless people in our town.
C)There are 13 rocks for every crayfish in this stream.
D)It costs 52 cents per minute to keep our business open.
E)Half of my students are getting at least an 80%, while the other half are not doing that well.

Question 10

In logic, statistics:

A)are considered to be the only real evidence of anything
B)can sometimes be valuable as evidence
C)are never considered to be real evidence of anything
D)should never be used since that would always commit the statistician's fallacy
E)are never used outside of political arguments

Question 11

Some statistics simply tell us how many of something there are.These statistics are called:

A)ratios
B)products
C)basic statistics
D)quotients
E)totals

Question 12

What sort of statistic does the following most clearly exemplify? There is one polling booth for every seven voters expected to vote today.

A)average
B)total
C)absolute frequency
D)median
E)ratio

Question 13

Which of the following could be a variable?

A)Andy Kaufman
B)Kuala Lumpur, Malaysia
C)Taj Mahal
D)chemical element
E)Mount Everest

Question 14

What sort of statistic does the following most clearly exemplify? If you add up the total rainfall in the Amazon rain forest over the last 10 years and then divide by 10, you find that in a typical year, the rain forest gets about 108 inches of rain.

A)total
B)ratio
C)distribution
D)average
E)median

Question 15

What sort of statistic does the following most clearly exemplify? Seventy-eight percent of the books in this library were written before 1938.

A)total
B)median
C)relative frequency
D)distribution
E)average

Question 16

What sort of statistic does the following most clearly exemplify? Of the people in this stadium, 39% have black hair, 29% have brown hair, 19% have blond hair, 6% have red hair, 4% have white hair, and 3% are bald.

A)total
B)ratio
C)distribution
D)average
E)median

Question 17

What sort of statistic does the following most clearly exemplify? I timed myself running to the bus stop and then back to my house and it took 3.28 minutes.Then I did it again 14 more times.About half of my runs were faster than that, and the other half were slower.

A)total
B)absolute frequency
C)median
D)ratio
E)average

Question 18

In statistical reasoning, a generic quality is a called a(n) _____ and its specific qualities are called _____.

A)property; specifiers
B)quality; quantities
C)variable; values
D)abstractum; particuli
E)genus; identifiers

Question 19

Can a concept be a value?

A)Yes, because concepts cannot be variables.
B)Yes, because the variable of which the concept is a value could be the concept's genus.
C)No, because only referents can be values.
D)No, because concepts can only be variables.
E)No, because then there would be no other values for the variable, so it wouldn't be a true variable.

Question 20

What sort of statistic does the following most clearly exemplify? "Four out of five dentists surveyed recommend sugarless gums for their patients who chew gum."-From a commercial for Trident gum.

A)total
B)ratio
C)distribution
D)average
E)median

Question 21

Is it possible to provide a reliable ratio between two classes if we don't know how many members are in each?

A)Yes, because if we don't know how many members each class has, we can assume that they are approximately the same size.
B)Yes, because we could extrapolate a ratio from the ratio we find in a large sample.
C)No, because we have to know how many members there are in at least one of the classes.
D)No, because we have no basis for calculating a ratio unless we know how many members are in both classes.
E)No, because in that case, we couldn't provide any statistics about the two classes at all.

Question 22

Do distributions tell us the actual number of members in each class, or do they simply tell us the percentage of members in each class?

A)They can either tell us the actual number or the percentage.
B)They can only tell us the percentage, since they involve multiple categories.
C)They can only tell us the percentage, since they are only used when actual counts aren't available.
D)They must always tell us the actual number, since we could never know the percentage in each class without knowing the actual number first.
E)They must always tell us the actual number, since if they only told us the percentage, they would be frequencies rather than distributions.

Question 23

If we have a distribution that tells us what percentage of the members of S belong to each of the mutually exclusive classes N, O, P, Q, and R, is that enough information to calculate the ratio of N and R?

A)No, because we don't know the actual number of members in N and R.
B)No, because we could not isolate N and R from their relations to O, P, and Q.
C)No, because we know how S relates to N and how S relates to R, but not how N and R relate to each other.
D)Yes, because how they relate to S tells us enough about how they relate to each other.
E)Yes, because since they both relate to S, they will necessarily have a 1 to 1 ratio.

Question 24

Some statistics tell us, absolutely or relatively, how many members of one class (S) belong to another class (P).These statistics are called:

A)frequencies
B)margins
C)quantifiers
D)categorical statistics
E)class relations

Question 25

Which of the following statistics is a relative frequency?

A)Three of the kids from my class also live in my neighborhood.
B)One out of every four babies born on Earth is Chinese.
C)Hilda's book collection is worth $13,800 and she has 400 books, so that's $34.50 per book.
D)There are four Cokes, two Pepsis, one Mountain Dew, and one Dr.Pepper in the refrigerator.
E)This factory has produced over 200,000 baseball caps.

Question 26

Which of the following statistics is a ratio?

A)Half of all patients diagnosed with this cancer will live at least two years, while the other half will die earlier.
B)There are 1.3 cars per household in our state.
C)My local deli sells 28 different sliced meats.
D)The average life expectancy in Japan is 82.5 years.
E)The majority of popes have been Italian, but 63 were not.

Question 27

In order for a frequency distribution to be meaningful, the classes into which things are being sorted must:

A)be limited to three
B)be limited to five
C)overlap with each other
D)be chosen at random
E)be well defined

Question 28

Which of the following statistics is a distribution?

A)One thousand three hundred eighty-six people were killed by Hurricane Katrina.
B)There were 18% more serious injuries at the park this year than last year.
C)The average cost of a home where Sam lives is $129,000.
D)Of all the cast members who have ever been a part of Saturday Night Live, eight died prematurely.
E)In her will, Aunt Sarah left 50% of her estate to her children, 30% to her grandchildren, and 20% to charities.

Question 29

A pie chart or bar graph typically represents a(n):

A)ratio
B)total
C)average
D)distribution
E)mean

Question 30

Some statistics are derived by adding up the quantitative values of all the members of a class, and then dividing the total by the number of quantitative values in the class.These statistics are called:

A)averages
B)frequencies
C)totals
D)ratios
E)medians

Question 31

Which of the following statistics is a ratio?

A)The firefighters saved 23 people from the apartment fire.
B)Seventy-five percent of my class is Christian, 5% Jewish, and 20% prefer not to answer.
C)The most common score on the test was a 92%.
D)Half of the plumbers in our city earn more than $52,000 per year, while the other half earn less.
E)For every three weeks that I work, I earn one day of paid vacation.

Question 32

Which of the following statistics is an absolute frequency?

A)Half of the apples that fell from the tree have rotted already.
B)My uncle gives a tenth of his income to charity.
C)For every month starting with a vowel, there are three starting with a consonant.
D)Six members of the local Rotary Club are police officers.
E)At this time of year, half of the honeybees in the hive are at least four weeks old and the other half are younger.

Question 33

Which of the following statistics is a distribution?

A)Half of all homes possess more than 1.7 bicycles, while the other half possess fewer.
B)Sixty percent of American homes have pets, such as dogs, cats, ferrets, hamsters, and fish.
C)Of the leaves on the ground, 84% are brown, 6% are yellow, 4% are red, and 6% are orange.
D)No U.S.state lies on the equator.
E)For every $100 that the charity receives, only $6 is spent on administrative costs.

Question 34

Some statistics tell us how many members of one class (S) belong to each of a number of other classes (such as P, Q, and R).These statistics are called:

A)spreadsheets
B)distributions
C)scatter totals
D)pigeonhole tallies
E)arrays

Question 35

Which of the following statistics is an absolute frequency?

A)Of all the people living in southern states, only 28 are U.S.senators.
B)Twenty-eight percent of the recipes in this book require eggs.
C)There are two pods of dolphins living just off of the coast.
D)Twenty-two percent of the criminals who leave this prison will be rearrested within a year.
E)The average Canadian goose weighs 12.5 pounds.

Question 36

Some statistics specify the number of items in a class, or the sum of their values on a variable, per unit of some other class.These statistics are called:

A)ratios
B)products
C)basic statistics
D)quotients
E)totals

Question 37

If we know the relative frequency with which members of class A also belong to class B, we can calculate the absolute frequency if we also know:

A)the relative frequency with which members of class A belong to a third group, class C
B)the absolute frequency with which members of class A belong to a third group, class C
C)whether class A or class B is larger
D)the sum of the members in class A and the members in class B
E)the number of members in class A

Question 38

An absolute frequency is a special sort of _____, and a relative frequency is a special sort of _____.

A)median; average
B)average; median
C)total; ratio
D)ratio; total
E)total; average

Question 39

Which of the following statistics is a relative frequency?

A)Sixty percent of the pedestrians who pass my lemonade stand refuse to make eye contact with me.
B)There have been 44 American presidents.
C)For every proton in the nucleus of an atom, the atom has one electron.
D)One hundred ninety-three people attended my brother's funeral.
E)42% of those surveyed favored the legislation, 29% opposed it, and another 29% were undecided.

Question 40

Which of the following statistics is a total?

A)One in 50 children is born with autism.
B)The average life span of a cat is around 12 years.
C)Seven modern countries were parts of the former Yugoslavia.
D)20% of known mammal species are bats.
E)15% of our revenue is put back into paying for our overhead costs.

Question 41

A factor that is neither necessary nor sufficient to bring about an effect but does play a role in bringing it about is called a(n) _____ factor.

A)irrelevant
B)contributing
C)fool's
D)circumstantial
E)coincidental

Question 42

Some statistics identify the central value on a quantitative variable, such that half of the quantitative values would be higher than this value and half would be lower.These statistics are called:

A)averages
B)frequencies
C)totals
D)ratios
E)medians

Question 43

If a population is quite small, does that justify making a statistical generalization from a very small sample ?

A)No.If the population size is quite small, we should attempt a complete survey of it.
B)No.If the entire population is quite small, nothing significant can be said about it.
C)Yes, because we would still be sampling a large percentage of the whole population (4 out of 25 is 16%!).
D)Yes, because if the population is very small, its members are likely to be very similar, so even a very small sample will be representative of the whole population.
E)Yes, because generalizations about smaller populations require less evidence.

Question 44

A statistic that is generalized from a sample can be made more accurate by:

A)excluding the more unusual members of the sample
B)including more unusual members in the sample
C)increasing the size of the sample
D)decreasing the size of the sample
E)averaging the measured value with the expected value

Question 45

Suppose that the following is a list of student test scores: 97, 89, 85, 82, and 80.What is the median value?

A)97
B)80
C)85
D)86.6
E)84

Question 46

Are statistical values based on a complete survey of the entire population or on a sample of it?

A)They are always based on a complete survey because otherwise they would be meaningless.
B)They are always based on a sample since a complete survey is never possible.
C)They are always based on a sample since a complete survey is always a waste of time and energy.
D)Sometimes they are based on a complete survey and sometimes on a sample.
E)There is a general rule that when the population has 95 members or fewer, there must be a complete survey, but for more than 95, a sample must be used.

Question 47

Which of the following statistics is an average?

A)Half of my friends live within 20 miles and half live further away than that.
B)There are 25 houses on our block and 78 trees, so that's 3.12 trees per yard.
C)Sixty percent of Americans are political centrists.
D)Eighteen percent of students are getting a C in this class.
E)Of my wisest friends, only two support my decision to spend a year in Europe.

Question 48

Which of the following statistics is a median?

A)Seventy percent of the Earth's surface is covered by ocean.
B)Half of the people on Earth are younger than 26.4 years, and half are older.
C)Earth orbits the Sun about once every 365.25 days.
D)Eighty-eight percent of the Earth's population lives north of the equator, the rest to the south.
E)The Earth has only one moon.

Question 49

Suppose that the following is a list of student test scores: 97, 89, 85, 82, and 80.What is the average value?

A)97
B)80
C)85
D)86.6
E)84

Question 50

Can the median value be the same as the average value?

A)Yes, because median and average are two names for the same thing.
B)Yes, because sometimes they will just happen to be the same value.
C)No, because the median value is always higher than the average value.
D)No, because they are determined by two completely different methods.
E)No, because the two terms don't mean the same thing.

Question 51

A statistic that is generalized from a sample will:

A)be completely useless
B)be completely accurate
C)always be misleading
D)have a margin of error
E)be more reliable than one based on a complete enumeration

Question 52

How does one find the median value in a class that has an even number of members?

A)There is no median value since only classes with an odd number of members have median values.
B)Average the two most central values.
C)Choose the lower of the two most central values.
D)Choose the higher of the two most central values.
E)Use the average of the entire class as the median value.

Question 53

Which of the following statistics is an average?

A)Most American men are between 5 feet 4 inches and 6 feet 3 inches tall.
B)Half of American men are shorter than 5 feet 9 inches, and half are taller.
C)The collective height of American women, divided by the total number of American women, comes out to 5 feet 4 inches per woman.
D)The most common height for an American woman is 5 feet 4 inches.
E)Aunt Cindy is two inches taller than Uncle Dan.

Question 54

When a statistic is based on a sample, the sample should be:

A)made up of the most unusual members of the population
B)at least 95% of the total population
C)chosen on the basis of what the statistical value is expected to be
D)as small as possible
E)random

Question 55

Which of the following is a contributing factor for becoming a governor?

A)winning an election
B)getting your name on the ballot
C)being the lieutenant governor at the time that the previous governor died
D)being old enough to hold the office
E)giving an outstanding campaign speech

Question 56

If a statistical generalization has a small margin of error, that means:

A)it is completely unreliable
B)it is close to the true value, but off from it by a little bit
C)either it is the true value or it is very close to it
D)it is extremely likely that it is identical to the true value
E)the true value can never be known

Question 57

Is it possible for a median to be twice the average?

A)No, because the median and average are always the same number.
B)No, because the median is always approximately the same number as the average.
C)No, because the median is always smaller than or equal to the average.
D)Yes, because the average is always calculated by dividing the median by two.
E)Yes, because the average could be pulled down by a small number of very low values.

Question 58

Which of the following statistics is a median?

A)The temperature at noon today was 78.3 degrees.
B)The atomic number of lead is 82.
C)11 of the 12 apostles were martyred.
D)Half of the jog-a-thon participants had dropped out by 13 hours and 28 minutes into the event.But the rest continued on.
E)The 14 guests at the party used 200 ice cubes, which comes out to 14.29 ice cubes per person.

Question 59

Statistical generalization means:

A)generalizing about an entire population based on what is known about a statistical property of a sample
B)using an approximate statistical value instead of a precise one
C)making up a statistic without any basis in fact
D)saying that every member of a population has a certain property just because a statistic shows that most do
E)manipulating a survey to obtain the results that you desire instead of objective results

Question 60

A statistic gives us numerical information about some class of things.In statistics, that class is a called a:

A)statistical base
B)numerator
C)population
D)contrivance
E)compilation

Question 61

Many surveys are conducted over the phone.Which of the following would be most likely to cast doubt on the external validity of these studies?

A)The person conducting the survey was not good at operating a telephone.
B)Some of the calls were dropped and the person had to be called back.
C)The phone surveys were conducted by 12 surveyors instead of one.
D)All of the people participating in the survey own telephones.
E)The phone calls were not all placed at the same time of day.

Question 62

How is an observational study different from an experiment?

A)An observational study is always done in a lab, whereas an experiment is always done outside of a laboratory.
B)An experiment is always done in a lab, whereas an observational study is always done outside of a laboratory.
C)It isn't.They are two names for the same thing.
D)In an observational study, variables are not controlled but rather observed as they naturally occur.
E)In an experiment, variables are not controlled but rather observed as they naturally occur.

Question 63

Suppose we find that there is a correlation between illegal drug use and suicide.By itself, this would not prove that illegal drug use causes suicide, because there could be a confounding variable.What is the most likely candidate?

A)smoking
B)depression
C)heart disease
D)levels of policing
E)illegal drug prices

Question 64

Suppose we want to know how the population of an anthill varies over time.It is difficult to make a direct observation of how many ants are in an anthill, so which of the following would be the best proxy variable?

A)the number of ants seen each day in a nearby house
B)the size of the ants
C)the speed at which a nearby piece of fruit disappears
D)the age of the anthill
E)the rate at which ants exit the anthill

Question 65

Suppose we want to study how a drug affects someone's happiness.It is difficult to make a direct observation of how happy someone is, so which of the following would be the best proxy variable?

A)time spent exercising
B)frequency of smiling
C)use of pain medication
D)alcohol consumption
E)frequency of social interaction

Question 66

Many psychological studies are conducted on college campuses.Which of the following would be most likely to cast doubt on the external validity of these studies?

A)Many of the researchers are college students.
B)Faculty and students disagree about the political implications of their findings.
C)All of the subjects in the study are college students.
D)The results of the studies are not published.
E)The studies do not have the professors' full attention since they are also teaching classes.

Question 67

Is it generally more difficult to draw causal conclusions from an experiment or from an observational study?

A)equally difficult for both
B)from an experiment
C)from an observational study
D)from an experiment if we are studying humans, but from an observational study if we are studying the natural world
E)from an experiment if we are studying the natural world, but from an observational study if we are studying humans

Question 68

Sometimes it is difficult to establish a causal relationship between two correlating variables due to the presence of a third variable that correlates with both of them.This third variable is called a _____ variable.

A)pure
B)confounding
C)surplus
D)superfluous
E)thwarting

Question 69

Which of the following could be a contributing factor for failing a class?

A)not taking notes in class
B)being enrolled in the class
C)not turning in any of the assignments or taking any of the tests
D)renting the textbook rather than buying it
E)triggering the attendance policy's automatic fail by missing 10 class sessions

Question 70

Suppose that a study finds a causal relationship between two variables.The study has external validity if its findings:

A)are derived entirely from valid deductive arguments
B)are derived entirely from valid inductive arguments
C)apply only to the individuals that were studied
D)apply to the general population and not merely to the individuals that were studied
E)are generally accepted by the mathematical and scientific communities

Question 71

Assuming that two things are causally related simply because they correlate is most similar to committing which logical fallacy?

A)post hoc
B)division
C)subjectivism
D)false alternative
E)existential fallacy

Question 72

Compared with experiments, one drawback of observational studies is that they lack:

A)a detailed statistical analysis
B)scientific objectivity
C)real scientific value
D)a clear methodology
E)a randomly assigned control group

Question 73

In order to establish a statistical correlation between a and E, we compare two groups that are basically the same, except that a is present in one and not present in the other.If it turns out that E is more common when a is present, is this enough to show that they correlate?

A)Yes, any slight difference in the presence of E proves a correlation.
B)It depends on how big the difference is between the presence of E in the two groups.
C)No, because it only proves a causal relationship, not a correlation.
D)No, because a correlation could only be shown if a were present in both groups.
E)No, because a correlation could only be shown if E were equally present in both groups.

Question 74

In order to establish a statistical correlation between a and E, we need to compare two groups that are basically the same, except that a is present in one and not present in the other.Given that the individual members of these groups might vary quite a lot, how can we make it likely that, apart from the presence of a, the two groups are basically the same?

A)Use large, randomly chosen groups.
B)Use very small, randomly chosen groups.
C)The only way is to put exactly the same individual members into both groups.
D)The only way is to match each individual in the first group with an individual that has all of the same characteristics in the second group.
E)The two groups can never be similar enough to provide any meaningful information about whether or not there is a correlation.

Question 75

Suppose we find that there is a correlation between people wearing T-shirts and people having flies in their homes.By itself, this would not prove that wearing T-shirts attracts insects, because there could be a confounding variable.What is the most likely candidate?

A)unemptied trash
B)fashion trends
C)changing seasons
D)hygiene habits
E)spider population

Question 76

In order to establish a statistical correlation between a and E, we compare the presence of E in two groups, one in which a is present (called the _____ group) and one in which a is not present (called the _____ group).

A)experimental; power
B)power; control
C)control; power
D)control; experimental
E)experimental; control

Question 77

Is a correlation between A and B enough to show that A causes B?

A)Yes.
B)No, but it does show that A must be a contributing factor.
C)No, because it shows that B causes A.
D)No, but it definitely shows that A and B are causally related.
E)No, because, for example, the correlation might be coincidental.

Question 78

Are the motions of the planets studied by means of observational studies or experiments?

A)Neither experiments nor observational studies can be used to study planetary motion.
B)motions of Earth by experiments, other planets by observational studies
C)motions of Earth by observational studies, other planets by experiments
D)experiments only
E)observational studies only

Question 79

Sometimes a variable cannot be studied directly, but can be studied indirectly by means of some other variable.This other variable is a called a _____ variable.

A)proxy
B)differential
C)mediating
D)final
E)hidden

Question 80

Suppose we find that there is a correlation between the cleanliness of a student's room and how much time that student spends studying.By itself, this would not prove that having a clean room causes students to study longer, because there could be a confounding variable.What is the most likely candidate?

A)difficulty of classes
B)number of roommates
C)noise level in the room
D)self-discipline of the student
E)availability of cleaning products