Deck 3: Finding Relationships Among Variables

Question 1

If the sample is a good representation of the population, what percentage of the students in the population should we expect to spend the weekend studying and do poorly on the final exam?

Answer 1

15 out of 150, or 10%

Question 2

We must specify appropriate bins for side-by-side histograms in order to make fair comparisons of distributions by category.

Answer 2

True

Question 3

What percentage of the students in the sample spent the weekend studying and did well in the final exam?

Answer 3

60 out of 150, or 40%

Question 4

Side-by-side box plots allow you to quickly see how two or more categories of a numerical variable compare.

Question 5

Comparing a numerical variable across two or more subpopulations is known as a comparison problem.

Question 6

Which Excel^® function allows you to count using more than one criterion?

A) COUNTIF
B) COUNTIFS
C) SUMPRODUCT
D) VLOOKUP
E) HLOOKUP

Question 7

Of those in the sample who went partying the weekend before the final exam, what percentage of them did poorly in the exam?

Question 8

A sample of 150 students at a state university was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result.
Of those in the sample who did well on the final exam, what percentage of them went partying the weekend before the exam?

Question 9

What percentage of the students in the sample went partying the weekend before the final exam and did well in the exam?

Question 10

A sample of 150 students at a state university was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result.
Of those in the sample who went partying the weekend before the final exam, what percentage of them did well in the exam?

Question 11

If the sample is a good representation of the population, what percentage of those who spent the weekend studying should we expect to do poorly on the final exam?

Question 12

Examples of comparison problems include:

A) salary broken down by male and female subpopulations
B) cost of living broken down by region of a country
C) recovery rate for a disease broken down by patients who have taken a drug and patients who have taken a placebo
D) starting salary of recent graduates broken down by academic major
E) all of these choices

Question 13

The most common data format is:

A) long
B) short
C) stacked
D) unstacked

Question 14

A useful way of comparing the distribution of a numerical variable across categories of some categorical variable is with:

A) a side-by-side box plot
B) a side-by-side pivot table
C) a side-by-side plot or side-by-side pivot table
D) neither a side-by-side box plot nor side-by-side pivot table

Question 15

If the sample is a good representation of the population, what percentage of those who did poorly on the final exam should we expect to have spent the weekend studying?

Question 16

Tables used to display counts of a categorical variable are called:

A) crosstabs
B) contingency tables
C) either crosstabs or contingency tables
D) neither crosstabs nor contingency tables

Question 17

What percentage of the students in the sample went partying the weekend before the final exam and did poorly on the exam?

Question 18

An example of a joint category of two variables is the count of all non-drinkers who are also nonsmokers.

Question 19

To examine relationships between two categorical variables, we can use:

A) counts and corresponding charts of the counts
B) scatter plots
C) histograms
D) none of these choices

Question 20

Of those in the sample who did well in the final exam, what percentage of them spent the weekend before the exam studying?

Question 21

We cannot attempt to interpret correlations numerically, with the one possible exception of indicating whether they are positive or negative.

Question 22

Strongly related variables may have a correlation close to zero if the relationship is nonlinear.

Question 23

Correlation can be affected by the measurement scales applied to X and Y variables.

Question 24

The correlation between two variables is unitless and always between -1 and +1.

Question 25

Which of the following are considered numerical summary measures?

A) mean and variance
B) variance and correlation
C) correlation and covariance
D) covariance and variance
E) first quartile and third quartile

Question 26

Displaying all correlations between 0.6 and 0.999 on a scatterplot as green and all correlations between -1.0 and -0.6 as red is known as:

A) rank-order formatting
B) categorical formatting
C) conditional formatting
D) numerical formatting

Question 27

The limitation of covariance as a descriptive measure of association is that it

A) only captures positive relationships
B) does not capture the units of the variables
C) is very sensitive to the units of the variables
D) is invalid if one of the variables is categorical
E) none of these options

Question 28

If the standard deviations of X and Y are 15.5 and 10.8, respectively, and the covariance of X and Y is 128.8, then the correlation coefficient is approximately 0.77.

Question 29

Correlation is a single-number summary of a scatterplot.

Question 30

A line or curve superimposed on a scatterplot to quantify an apparent relationship is known as a(n):

A) average
B) trend line
C) data point
D) positive variable
E) slope

Question 31

Scatterplots are also referred to as:

A) crosstabs
B) contingency charts
C) X-Y charts
D) all of these choices
E) none of these choices

Question 32

We can infer that there is a strong relationship between two numerical variables when:

A) the points on a scatterplot cluster tightly around an upward sloping straight line
B) the points on a scatterplot cluster tightly around a downward sloping straight line
C) both of these choices
D) neither of these choices

Question 33

We study relationships among numerical variables using:

A) correlation
B) covariance
C) scatterplot charts
D) all of these choices
E) none of these choices

Question 34

Which correlation coefficient suggests the strongest relationship?

A) +1
B) -0.1
C) 0
D) +0.5

Question 35

If the correlation of variables is close to 0, then we expect to see:

A) an upward sloping cluster of points on the scatterplot
B) a downward sloping cluster of points on the scatterplot
C) a cluster of points around a trendline on the scatterplot
D) a cluster of points with no apparent relationship on the scatterplot
E) no explanation of how the scatterplot looks based on the correlation

Question 36

Correlation is useful only for:

A) assessing the weakness of a linear relationship
B) conveying the same information in a simpler format than a scatterplot
C) measuring the strength of a linear relationship
D) automatically calculating covariances
E) measuring the strength of a nonlinear relationship

Question 37

Correlation and covariance measure:

A) the strength of a linear relationship between two numerical variables
B) the direction of a linear relationship between two numerical variables
C) the strength and direction of a linear relationship between two numerical variables
D) the strength and direction of a linear relationship between two categorical variables
E) none of these choices

Question 38

One characteristic of "paired variables" is that:

A) one variable is a negative value and the other is a positive value
B) both variables are positive values
C) each variable has the same number of observations
D) each variable has a different number of observations

Question 39

The cutoff for defining a large correlation is 0.5.

Question 40

To form a scatterplot of X versus Y, X and Y must be paired variables.

Question 41

An economic development researcher wants to understand the relationship between the average monthly expenditure on utilities for households in a particular middle-class neighborhood and each of the following household variables: family size, approximate location of the household within the neighborhood, and indication of whether those surveyed owned or rented their home, gross annual income of the first household wage earner, gross annual income of the second household wage earner (if applicable), size of the monthly home mortgage or rent payment, and the total indebtedness (excluding the value of a home mortgage) of the household.
The correlation for each pairing of variables are shown in the table below:
Table of correlations
Which of the variables have a positive linear relationship with the household's average monthly expenditure on utilities?

Question 42

What other data would you need to be more confident that increased income inequality leads to lower unemployment?

Question 43

An economic development researcher wants to understand the relationship between the average monthly expenditure on utilities for households in a particular middle-class neighborhood and each of the following household variables: family size, approximate location of the household within the neighborhood, and indication of whether those surveyed owned or rented their home, gross annual income of the first household wage earner, gross annual income of the second household wage earner (if applicable), size of the monthly home mortgage or rent payment, and the total indebtedness (excluding the value of a home mortgage) of the household.
The correlation for each pairing of variables are shown in the table below:
Table of correlations
Which of the variables have essentially no linear relationship with the household's average monthly expenditure on utilities?

Question 44

Below you will find current annual salary data and related information for 30 employees at Gamma Technologies, Inc. These data include each selected employees gender (1 for female; 0 for male), age, number of years of relevant work experience prior to employment at Gamma, number of years of employment at Gamma, the number of years of post-secondary education, and annual salary. The tables of correlations and covariances are presented below.
Table of Correlations Table of Covariances (variances on the diagonal)
Which two variables have the strongest linear relationship with annual salary?

Question 45

For which of the two variables, number of years of prior work experience or number of years of post-secondary education, is the relationship with salary stronger? Justify your answer.

Question 46

Suppose that the table shown below contains information technology (IT) investment as a percentage of total investment for eight countries during a recent decade. It also contains the average annual percentage change in employment during this decade. Explain how these data shed light on the question of whether IT investment creates or costs jobs. (Hint: Use the data to construct a scatterplot.)

Question 47

Economists believe that historically, countries with more income inequality have had lower unemployment rates. For example, an economist in 1996 developed the table below containing the following information for 10 countries during the 1980-1995 time period:
· The change from 1980 to 1995 in ratio of the average wage of the top 10% of all wage earners to the median wage
· The change from 1980 to 1995 in unemployment rate.
Income inequality vs. Unemployment rate
Explain why the ratio of the average wage of the top 10% of all wage earners to the median measures income inequality.

Question 48

What does a scatterplot illustrate?

A) whether there is any relationship between two variables
B) what type of relationship there is between two variables
C) both of these choices
D) neither of these choices

Question 49

Data has been collected on store size in square feet and profit per square foot, yielding the following observations: How is the value of the correlation affected in each of the following cases?
a) Each X value is multiplied by 4.
b) Each X value is switched with the corresponding Y value.
c) Each X value is increased by 2.

Question 50

It is possible that the data points close to a curve have a correlation close to 0, because correlation is relevant only for measuring linear relationships.

Question 51

If the coefficient of correlation r = 0 .80, the standard deviations of X and Y are 20 and 25, respectively, then Cov(X, Y) must be 400.

Question 52

Do these data help to confirm or contradict the hypothesis that increased wage inequality is associated with lower unemployment levels? [Hint: construct a scatterplot.]

Question 53

The following scatterplot compares the selling price and the appraised value. Is there a linear relationship between these two variables? If so, how would you characterize the relationship?

Question 54

There are two scatterplots shown below. The first chart shows the relationship between the size of the home and the selling price. The second chart examines the relationship between the number of bedrooms in the home and its selling price. Which of these two variables (the size of the home or the number of bedrooms) seems to have the stronger relationship with the home's selling price? Justify your answer.

Question 55

If the standard deviation of X is 15, the covariance of X and Y is 94.5, and the correlation is 0.90, then the variance of Y is 7.0.

Question 56

Suppose that the percentage of a country's population without health insurance coverage based on samples from all its regions for both 2016 and 2017 produced the following table of correlations.
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What does the table for the two given sets of percentages tell you in this case?

Question 57

How would you characterize the relationship between gender and annual salary?

Question 58

The scatterplot is a graphical technique used to indicate the relationship between two numerical variables.

Question 59

The advantage that correlation has over covariance is that the former has a set lower and upper limit.

Question 60

An economic development researcher wants to understand the relationship between the average monthly expenditure on utilities for households in a particular middle-class neighborhood and each of the following household variables: family size, approximate location of the household within the neighborhood, and indication of whether those surveyed owned or rented their home, gross annual income of the first household wage earner, gross annual income of the second household wage earner (if applicable), size of the monthly home mortgage or rent payment, and the total indebtedness (excluding the value of a home mortgage) of the household.
The correlation for each pairing of variables are shown in the table below:
Table of correlations
Which of the variables have a negative linear relationship with the household's average monthly expenditure on utilities?

Question 61

A recent survey collected data from 1000 randomly selected Internet users. The characteristics of the users include their gender, age, education, marital status, and annual income. Using Excel^®, the following pivot tables are produced.
​
Approximate the percentage of these Internet users who are men under the age of 30.

Question 62

A sample of 30 schools produced the pivot table shown below for the average percentage of students graduating from high school. Use this table to determine how the type of school (public or Catholic) that students attend affects their chance of graduating from high school.

Question 63

A recent survey collected data from 1000 randomly selected Internet users. The characteristics of the users include their gender, age, education, marital status, and annual income. Using Excel^®, the following pivot tables are produced.
​
Approximate the percentage of these Internet users who are currently employed.

Question 64

Suppose that a health magazine reports that a man's weight at birth has a significant impact on the chance that the man will suffer a heart attack during his life. A statistician analyzes a data set from a sample of 798 men, and produces the pivot table and histogram shown below. Determine how birth weight influences the chances that a man will have a heart attack.

Question 65

Relationships between two variables are less evident when counts are expressed as percentages of row totals or column totals.

Question 66

A data set from a sample of 399 Michigan families was collected. The data include family size (large or small), number of cars owned by family (1, 2, 3, or 4), and whether family owns a foreign car. Excel^® produced the pivot table shown below. Use this pivot table to determine how family size and number of cars owned influence the likelihood that a family owns a foreign car.

Question 67

A recent survey collected data from 1000 randomly selected Internet users. The characteristics of the users include their gender, age, education, marital status, and annual income. Using Excel^®, the following pivot tables are produced.
​
Approximate the percentage of these Internet users who are single with no formal education beyond high school.

Question 68

The students at a small community college in Iowa apply to study either English or Business. Some administrators at the college are concerned that women are being discriminated against in being allowed admittance, particularly in the business program. Below, you will find two pivot tables that show the percentage of students admitted by gender to the English program and the Business school. The data has also been presented graphically. What do the data and graphs indicate? Business school

Question 69

Changing the location of fields in a pivot table is known as:

A) slicing
B) dicing
C) sorting
D) pivoting

Question 70

The four areas of a pivot table are:

A) Crosstabs, Fields, Rows, and Columns
B) Data, Count, Contingency, and Percentage
C) Filters, Rows, Columns, and Values
D) Sort, Rows, Columns, and Count

Question 71

The Filters field of a pivot table contains the data that you want summarized.

Question 72

What is the average annual salary of the employed Internet users in this sample?

Question 73

Statisticians often refer to the pivot tables that display counts as contingency tables or crosstabs.

Question 74

A trend line on a scatterplot is a line or a curve that "fits" the scatter as well as possible.

Question 75

Approximate the percentage of these Internet users who are married with formal education beyond high school.

Question 76

Correlation and covariance can be used to examine relationships between numerical variables as well as for categorical variables that have been coded numerically.

Question 77

Approximate the percentage of these Internet users who are married.

Question 78

The tool that provides useful information about a data set by breaking it down into categories is the:

A) histogram
B) scatterplot
C) pivot table
D) spreadsheet

Question 79

The tables of counts that result from pivot tables are often called:

A) samples
B) sub-tables
C) specimens
D) crosstabs

Question 80

Counts for categorical variable are often expressed as percentages of the total.