Deck 13: Hypothesis Testing and Measures of Association for Variables Measured at the Interval-Ratio Level

Question 1

A researcher wants to understand whether age causes declines in sexual frequency among European adults. As a first step in understanding this association, she makes a scatterplot. Which variable belongs on the Y (vertical) column?

A) There is not enough information given to decide.
B) age
C) European nationality
D) sexual frequency

Answer 1

sexual frequency

Question 2

What visual piece of information can be included in a scatterplot to summarize the clarity of a pattern?

A) regression line
B) scatterplot curve
C) conditional mean parabola
D) Pearson's curve

Answer 2

regression line

Question 3

Which of the following indicates the existence of an association between variables on a scatterplot?

A) The regression line is perpendicular to the horizontal axis.
B) The regression line is parallel to the horizontal axis.
C) The distribution of Y changes as X changes.
D) No single regression line can be found.

Answer 3

The distribution of Y changes as X changes.

Question 4

When can a perfect association between variables be seen on a scatterplot?

A) when the regression line forms a right angle at its intersection with the X axis
B) when the regression line is parallel to the X axis
C) when all dots lie an equal distance from the regression line
D) when all dots lie on the regression line

Question 5

A scatterplot line crosses the Y axis at "5" and is completely horizontal across the full range of X. Which of these statements best describes the relationship between X and Y?

A) There is a negative, linear association between X and Y.
B) There is a positive, linear association between X and Y.
C) There is no association between X and Y.
D) The association between X and Y is statistically significant.

Question 6

Which statement about variables is among the key assumptions of correlation analysis?

A) The relationship of the variables is essentially linear.
B) The relationship of the variables is essentially curvilinear.
C) The relationship of the variables is essentially non-linear.
D) The relationship of the variables is essentially circular.

Question 7

According to the text, what could an analyst do if she intends to document an association between two interval-ratio variables that have a clearly non-linear relationship?

A) treat the variables as though they are nominal, not interval-ratio
B) treat the variables as though they are ordinal, not interval-ratio
C) rearrange the scatterplot so that the X and Y variables switch places
D) use correlation instead of regression

Question 8

Suppose the predicted value of Y in a regression equation is 10. X = 2 and b = 4. What would the Y intercept value be?

A) 1
B) 2
C) 4
D) 20

Question 9

For the least-squares regression equation , what does
indicate?

A) The line's intercept is multiplied by the value of X.
B) The conditional distribution of X is multiplied by the line's intercept.
C) The score on the dependent variable is multiplied by the regression line slope.
D) The slope of the regression line is multiplied by the value of X.

Question 10

Suppose that the slope of a regression line is 1.5. How should this number be interpreted?

A) The regression line crosses the vertical axis of the scatterplot at a value of 1.5.
B) The score of each case is 1.5 times higher on Y than on X.
C) For every unit of change in Y there is a change of 1.5 in X.
D) For every unit of change in X there is a change of 1.5 units in Y.

Question 11

Which of the following describes the slope (b) if a regression line is parallel to the horizontal axis of the scatterplot?

A) 1.00
B) 0.45
C) 0.00
D) -1.00

Question 12

A regression line from a sample of high-school students shows that the association between number of days drunk per month and achievement test scores is -5.5. Which of the following could be concluded from this result?

A) that students who drink once per month get scores 5.5 points higher than those who drink every day
B) that scores decrease by 5.5 points for every day drunk per month
C) that students who never drink score 5.5 on the test
D) that there is a moderate association between drinking and test performance

Question 13

What is a special feature of the least-squares regression line?

A) It passes through all observations in a scatterplot.
B) It establishes causal relationships between variables.
C) It detects both linear and curved relationships.
D) It comes as close as possible to all conditional means of Y.

Question 14

What is the best way to describe a slope that has a value close to zero?

A) There is a weak effect of X on Y.
B) There is a moderate effect of X on Y.
C) There is a strong effect of X on Y.
D) It is impossible to say without knowing the coefficient of determination.

Question 15

In what sense does "Y-predicted" provide only an "educated guess" of Y?

A) Exact predictions of Y are extremely rare: exactness is achieved only when the relationship between X and Y is perfectly linear.
B) Y-predicted typically loses precision when X and Y are both interval-ratio variables; it is more exact when at least one variable is measured on a nominal scale.
C) Y-predicted predicts Y without taking into account values of X.
D) Y-predicted is based on Y's overall mean and ignores the conditional mean of Y.

Question 16

A regression slope (b) is 2.5. What does this slope tell us about the strength of the relationship between X and Y?

A) This is a strong relationship; actual observations are very closely clustered around the regression line.
B) There is a weak relationship; actual observations are scattered widely around the regression line.
C) There is no relationship between X and Y.
D) By itself, knowing the regression slope tells us nothing about the strength of relationship between X and Y.

Question 17

The Pearson's r correlation between pets owned during one's lifetime and longevity is zero. What is the value of the slope (b)?

A) -1.00
B) 0
C) 0.50
D) 1.00

Question 18

Researchers wish to understand the strength of relationship between the digital readership of 80 North American newspapers (average Web page views per month) and the average age of the staff of those newspapers. What would be the most appropriate measure of association?

A) phi
B) gamma
C) Pearson's r
D) regression slope (b)

Question 19

A researcher asked a sample of dual-wage-earner families about the percentage of the family budget that is contributed by the wife's job (Y), and about the total number of children (X). Pearson's r for this relationship is -0.34. Which of the following is an appropriate interpretation of these results?

A) Every additional child lowers the economic well-being of the family.
B) For every additional child, the wife must work longer hours.
C) As the number of children increases, the percentage of the budget contributed by the wife decreases.
D) For every dollar contributed by the wife, the number of children increases by 0.34.

Question 20

Suppose we want to know the association between Spotify song listens and touring revenues of punk bands. What would be the most appropriate measure of association to use?

A) Pearson's r
B) gamma
C) chi square
D) eta-squared

Question 21

What does squaring Pearson's r give us?

A) the change in Y associated with a one unit change in X
B) the proportional reduction in error for predicting Y when we have knowledge of X
C) a clear index of relationship strength based on whether r² is between 0 and 0.1, 0.1 and 0.3, or over 0.3
D) a clear index of relationship strength based on whether r² is less than or greater than 0.5

Question 22

A researcher is interested in the relationship between years of schooling and number of alcoholic drinks consumed per week. What would be an appropriate measure of association for these two variables?

A) phi
B) Kendall's tau-b
C) Pearson's r
D) lambda

Question 23

A study finds a Pearson's r value of -0.22 between proportion of women in management and sexual harassment claims in a sample of 425 company corporate offices. Which of these statements is the best interpretation of that finding?

A) Sexual harassment is more common in firms where more women are in management.
B) High levels of sexual harassment cause fewer women to seek management jobs.
C) There is a moderate, negative correlation between women in management and sexual harassment claims.
D) Knowing the proportion of female managers in a firm explains 44% of the variance in sexual harassment reports.

Question 24

What are the two components of variation used in calculating the coefficient of determination?

A) explained variation and unexplained variation
B) sampling variation and population variation
C) standard variation and homoscedastic variation
D) conditional variation and linear variation

Question 25

The association between number of Facebook friends and screen time per day has an r² value of 0.18. Which of these statements is the best interpretation of this statistic?

A) There is a moderate, positive relationship between Facebook friends and screen time.
B) There is a strong, negative relationship between Facebook friends and screen time.
C) There is a weak, linear relationship between Facebook friends and screen time.
D) Screen time explains 18% of the total variance in number of Facebook friends.

Question 26

Which of the following best represents r²?

A) the ratio of total variation to unexplained variation
B) the ratio of explained variation to total variation
C) the ratio of unexplained variation to explained variation
D) the ratio of the regression slope to the Y intercept

Question 27

A basketball coach claims that all variability in free-throw shooting accuracy can be explained by hours of foul shot practice spent per season. What is he claiming about the value of r²?

A) It is equal to 0.
B) It is equal to 1.
C) It is equal to 100.
D) It is equal to 1000.

Question 28

Knowing the value of someone's body mass index helps explain 9% of the variance in blood pressure. What is the value of Pearson's r for this association?

A) r = 0.045
B) r = 0.09
C) r = 0.30
D) r = 0.90

Question 29

Which of the following is the null hypothesis when testing Pearson's r for significance?

A) No difference exists between the sample and the population from which the sample was drawn.
B) No linear association exists between the variables in the sample.
C) No difference exists between the variables in the sample.
D) No linear association exists between the variables in the population from which the sample was drawn.

Question 30

What assumption about the nature of a relationship is necessary for testing Pearson's r for significance?

A) The relationship must be positive.
B) The relationship must be linear.
C) The relationship cannot be homoscedastic.
D) The relationship can include only one interval-ratio variable.

Question 31

Suppose a correlation of r = 0.12 fails to fall within the critical region for a hypothesis test. Which of the following should be concluded?

A) The correlation value is greater than 0.12 in the population.
B) The correlation value is between 0.00 and 0.12 in the population.
C) The correlation in the population is negative.
D) No inference can be made about the relationship of the two variables in the population.

Question 32

We wish to test whether the correlation between two variables is significantly different from 0 (i.e., no relationship between X and Y in the population). When we look at the scatterplot of our data, we find that values of Y are tightly clustered together at low values of X, but much more spread out at high values of X. What assumption have we violated?

A) the assumption of a linear relationship
B) the assumption of homoscedasticity
C) the assumption of interval-ratio measurement
D) the coefficient of determination assumption

Question 33

A sociologist is interested in how family income (in 1,000s of dollars) predicts number of books in the home. He produces a regression equation stating that Y = 50 + 0.25(X).

-Which of the following would be an accurate interpretation of this finding?

A) For each additional $1,000 of income, families have an average of 50 additional books.
B) For each additional $50 of income, families gain an average of 0.25 extra books.
C) For each additional 0.25 books, families have an extra $50.
D) For each additional $1,000 of income, families have an average of 0.25 additional books.

Question 34

A sociologist is interested in how family income (in 1,000s of dollars) predicts number of books in the home. He produces a regression equation stating that Y = 50 + 0.25(X).

-From this equation, how many books would we predict for a family with an income of $40,000?

A) 40 books
B) 50 books
C) 60 books
D) 80 books

Question 35

Identify one similarity and one difference between least-squares regression and correlation coefficient (r).

Question 36

Explain what is meant by a "linear relationship" and provide a brief example of such an association.