Question 1

What does squaring Pearson's r give us?

Accepted Answer

Squaring Pearson's r gives us the coefficient of determination (r²), which represents the proportion of variance in the dependent variable that is predictable from the independent variable, indicating the proportional reduction in error for predicting Y when we have knowledge of X.

Question 2

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?

Accepted Answer

Pearson's r is appropriate for measuring the linear relationship between two continuous variables, such as years of schooling and number of alcoholic drinks consumed per week.

Question 3

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?

Accepted Answer

The Pearson's r value of -0.22 indicates a weak, negative correlation between the proportion of women in management and sexual harassment claims, not a moderate one. However, among the given options, C is the closest interpretation, as it correctly identifies the direction of the correlation.

Question 4

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

Accepted Answer

The coefficient of determination, often denoted as R², is calculated using explained variation (variation explained by the model) and unexplained variation (variation not explained by the model).

Question 5

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?

Accepted Answer

The r² value of 0.18 indicates that 18% of the variance in the number of Facebook friends can be explained by screen time, which is what option D states.

Question 6

Which of the following best represents r²?

Accepted Answer

r², or the coefficient of determination, represents the ratio of explained variation to total variation in a regression model.

Question 7

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?

Accepted Answer

The coach is claiming that the coefficient of determination (r²) is equal to 1, meaning that 100% of the variability in free-throw shooting accuracy is explained by the hours of practice.

Question 8

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?

Accepted Answer

The value of Pearson's r is the square root of the explained variance. Since 9% of the variance is explained, r = sqrt(0.09) = 0.30.

Question 9

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

Accepted Answer

The answer of Which of the following is the null...

Question 10

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

Accepted Answer

Pearson's r assumes that the relationship between the two variables is linear, meaning that the data points should form a straight line when plotted on a scatterplot.

Question 11

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?

Accepted Answer

If the correlation does not fall within the critical region, it means the test is not statistically significant, and no inference can be made about the population correlation.

Question 12

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?

Accepted Answer

The assumption of homoscedasticity has been violated. Homoscedasticity assumes that the variance of the dependent variable is the same at all values of the independent variable. In this case, the variance of Y is smaller at low values of X than at high values of X.

Question 13

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?

Accepted Answer

The regression equation Y = 50 + 0.25(X) indicates that for each additional $1,000 of income (X), the number of books (Y) increases by 0.25 on average.

Question 14

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?

Accepted Answer

The regression equation is Y = 50 + 0.25(X). For an income of $40,000, X = 40 (since income is in thousands). Plugging in, Y = 50 + 0.25(40) = 50 + 10 = 60 books.

Question 15

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

Accepted Answer

The answer of Identify one similarity and one difference between...

Question 16

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

Accepted Answer

The answer of Explain what is meant by a "linear...

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

What does squaring Pearson's r give us?

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 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?

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

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?

Which of the following best represents r²?

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?

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?

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

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

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 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 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?

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

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

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

What does squaring Pearson's r give us?

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 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?

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

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?

Which of the following best represents r2?

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?

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?

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

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

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 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 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?

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

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

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?

Which of the following best represents r²?

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?