Question 1

Which of the following best describes the difference between univariate and bivariate data?

Accepted Answer

Univariate data involves one variable measured on each individual, while bivariate data involves two variables measured on each individual.

Question 2

In a scatter diagram, which variable is typically plotted on the x-axis?

Accepted Answer

The explanatory variable

Question 3

Given the following data pairs: $$(1, -4), (2, -2), (3, -1), (4, 0), (5, 2)$$, what is the sign of the correlation coefficient $$r$$?

Accepted Answer

Positive

Question 4

Which of the following statements about the correlation coefficient $$r is $$TRUE?

Accepted Answer

$$r is a $$unitless measure of association.

Question 5

A scatter plot shows a strong downward trend from left to right. Which of the following best describes the correlation?

Accepted Answer

Strong negative correlation

Question 6

Suppose the sample correlation coefficient $$r = 0.901$$ for $$n = 5$$ pairs of data. If the critical value from the table is $$0.878$$, what conclusion can you draw?

Accepted Answer

There is enough evidence to conclude that the population correlation coefficient $$\rho is $$significant.

Question 7

Which of the following is a correct interpretation of a correlation coefficient $$r = 0.94$$ between two variables measured over time?

Accepted Answer

There is a strong positive linear association, but this does not imply causation.

Question 8

Which of the following scenarios is most likely to involve a lurking variable?

Accepted Answer

A strong correlation between ice cream sales and crime rates.

Question 9

If the correlation coefficient $$r is $$close to $$0$$, what does this indicate about the relationship between two variables?

Accepted Answer

There is no linear relationship.

Question 10

Which of the following is NOT a property of the correlation coefficient $$r$$?

Accepted Answer

$$r is $$resistant to outliers.

Question 11

A researcher finds a correlation of $$r = -0.95$$ between age and hours of sleep per night in a sample of adults. Which of the following is the best interpretation?

Accepted Answer

As age increases, hours of sleep per night tend to decrease.

Question 12

Which of the following best describes why correlation does not imply causation?

Accepted Answer

Because a third variable may be influencing both variables.

Question 13

Given the following scenario: As the number of hours spent exercising increases, the risk of heart disease decreases. What type of correlation is most likely present?

Accepted Answer

Negative correlation

Question 14

Which of the following is the correct formula for the sample correlation coefficient $$r$$?

Accepted Answer

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{(n-1)s_x s_y}$$

Question 15

A study finds a correlation of $$r = 0.02$$ between shoe size and intelligence. What is the best conclusion?

Accepted Answer

There is no significant linear relationship between shoe size and intelligence.

Question 16

Which of the following is an example of bivariate data?

Accepted Answer

Measuring both the height and weight of each student in a class.

Question 17

If a scatter plot shows points that are widely scattered with no apparent pattern, what can you conclude about the correlation?

Accepted Answer

There is no linear correlation.

Question 18

Which of the following best describes a lurking variable?

Accepted Answer

A variable that influences both the explanatory and response variables, creating a spurious association.

Question 19

Suppose you calculate $$r = 0.85$$ for a sample of $$n = 10$$ pairs of data. If the critical value from the table is $$0.632$$, what does this mean?

Accepted Answer

There is enough evidence to conclude a significant linear relationship.

Question 20

Which of the following is a real-world example where correlation does NOT imply causation?

Accepted Answer

A strong correlation between the number of firefighters at a fire and the amount of damage caused.

Describing the Relation Between Two Variables: Scatter Diagrams and Correlation

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