Free Practice Quiz Question List

10 Correlation Online Quiz Questions

Use this free practice quiz with 20 questions to review 10 Correlation, test your knowledge, and prepare for your next test or exam.

20 questions

True or false

1 point

True or false: Pearson's correlation coefficient is unit-free, so changing a variable's measurement units does not change the value of the correlation coefficient.

A
True
B
False

Choose one

1 point

A study finds a statistically significant correlation between two variables. Which conclusion is justified?

A
A statistically significant correlation proves that the explanatory variable causes the response variable.
B
A statistically significant correlation provides evidence of a population linear association but does not by itself prove causation.
C
A statistically significant correlation proves that no third variable affects either variable.
D
A statistically significant correlation proves that every individual follows the observed pattern.

Choose one

1 point

A dataset has Pearson correlation $r$ = -0.85. How should the linear association be described?

A
A weak positive linear association
B
A strong negative linear association
C
A strong positive linear association
D
A weak negative linear association

Choose one

1 point

Why can covariance be difficult to compare across two datasets that measure the same variables using different scales?

A
It is always between -1 and 1.
B
It has no units because it is standardized.
C
Its numerical value depends on the measurement units of the variables.
D
It can only be positive when both variables are quantitative.

Choose all

1 point

Select all explanations that could account for an observed correlation between two variables.

A
A third variable influences both measured variables.
B
The observed association results from sampling variation.
C
The response variable influences the explanatory variable.
D
The explanatory variable directly influences the response variable.

Choose all

1 point

Select all conditions that should be checked before carrying out a test of a population correlation.

A
The observations are paired correctly and are independent.
B
The relationship is reasonably linear.
C
There are no extreme outliers that dominate the result.
D
The variation around the linear pattern is reasonably consistent.
E
The data come from a suitable random sample or randomized design when population inference is intended.
F
The sample correlation must be exactly equal to zero before the test can be performed.

Written response

1 point

A correlation test uses a sample of n=18 paired observations. How many degrees of freedom should be used for the t-distribution?

Fill in the blank

1 point

Complete the description: In a scatterplot, a pattern that falls from left to right indicates a association, while a roughly straight overall pattern has an form.

Fill in the blank

1 point

Complete the statement: The usual null hypothesis for testing a nonzero population linear association is $H_0:$ , and the test statistic is compared with a t-distribution having degrees of freedom.

Open ended

1 point

Explain why a scatterplot should be examined before calculating or interpreting a correlation coefficient. Give at least two specific features that the plot might reveal and explain why they matter.

Choose one

1 point

A correlation test is conducted at $\alpha=0.05$ , and the p-value is 0.012. Which conclusion is most appropriate?

A
Fail to reject $H_0$ because a small p-value supports the null hypothesis.
B
Reject $H_0$ and conclude that the population represented by the sample has evidence of a nonzero linear association.
C
Reject $H_0$ and conclude that the explanatory variable causes the response variable.
D
Accept $H_0$ and conclude that the population correlation is exactly zero.

True or false

1 point

True or false: If Pearson's correlation coefficient is $r=0$ , then the two variables have no relationship of any kind.

A
True
B
False

Written response

1 point

What is the standardized measure that describes the direction and strength of a linear association between two quantitative variables?

Choose one

1 point

A scatterplot shows points that generally rise from left to right. What type of association does this pattern indicate?

A
A negative association
B
A positive association
C
No association
D
A causal relationship

True or false

1 point

True or false: If two quantitative variables have a strong correlation, that correlation alone proves that changes in one variable cause changes in the other.

A
True
B
False

Written response

1 point

Ice-cream sales and drowning incidents increase during warm months. What term describes a third variable, such as warm weather, that influences both variables and can create an apparent association?

Choose one

1 point

Which type of evidence generally provides the strongest support for concluding that one variable causes changes in another?

A
A larger observational sample with the same uncontrolled variables
B
A well-designed randomized experiment
C
A scatterplot with a curved pattern
D
A covariance measured in different units

Choose one

1 point

A sample contains the paired observations $(1,2)$ , $(2,4)$ , and $(3,6)$ . Using the sample covariance formula $s_{xy}=\frac{\sum (x_i-\bar{x})(y_i-\bar{y})}{n-1}$ , what is the sample covariance?

Choose one

1 point

A study reports a sample correlation of $r=0.6$ from $n=12$ paired observations. Using $t=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$ , which value is closest to the test statistic?

A
0.750
B
1.500
C
2.372
D
3.750

Written response

1 point

For a sample correlation of $r=0.6$ based on $n=12$ paired observations, calculate $t=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$ . Enter the test statistic rounded to three decimal places; an absolute tolerance of 0.001 is allowed.