Question 1

Which of the following best describes the relationship between two variables if their correlation coefficient $$r is $$close to 0?

Accepted Answer

There is no linear correlation.

Question 2

A researcher finds $$r = 0.98$$ for the relationship between GDP and CO$$_2$$ emissions for 10 countries. What does this value of $$r$$ indicate?

Accepted Answer

There is a strong positive linear correlation.

Question 3

Given the following hypotheses for a two-tailed test of the population correlation coefficient $$ho$$:

$$H_0$$: ho = 0$$

H_a$$: ho 
eq 0$$

Which of the following statements is correct?

Accepted Answer

The null hypothesis states there is no significant correlation.

Question 4

Suppose you have 5 pairs of data and you calculate $$r = 0.97. $$Using a significance level of $$\alpha = 0.01$$, is the correlation significant? (Use the critical value $$0.959$$ for $$n=5$$ and $$\alpha=0.01.)$$

Accepted Answer

Yes, because $$|r| \u003e 0.959.$$

Question 5

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

Accepted Answer

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2$ \sum (y_i - \bar{y})^2$}}$$

Question 6

A student finds a significant positive correlation between ice cream sales and drowning incidents. Which of the following best explains this result?

Accepted Answer

A lurking variable, such as temperature, may be responsible for both.

Question 7

If the correlation coefficient $$r = -1$$, what does this indicate about the relationship between $$x$$ and $$y$$?

Accepted Answer

There is a perfect negative linear relationship.

Question 8

Which of the following is NOT a possible explanation for a significant correlation between two variables?

Accepted Answer

A guarantee of causation.

Question 9

You are testing the significance of a correlation coefficient using the $$t-$$test. Which formula gives the test statistic?

Accepted Answer

$$t = \frac{r \sqrt{n-2}}{\sqrt{1 - r^2$}}$$

Question 10

A scatter plot of the number of hours studied and exam scores shows points that rise from left to right in a straight line. What type of correlation is this?

Accepted Answer

Positive linear correlation

Question 11

Which of the following best describes a lurking variable?

Accepted Answer

A variable that affects the variables being studied but is not included in the study.

Question 12

Suppose you have $$n = 25$$ pairs of data and $$r = 0.979. At$$ $$\alpha = 0.05$$, is the correlation significant if the critical value is $$0.396$$?

Accepted Answer

Yes, because $$|r| \u003e 0.396.$$

Question 13

Which of the following is a correct interpretation if you fail to reject the null hypothesis in a test for the population correlation coefficient $$\rho$$?

Accepted Answer

There is not enough evidence to conclude a significant correlation exists.

Question 14

A scatter plot shows no apparent pattern between two variables. What is the most likely value for the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to 0

Question 15

Which of the following is a possible value for a correlation coefficient?

Accepted Answer

-0.8

Question 16

If $$r = 0.04$$ for the relationship between IQ score and height, what does this indicate?

Accepted Answer

There is no correlation.

Question 17

Which of the following steps is NOT required when calculating the sample correlation coefficient $$r$$?

Accepted Answer

Divide each $$x-$$value by the corresponding $$y-$$value and sum the results.

Question 18

Which of the following is true about correlation and causation?

Accepted Answer

Correlation does not imply causation, but it may suggest a possible relationship.

Question 19

A hypothesis test for the population correlation coefficient $$\rho$$ uses which distribution for the test statistic?

Accepted Answer

t-distribution with $$n-2$$ degrees of freedom

Chapter 9: Correlation and Regression – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards