Question 1

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

Accepted Answer

There is no linear correlation.

Question 2

A researcher wants to predict cholesterol levels based on age. Which is the explanatory variable?

Accepted Answer

Age

Question 3

Given the formula for the sample correlation coefficient $$r$$:
$$
 r = \frac{n\sum xy - \sum x \sum y}{\sqrt{[n\sum x^2$ - (\sum x)^2$][n\sum y^2$ - (\sum y)^2$]}} 
$$
What does $$n$$ represent?

Accepted Answer

The number of pairs of data

Question 4

A scatter plot shows that as the number of hours studied increases, exam scores tend to increase. What type of correlation is this?

Accepted Answer

Positive linear correlation

Question 5

If the correlation coefficient $$r = -0.92$$, what can you conclude about the relationship between the variables?

Accepted Answer

There is a strong negative linear correlation.

Question 6

A dentist wants to predict the number of cavities based on the type of toothbrush used. Which is the response variable?

Accepted Answer

Amount of cavities

Question 7

You calculate $$r = 0.056$$ for the relationship between height and IQ score in high school girls, with $$n = 8$$ and $$\alpha = 0.01. $$The critical value is $$0.834. $$What is the correct conclusion?

Accepted Answer

There is not enough evidence to conclude the correlation is significant.

Question 8

Which of the following is NOT a possible value for the correlation coefficient $$r$$?

Accepted Answer

$$r = 1.2$$

Question 9

A scatter plot of age versus vocabulary size in children shows that as age increases, vocabulary size increases. The calculated $$r is$$ $$0.982$$ for $$n = 11$$ and $$\alpha = 0.05. $$The critical value is $$0.602. $$What is the correct interpretation?

Accepted Answer

There is a significant positive linear correlation.

Question 10

Which of the following best describes a scatter plot with points forming a straight line that slopes downward from left to right?

Accepted Answer

Negative linear correlation

Question 11

If $$|r| is $$greater than the critical value from Table 11 for a given $$n$$ and $$\alpha$$, what should you conclude?

Accepted Answer

There is a significant linear correlation.

Question 12

In a real-world scenario, a medical researcher finds $$r = 0.911$$ between age and systolic blood pressure for $$n = 10$$ men. What does this value of $$r$$ suggest?

Accepted Answer

A strong positive linear correlation

Question 13

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

Accepted Answer

$$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{[n\sum x^2$ - (\sum x)^2$][n\sum y^2$ - (\sum y)^2$]}}$$

Question 14

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

Accepted Answer

$$r is $$close to 0

Question 15

If a scatter plot shows a curved pattern, which type of correlation is most likely present?

Accepted Answer

Nonlinear correlation

Question 16

A researcher tests the significance of a correlation coefficient with $$n = 5$$ pairs of data at $$\alpha = 0.01. $$What is the critical value?

Accepted Answer

$$0.959$$

Question 17

Which step is NOT part of testing the significance of a population correlation coefficient $$\rho$$?

Accepted Answer

Calculate the mean of $$x$$ and $$y$$

Question 18

In a study, the correlation coefficient between income and amount spent on milk per year is $$r = 0.45. $$How would you describe this correlation?

Accepted Answer

Weak positive correlation

Question 19

If the critical value for $$n = 11$$ and $$\alpha = 0.05 is$$ $$0.602$$, and your calculated $$r is$$ $$0.982$$, what is the correct decision?

Accepted Answer

There is a significant linear correlation.

Question 20

Which of the following real-world examples is most likely to show a negative linear correlation?

Accepted Answer

Number of hours spent exercising and body fat percentage

Correlation and Regression: Structured Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards