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 that as the number of hours studied increases, exam scores also increase. The scatter plot of the data shows points trending upward from left to right. What type of correlation is most likely present?

Accepted Answer

Positive linear correlation

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 in this formula?

Accepted Answer

The number of data pairs

Question 4

Suppose you calculate a sample correlation coefficient $$r = 0.82$$ for 15 pairs of data. Using a critical value table, you find the critical value for $$n = 15 at$$ $$\alpha = 0.05 is$$ $$0.514. $$What can you conclude?

Accepted Answer

The correlation is significant at the 5% level.

Question 5

Which of the following statements about correlation and causation is correct?

Accepted Answer

Correlation does not imply causation.

Question 6

A study finds a strong 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, affects both variables.

Question 7

You are testing the significance of a correlation coefficient using a t-test. The test statistic is calculated as:

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

If$$ $$r = 0.7$$ and $$n = 12$$, what is the value of the test statistic $$t$$? (Round to two decimal places)

Accepted Answer

$$ t = 3.08 $$

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

A scatter plot of the number of hours spent watching TV per week and GPA for a group of students shows no apparent pattern. What is the most appropriate conclusion?

Accepted Answer

There is no linear correlation.

Question 10

If the correlation coefficient $$r$$ for a data set is $$-0.95$$, which of the following best describes the relationship between the variables?

Accepted Answer

Strong negative linear correlation

Question 11

A researcher uses Excel to calculate the correlation coefficient between eruption durations and times until the next eruption for a geyser, obtaining $$r = 0.9787. $$What does this value suggest?

Accepted Answer

There is a strong positive linear correlation.

Question 12

Which of the following is the correct null hypothesis for testing the significance of a population correlation coefficient $$\rho$$?

Accepted Answer

$$ H_0$: \rho = 0 $$

Question 13

Suppose you have $$n = 25$$ pairs of data and calculate $$r = 0.65. $$Using a critical value table, you find the critical value for $$n = 25 at$$ $$\alpha = 0.05 is$$ $$0.396. $$What is the correct conclusion?

Accepted Answer

There is enough evidence to conclude the correlation is significant.

Question 14

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 15

A student uses a TI-84 Plus calculator to perform a linear regression and finds $$r^2 = 0.9578$. What does r^2$ represent in this context?

Accepted Answer

The proportion of variation in the dependent variable explained by the independent variable.

Chapter 9: Correlation and Regression – Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard