Question 1

Which of the following best describes the meaning of a positive linear correlation between two variables?

Accepted Answer

As one variable increases, the other variable also increases.

Question 2

Suppose a scatterplot of two variables shows points that closely follow a straight line sloping downward. What can you infer about the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to $$-1$$

Question 3

A researcher finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores for a group of students. What does this imply?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam scores.

Question 4

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

Accepted Answer

Correlation does not necessarily imply causation.

Question 5

Given a dataset with 25 pairs of values and a calculated correlation coefficient $$r = 0.979$$, the critical value from the table is $$0.396. $$What can you conclude?

Accepted Answer

The correlation is significant because $$r \u003e 0.396$$

Question 6

Which variable is typically plotted on the horizontal axis in a scatterplot when investigating correlation?

Accepted Answer

The explanatory variable

Question 7

A scatterplot shows a curved pattern rather than a straight line. What does this suggest about the correlation between the variables?

Accepted Answer

The relationship is nonlinear and the linear correlation coefficient may not be appropriate.

Question 8

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

Accepted Answer

There is little to no linear relationship.

Question 9

Which of the following is a correct step when using technology to compute the correlation coefficient for a dataset?

Accepted Answer

Use the STAT menu to select 'Edit' and enter data into L1 and L2.

Question 10

Which of the following scenarios is most likely to result in a negative correlation?

Accepted Answer

Interest rates and number of cars sold.

Question 11

What is the main purpose of using a table of critical values for the Pearson correlation coefficient?

Accepted Answer

To test if the observed correlation coefficient is statistically significant.

Question 12

Which of the following best describes a scatterplot?

Accepted Answer

A graph in which paired sample data values are plotted as points.

Question 13

If a scatterplot of two variables shows points that are widely scattered and do not follow any clear pattern, what is the likely value of the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to $$0$$

Question 14

Which of the following is an example of a situation where there is likely to be no correlation?

Accepted Answer

Height and GPA of students.

Question 15

A scientist finds a correlation coefficient $$r = -0.92$$ between the amount of smoking and life expectancy. What does this mean?

Accepted Answer

There is a strong negative linear relationship.

Question 16

Which of the following is true about the linear correlation coefficient $$r$$?

Accepted Answer

$$r$$ can only take values between $$-1$$ and $$1$$

Question 17

If the points in a scatterplot fall exactly on a straight line with a positive slope, what is the value of the correlation coefficient $$r$$?

Accepted Answer

$$r = 1$$

Question 18

Which of the following best describes a negative correlation?

Accepted Answer

As one variable increases, the other variable decreases.

Question 19

A student claims that a high correlation between two variables means that one variable causes the other. What is the best response?

Accepted Answer

Correlation does not imply causation; other factors may be involved.

Question 20

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

Accepted Answer

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

Correlation in Statistics: Understanding Relationships Between Variables

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