Question 1

Which of the following best describes the purpose of a scatterplot in statistics?

Accepted Answer

To show the relationship between two numerical variables

Question 2

A researcher plots the number of hours students study (x) against their test scores (y) and observes that as $$x$$ increases, $$y$$ also increases in a roughly straight line. What type of correlation is this?

Accepted Answer

Positive linear correlation

Question 3

Which statement is TRUE regarding correlation and causation?

Accepted Answer

Correlation does NOT imply causation

Question 4

Given the following data: as the number of pins on a backpack increases, test scores decrease. What is the likely sign of the correlation coefficient $$r$$?

Accepted Answer

Negative

Question 5

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

Accepted Answer

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

Question 6

A correlation coefficient $$r = -0.92 is $$calculated for two variables. Which of the following best describes the relationship?

Accepted Answer

Strong negative linear correlation

Question 7

A scientist finds $$r = 0.13$$ for the relationship between two variables. What does this indicate?

Accepted Answer

Weak positive correlation

Question 8

Which of the following scenarios is most likely to have a correlation coefficient $$r$$ close to zero?

Accepted Answer

Number of siblings and test scores

Question 9

Engineers study how cargo weight affects drone flight duration. As cargo weight increases, flight duration decreases. What type of correlation is this?

Accepted Answer

Negative linear correlation

Question 10

Which of the following best describes a strong correlation?

Accepted Answer

Data points are tightly clustered around the trend line

Question 11

A marketing researcher finds $$r = 0.59$$ between advertising budget and sales revenue. What does this value suggest?

Accepted Answer

A moderate positive linear correlation

Question 12

Which of the following steps is NOT required when creating a scatterplot on a TI-84 calculator?

Accepted Answer

Calculating the mean and standard deviation

Question 13

If the correlation coefficient $$r$$ for a data set is $$-0.96$$, what can you conclude?

Accepted Answer

There is a strong negative linear correlation

Question 14

Which menu option on a TI-84 calculator is used to calculate the correlation coefficient?

Accepted Answer

STAT \u003e CALC \u003e LinReg(ax+b)

Question 15

A scientist measures the speed of sound at different altitudes and finds $$r = -0.98. $$What does this indicate about the relationship?

Accepted Answer

Speed of sound decreases as altitude increases

Question 16

Which of the following is a common misconception about correlation?

Accepted Answer

A high correlation means one variable causes the other

Question 17

If a scatterplot shows a curved pattern, which of the following is true about the correlation coefficient $$r$$?

Accepted Answer

$$r$$ may be close to $$0$$ even if there is a strong nonlinear relationship

Question 18

Which of the following best describes the effect of outliers on the correlation coefficient $$r$$?

Accepted Answer

Outliers can greatly increase or decrease $$r$$

Question 19

A data set has $$r = 0. $$What does this mean?

Accepted Answer

There is no linear relationship

Question 20

Which of the following is NOT a requirement for using the correlation coefficient $$r$$?

Accepted Answer

The variables must be measured on the same scale

Scatterplots and Correlation: Describing the Relation Between Two Variables

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