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 collects data on hours studied (x) and exam scores (y) for a group of students. The scatterplot shows that as $$x$$ increases, $$y$$ also increases in a roughly straight-line pattern. What type of correlation is present?

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: Mean driving speed (x) and number of speeding tickets (y) in a 55 mph zone, what type of correlation would you expect between $$x$$ and $$y$$?

Accepted Answer

Positive correlation

Question 5

If a scatterplot shows points that are tightly clustered around a downward-sloping straight line, which of the following is most likely true about the correlation coefficient $$r$$?

Accepted Answer

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

Question 6

A scientist finds $$r = 0.13$$ for the relationship between two variables. Which statement best describes this correlation?

Accepted Answer

Weak correlation

Question 7

Which of the following values of $$r$$ indicates the strongest linear relationship?

Accepted Answer

$$r = -0.96$$

Question 8

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

Accepted Answer

There is a moderate positive linear relationship

Question 9

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 10

Engineers studying drone flight find that as cargo weight increases, flight duration decreases. What type of correlation is this?

Accepted Answer

Negative correlation

Question 11

Which of the following best describes a situation where $$r = 0$$?

Accepted Answer

There is no linear relationship

Question 12

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

Accepted Answer

A strong negative linear relationship

Question 13

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

Accepted Answer

Calculating the mean and median

Question 14

If the points on a scatterplot are widely scattered and do not form any clear pattern, what can you conclude about the correlation?

Accepted Answer

There is no correlation

Question 15

Which of the following is a common misconception about the correlation coefficient $$r$$?

Accepted Answer

The value of $$r is $$affected by the slope of the best-fit line

Question 16

A data set has $$r = -0.92. $$Which scatterplot best represents this relationship?

Accepted Answer

Points tightly clustered around a line sloping downward

Question 17

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

Accepted Answer

Outliers can greatly affect the value of $$r$$

Question 18

A teacher finds that students who sleep more hours tend to have higher test scores, but the relationship is not perfect. Which value of $$r is $$most likely?

Accepted Answer

$$r = 0.75$$

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

$$r = 1.2$$

Scatterplots and Correlation: Describing the Relation Between Two Variables

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