Question 1

Given the data set $$x = \{7, 9, 6, 7, 9\}$$ and $$y = \{10, 6, 8, 7, 9\}$$, which scatter plot best represents the relationship between $$x$$ and $$y$$?

Accepted Answer

A plot with points scattered with no clear linear trend.

Question 2

If the correlation coefficient $$r$$ for a data set is $$-0.09$$, what does this indicate about the relationship between the variables?

Accepted Answer

There is little to no linear relationship.

Question 3

Given a sample size $$n = 5$$, what is the critical value for the correlation coefficient at the 0.05 significance level?

Accepted Answer

$$0.878$$

Question 4

Suppose you calculate a correlation coefficient $$r = -0.09$$ for a data set with $$n = 5. Is $$this correlation statistically significant at the 0.05 level?

Accepted Answer

No, because $$|-0.09| \u003c 0.878.$$

Question 5

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

Accepted Answer

It measures the strength and direction of a linear relationship between two variables.

Question 6

A researcher finds $$r = 0.008$$ for a data set. What is the best interpretation?

Accepted Answer

There is virtually no linear relationship.

Question 7

If the absolute value of the correlation coefficient $$|r| is $$less than the critical value for a given sample size, what conclusion should be drawn?

Accepted Answer

There is no evidence of a linear relationship.

Question 8

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

Accepted Answer

$$1.2$$

Question 9

A medical researcher collects data on hours of sleep ($$x) $$and reaction time ($$y) $$for 5 subjects. The correlation coefficient is $$r = -0.09. $$What does this suggest about the relationship between sleep and reaction time?

Accepted Answer

There is no significant linear relationship between sleep and reaction time.

Question 10

Which of the following best describes the meaning of a negative correlation coefficient?

Accepted Answer

As one variable increases, the other tends to decrease.

Question 11

If a data set has $$n = 10$$ and the calculated $$r = 0.65$$, is the correlation statistically significant at the 0.05 level?

Accepted Answer

Yes, because $$|0.65| \u003e 0.632.$$

Question 12

Which formula is used to calculate the sample 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 13

A student calculates $$r = 0.707$$ for a data set with $$n = 7. Is $$this correlation statistically significant at the 0.05 level?

Accepted Answer

Yes, because $$|0.707| = 0.707.$$

Question 14

Which of the following is a common misconception about correlation?

Accepted Answer

Correlation implies causation.

Question 15

If the correlation coefficient between two variables is $$r = 1$$, what does this mean?

Accepted Answer

There is a perfect positive linear relationship.

Question 16

A scientist finds $$r = -0.95$$ between two variables. What can be concluded?

Accepted Answer

There is a strong negative linear relationship.

Question 17

Which of the following best describes the critical value for the correlation coefficient?

Accepted Answer

It is the minimum absolute value of $$r$$ required for statistical significance.

Question 18

If $$r = 0.008$$ for a data set, which of the following is true?

Accepted Answer

The variables are almost uncorrelated.

Question 19

A psychologist collects data on stress level ($$x) $$and hours of sleep ($$y) $$for 5 subjects and finds $$r = -0.09. $$What is the best conclusion?

Accepted Answer

There is no significant linear relationship between stress and sleep.

Correlation Coefficient and Scatter Diagrams in Statistics

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