Question 1

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

Accepted Answer

A relationship where the plotted points of paired data result in a pattern that can be approximated by a straight line.

Question 2

Which of the following is a common error when interpreting correlation results?

Accepted Answer

Assuming that correlation implies causality.

Question 3

Given the following hypotheses for a correlation test, what does the null hypothesis $$H_0$$ state?

$$H_0$$: ho = 0$$
H_1$: ho 
eq 0$$

Accepted Answer

There is no linear correlation between the two variables in the population.

Question 4

Suppose you calculate a correlation coefficient $$r = 0.92146$$ with a critical value $$r_{critical} = \pm 0.75449$$ and a p-value of $$0.00318$$ for $$n = 7. $$What is the correct conclusion at $$\alpha = 0.05$$?

Accepted Answer

There is a significant linear correlation between the variables.

Question 5

Which formula is used to calculate the sample linear correlation coefficient $$r$$ using raw scores?

Accepted Answer

$$r = \frac{n\sum xy - (\sum x)(\sum y)}{\sqrt{[n\sum x^2$ - (\sum x)^2$][n\sum y^2$ - (\sum y)^2$]}}$$

Question 6

Which of the following statements about the properties of the linear correlation coefficient $$r is $$FALSE?

Accepted Answer

The value of $$r is $$not affected by outliers.

Question 7

A study finds a correlation coefficient $$r = 0.10484$$ with a critical value $$r_{critical} = \pm 0.16967$$ and a p-value of $$0.22799$$ for $$n = 134. $$What is the correct interpretation?

Accepted Answer

There is no significant linear correlation between the variables.

Question 8

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

Accepted Answer

The variables must be categorical.

Question 9

If a scatterplot shows a clear curved pattern but the calculated $$r is $$close to zero, what is the most likely explanation?

Accepted Answer

There is a nonlinear relationship between the variables.

Question 10

Which of the following scenarios best illustrates the concept of a lurking variable?

Accepted Answer

A study finds a correlation between ice cream sales and drowning incidents, but both are actually related to temperature.

Question 11

Given the following paired data for Exam 1 and Exam 2 scores, what is the sample size $$n$$?

Exam 1: 100, 95, 70.7, 64.5, 96, 90.5, 81
Exam 2: 100, 92.9, 77.2, 50.7, 100, 87.6, 86.7

Accepted Answer

$$n = 7$$

Question 12

Which of the following best describes the meaning of the Pearson product moment correlation coefficient?

Accepted Answer

It measures the strength of the linear association between two quantitative variables.

Question 13

If the correlation coefficient $$r = -0.81195$$ with a critical value $$r_{critical} = \pm 0.43286$$ and a p-value of $$0.00001$$ for $$n = 21$$, what can you conclude?

Accepted Answer

There is a significant negative linear correlation between the variables.

Question 14

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

Accepted Answer

$$\rho = \frac{\sum (x_i - \mu_x)(y_i - \mu_y)}{N \sigma_x \sigma_y}$$

Question 15

Which of the following is a property of the linear correlation coefficient $$r$$?

Accepted Answer

$$r is $$sensitive to outliers.

Question 16

A researcher finds $$r = 0.55156$$ with $$n = 134$$ and $$r_{critical} = \pm 0.16967. $$What does this indicate?

Accepted Answer

There is a significant positive linear correlation.

Question 17

Which of the following is an example of using data based on averages that may inflate the correlation coefficient?

Accepted Answer

Calculating the correlation between regional average incomes and education levels instead of individual data.

Question 18

If $$r = 0.074$$ for a data set, what does this indicate about the relationship between the variables?

Accepted Answer

There is no linear correlation.

Question 19

Which of the following is the best course of action if you suspect a nonlinear relationship between two variables?

Accepted Answer

Generate a scatterplot to visually inspect the relationship.

Correlation: Concepts, Calculation, and Interpretation

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