Test Bank

Chapter 13: Introduction: Hypothesis Testing With Two Continuous Variables: Correlation

Multiple Choice

1. The bivariate hypothesis-testing procedure that is used when both the independent and dependent variables are continuous is ______.

A. pearson’s correlation

B. Ω²

C.cramer’s V

D. t test

2. Bivariate relationships represented by correlations are ______.

A. linear

B. nonlinear

C.normal

D. bifurcated

3. When an independent variable increases by one unit and a dependent variable increases by one unit that is said to be ______.

A. a perfect negative correlation

B. a perfect positive correlation

C.a positive correlation

D. a nonlinear correlation

4. What is the test statistic for correlation?

A. r

B. ω z

C.μ µ

D. λ X²

5. The range of the correlation test statistic is ______.

A. 0 to 1

B. dependent upon the alpha level

C.the same as the degrees of freedom for the primary analytic test being conducted

D. −1 to +1

6. The population correlation coefficient is ______.

A. ρ

B. Λ

C.ρ

D. ϕ

7. A perfect correlation is indicated by which of the following?

A. 0

B. 0.5

C.±1

D. 0.05

8. What do correlations less than zero signify?

A. negative relationships

B. positive relationships

C.no relationships

D. nonlinear relationships

9. Which theoretical distribution is used in correlation?

A. z distribution

B. t distribution

C.χ² distribution

D. No theoretical distribution is used.

10. What is the null hypothesis for correlation?

A. H₀: ρ μ₁ = ρ μ₂

B. H₀: η₁ = η₂

C. H₀: ρ₁ = ρ₂

D. H₀: ρ = 0

11. Which of the following alternative hypotheses represents a two-tailed or nondirectional test in correlations?

A. H₁: ρ μ₁ ≠ ρ μ₂

B. H₁: ρ > 0

C. H₁: ρ < 0

D. H₁: ρ ≠ 0

12. An evaluation of the strength of the relationship between the two variables under study is accomplished by an examination of ______.

A. the significance of the z coefficient

B. the sign of the correlation coefficient

C.the magnitude of the correlation coefficient

D. the significance of the t coefficient

13. The coefficient of determination is defined as ______.

A. the magnitude adjustor for the theoretical distribution used in correlation

B. the statistical significance of the rho coefficient

C.the statistical significance of the correlation coefficient

D. the percentage of the variance in the dependent variable that is attributable to the independent variable

14. The coefficient of determination is symbolized by which of the following?

A. r

B. r²

C.t

D. t²

15. What is the range of the coefficient of determination?

A. 0.5 to 1.00

B. 0 to −1

C. −1 to +1

D. 0 to 1

16. What would a researcher say about a coefficient of determination equal to −.98?

A. The 98% of variance in my dependent variable can be explained by variance in the independent variable.

B. The 98% of variance in my independent variable can be explained by variance in my dependent variable.

C. Something must be wrong, because it is not possible for a coefficient of determination to be negative.

D. The relationship is not statistically significant due to the low value of the coefficient.

17. University administrators have recently realized that students who tend to spend more time in the library achieve higher grades on their final examinations. What type of relationship would a researcher call this tendency?

A. a positive relationship

B. a negative relationship

C.an inverse relationship

D. There is no correlational relationship between time spent in the library and subsequent final exam grades.

18. Correlational relationships are ______.

A. bivariate in nature

B. nonlinear in nature

C.multivariate in nature

D. curvilinear in nature

19. A researcher conducted a correlational analysis of two variables, number of convenience stores in the area and number of armed robberies committed. The correlational coefficient was found to be 0.87. What should the researcher conclude from this finding?

A. The relationship between convenience store prevalence and armed robbery is very weak.

B. The relationship between convenience store prevalence and armed robbery is curvilinear and relatively weak.

C. The relationship between convenience store prevalence and armed robbery is positive and weak.

D. The relationship between convenience store prevalence and armed robbery is positive and strong.

20. What is the range of the population coefficient in correlation?

A. 0 to −1

B. 0 to +1

C. There is no range, per se, as the population coefficient is established by the α level and the degrees of freedom.

D. −1 to +1

21. In SPSS, the significance of the correlation is represented by the ______ value.

A. p

B. α

C. λ

D. Ω

22. The output table in which the results of a correlation analysis in SPSS are displayed is called a ______ .

A. correlation table

B. correlation matrix

C.correlation graph

D. plotted correlation

23. Because they represent each variable’s correlation with itself, the numbers in the diagonal in a correlation output in SPPS all equal what value?

A. 0

B. .5

C.1.00

D. −1.00

24. In SPSS, the significance value of a correlation is compared to the ______ to determine whether the null hypothesis will be rejected.

A. α level

B. correlation coefficient

C. ρ

D. coefficient of determination

25. In SPSS, the number associated with Pearson’s correlation is represented by what?

A. r²

B. p

C.r

D. none of these

26. An appropriate one-tailed, directional hypothesis for a correlation is ______ .

A. H₁: ρ ρ < 0

B. H₁: ρ ρ = 0

C. H₁: ρ ρ ≤ 0

D. none of these

27. In SPSS, the correlation function is found under the ______ tab.

A.compute

B. regression

C. analyze

D. frequencies

28. The bivariate associations represented by correlations are ______.

A.constant

B. linear

C. quadratic

D. curvilinear

29. When examining the relationship between employment and crime, a correlation coefficient of 0.20 is produced. What is the magnitude of this correlation?

A.weak

B. moderate

C. large

D. extra large

30. When examining the relationship between neighborhood disadvantage and crime, a correlation coefficient of 0.35 is produced. What is the magnitude of this correlation?

A.weak

B. moderate

C. strong

D. very strong

31. When examining the relationship between delinquent peers and crime, a correlation coefficient of 0.60 is produced. What is the magnitude of this correlation?

A.weak

B. moderate

C. strong

D. very strong

32. What is the value of a variable correlated with itself?

A.0.0

B. 0.25

C. 0.50

D. 1.0

33. The statistical significance of r is tested using which of the following distributions?

A. t distribution

B. z distribution

C. f distribution

D. none of these

34. Which of the following is considered in order to determine the substantive/practical meaning of r?

A.sign

B. magnitude

C. coefficient of determination

D. all of these

35. Correlations are what kind of analysis?

A.univariate

B. bivariate

C. multivariate

D. none of these

1. A rejected null hypothesis is not in and of itself an indication that the variables are strongly correlated.

2. A nonlinear correlation occurs when an independent variable increases by one unit but the dependent variable fails to change.

3. A correlation greater than 1 indicates a perfect relationship.

4. The appropriate degrees of freedom for the distribution used in correlation is df = N – k.

5. The sign of the correlation indicates whether the correlation between the independent variable and dependent variable is negative or positive.

6. The greater the value of the coefficient of determination, the stronger the relationship between the two variables.

7. It is appropriate to model nonlinear relationships using correlational analysis.

8. The method for conducting a correlational analysis is to first calculate the correlation test statistic and then test for the statistical significance by comparing t_crit and t_obt.

9. Correlation employs the z distribution because this probability distribution adequately mirrors the sampling distribution of the correlation test statistic for small and large sample sizes.

10. In correlation, there are three options available for the phrasing of the alternative hypothesis.

11. The curve of the theoretical probability distribution used in correlation is symmetrical.

12. In correlation, if a researcher is conducting a one-tailed test, then there are two critical values.

13. Correlation is a relatively quick way to test for causality as well as statistical significance.

14. In correlation, the null hypothesis can be rejected even when a correlation is of little practical importance.

15. In correlation, there are very rigid, preestablished guidelines for interpreting the test statistic.

16. Pearson’s correlation was developed by Karl Pearson.

17. When an independent variable increases by one unit and a dependent variable decreases by one unit, then the two variables are positively correlated.

18. An independent variable-dependent variable relationship is curvilinear when the change in the dependent variable associated with a one-unit increase in the independent variable remains constant across all levels of the independent variable.

19. Correlations of zero are indicative of no relationship between the variables under study.

20. Correlations less than zero signify negative relationships.

1. A professor calculated a correlation coefficient of 0.65 in a recent analysis. Based on this value, what percentage of variance in the dependent variable is attributable to the independent variable?

2. Describe how to calculate the coefficient of determination.

3. For the data below, write an appropriate two-tailed, nondirectional null and alternative hypothesis, calculate the df, and find the critical value.

X Y

Years of Education Number of Arrests

12 5

9 9

17 0

15 0

13 2

10 6

4. For the data below, calculate the correlation test statistic.

X Y

Years of Education Number of Arrests

12 5

9 9

17 0

15 0

13 2

10 6

5. Now finish the correlation from above by calculating the coefficient of determination and making a decision about the null hypothesis.

r² = .90

t = –.95√6-2/1–..9

= –.95√4/.10

= –6.01

Remember, the critical value = 2.228 (and –2.228) with df = 10 and α =. 05.

Our test statistic of –6.01 is greater than the critical value, therefore the correlation is statistically significant.

There is a relationship between years of education and number of arrests.

The negative relationship indicates that the more years of education an individual has, the lower his or her subsequent number of arrests.

Cognitive Domain: Application

Answer Location: Beyond Statistical Significance: Sign, Magnitude, and Coefficient of Determination

Difficulty Level: Medium