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Chapter 20 – Data Analysis: Analyzing Multiple Variables Simultaneously
Multiple Choice
a 1. Which of the following is a technique that measures the closeness of the relationship between two or more variables by considering their joint variation?
a. Correlation analysis
b. Analysis of variance
c. Multiple regression analysis
d. z-test
e. F-test
c 2. Which of the following is a technique that measures the association between a criterion variable and one or more independent variables?
a. Correlation analysis
b. Analysis of variance
c. Regression analysis
d. z-test
e. F-test
b 3. Graphic representations of the criterion variable as the function of each of the predictor variables are called
a. predictor plots.
b. scatter diagrams.
c. probability plots.
d. criterion diagrams.
e. cartesian diagrams.
c 4. Which of the following statements about regression/correlation analysis is FALSE?
a. Correlation analysis involves the measurement of the closeness of the relationship between two or more variables.
b. Regression analysis involves the derivation of an equation that relates the criterion variable to one or more predictor variables.
c. Regression analysis can establish the causal relationship between two or more variables.
d. The regression line minimizes the sum of the squared deviations about the line.
e. It is much more common to conduct regression analyses using a computer.
d 5. Which of the following emphasizes the division of the sample into subgroups so as to learn how the dependent variable varies from subgroup to subgroup?
a. Longitudinal analysis
b. Coding
c. Crosssectional analysis
d. Cross tabulation
e. Oneway tabulation
d 6. In a simple regression equation, the a value refers to the
a. average value of the criterion variable.
b. slope of the regression line.
c. confidence level.
d. intercept of the regression line with the y-axis.
e. Terror term.
c 7. The error term in the regression model represents
a. a constant.
b. the standard error of the model.
c. all factors that determine the criterion variable that are not part of the model.
d. the coefficient of correlation.
e. nonsampling error.
b 8. Given a cross tabulation between years of education and income, we would compute percentages in the direction of years of education because
a. the probability that given X income you will have Y years of education makes sense.
b. the probability that given X years of education you will have Y income makes sense.
c. it doesn't matter which way you do it.
d. Both a and b.
e. None of the above.
Use the following information for the next three questions.
A researcher is interested in comparing the usage of bank debit cards by consumers in rural (r) and urban (u) areas. Each year for the past five years, she has surveyed 500 individuals (onehalf urban, one-half rural) randomly selected from across the United States. She is specifically interested in any differences that may exist between the two groups with regard to usage. The results of the current study indicate that people in urban areas use bank debit cards 12 times per month on average (u), while those in rural areas use bank cards 10 times per month on average (r).
c 9. Which of the following is the null hypothesis that the researcher should use in comparing the usage rates?
a. H0: u = r
b. H0: u - r = mu mr
c. H0: mu = mr
d. H0: mu > mr
e. Ha: u ¹ r
b 10. Assuming that the standard error of estimate for the difference in means is 1.5, calculate the value of the test statistic that would be used in the comparison of the two means.
a. 0.75
b. 1.33
c. 1.88
d. 1.96
e. None of the above.
c 11. Given that the critical value that the test statistic is to be compared with is equal to 1.645 at a 90% significance level, which of the following statements are true?
a. The researcher should reject the null hypothesis at the 90% significance level.
b. The researcher might be able to reject the null hypothesis at the 95% level of significance.
c. The researcher cannot reject the null hypothesis at this significance level.
d. The researcher has provided evidence that people in urban areas use bank debit cards more than people in rural areas.
e. More information is needed before a decision about the null hypothesis can be made.
Use the following information to answer the next two questions.
Suppose that the relationship between sales (Y, in $000) and number of salespeople (X) is represented by the following regression equation:
Y = 105.2 + 35.8X
c 12. What will be the average contribution to sales of one additional salesperson?
a. $35.80
b. $141,000
c. $35,800
d. $141.00
e. More information is needed to answer this question.
d 13. What will average sales be equal to when 10 salespeople are used?
a. $358,000
b. $463.20
c. $358.00
d. $463,200
e. More information is needed to answer this question.
c 14. Suppose the ordinary least-squares approach to a regression analysis produced the following
Y = 20 39X
R2 = .90
Which of the following statements is FALSE?
a. For every unit change in X there is a corresponding negative change in the average value of Y of 39 units.
b. 90 percent of the variation in Y is associated with variation in X.
c. The slope of the line is 20.
d. The average value of Y given x = 10 is 370.
e. If X = 0, then Y = 20.
e 15. What conclusion(s) can you make from the following cross tabulation?
Ever Divorced / 1 or less / 2 to 4 / 5 or more
Yes / 9% / 63% / 92%
No / 91% / 37% / 8%
Total / 100% / 100% / 100%
a. Having more children increases the divorce rate.
b. Getting divorced makes a couple have more children.
c. The more children a person has the more likely s/he is to be divorced.
d. All of the above can be correctly concluded from the cross-tabulation.
e. None of the above can be concluded from the cross-tabulation.
c 16. An analyst has a set of normally distributed intervally scaled data resulting from two observations on the same sample of subjects, and he wishes to investigate if there is any difference in these two means. The appropriate statistical procedure is
a. ztest for difference in two means.
b. analysis of variance.
c. paired samples ttest.
d. chisquare goodnessoffit test.
e. regression analysis.
c 17. If the correlation between two variables x and y is equal to 0.90, which of the following is TRUE?
a. x and y are highly related, whereby a positive change in x is accompanied by a positive change in y.
b. The two variables x and y are not related to one another.
c. x and y are highly related, whereby a negative change in x is accompanied by a positive change in y.
d. The coefficient of determination is equal to 0.81.
e. An increase in x is accompanied by a decrease in y.
e 18. A researcher wishes to test for differences in the means of two populations, A and B. The correct statement of the statistical hypotheses is
a. H0: mA > mB; Ha: mA < mB.
b. H0: mA ¹ mB; Ha: mA = mB.
c. H0: mA < mB; Ha: mA > mB.
d. H0: mA < mB; Ha: mA > mB.
e. H0: mA = mB; Ha: mA ¹ mB.
b 19. The value of the productmoment coefficient of correlation ranges from
a. 1.0 to 0.0.
b. 1.0 to 1.0.
c. 0.5 to 0.5.
d. 0.0 to 1.0.
e. ¥ to ¥.
b 20. In order to use the pooled sample variance when testing the difference in two population means, what must be assumed?
a. The sample means are unbiased estimates of the population means.
b. The population variances are equal.
c. The population means are equal.
d. The population variances are inversely proportional.
e. The sample means are unequal.
c 21. An analyst has a set of normally distributed intervally scaled data resulting from two observations on the same sample of subjects, and he wishes to investigate if there is any difference in these two means. The appropriate statistical procedure is
a. z-test for difference in two means.
b. Analysis of variance.
c. Paired sample t-test.
d. Chisquare goodnessoffit test.
e. Regression analysis.
e 22. When performing cross tabulations, percentages are always calculated in the direction of the
a. dependent variable.
b. independent variable.
c. causal variable.
d. Both a and b.
e. Both b and c.
c 23. In testing a multiple regression equation for statistical significance, the first step involves
a. testing the intercept term using a t-test.
b. using a t-test to examine the significance of the overall equation.
c. using an F-test to examine the significance of the overall equation.
d. testing each of the slope coefficients using a t-test.
e. testing each of the slope coefficients using an F-test.
d 24. Which of the assumptions listed below are necessary, in order for the coefficients in a partial regression equation to be interpreted as the average change in the criterion variable associated with a unit change in the appropriate predictor variable holding other predictor variables constant?
a. The predictor variables must be correlated.
b. The variance among predictor variables must be equal.
c. The criterion variable must be normally distributed.
d. The predictor variables must be uncorrelated.
e. None of the above are necessary assumptions.
d 25. Assuming the two predictors X1 and X2 are not correlated, the coefficients of
^ ^
partial regression, ßY1.2 and ßY1.3, can be interpreted as the
a. unit change in the criterion variable associated with an average change in the appropriate predictor variable while holding the other predictor variable constant.
b. change in the criterion variable associated with an average change in the predictor variables.
c. average change in the criterion variable associated with an average change in the appropriate predictor variable while holding the other predictor variable constant.
d. average change in the criterion variable associated with a unit change in the appropriate predictor variable while holding the other predictor variable constant.
e. average change in the criterion variable associated with a unit change in the appropriate predictor variable.
d 26. Multicollinearity is said to be present in a regression problem if the
a. predictor variables are independent.
b. criterion variables are independent.
c. criterion variables are correlated among themselves.
d. predictor variables are correlated among themselves.
e. error terms are correlated.
Use the following table to answer the next four questions.
Family Size and Ownership of a Microwave by Household(Figures in millions of households)
OWN A MICROWAVE
Family Size / Yes / No / Total
Less than 4 / 15 / 30 / 45
4 or more / 27 / 28 / 55
TOTAL / 42 / 58 / 100
b 27. The above table is an example of
a. oneway classification.
b. cross tabulation.
c. oneway tabulation.
d. fourway classification.
e. threeway cross tabulation.
d 28. The most appropriate way to calculate percentages in the above table to reflect cause and effect is by dividing
a. each of the entries by 100.
b. 45 and 55 by 100.
c. 42 and 58 by 100.
d. entries in the first row by 45 and those in the second row by 55.
e. entries in the first column by 42 and those in the second column by 58.
c 29. In absolute numbers, how many millions of households own a microwave?
a. 15 million
b. 100 million
c. 42 million
d. 55 million
e. 27 million
e 30. What relationship can be inferred from the above table between family size and owing a microwave?
a. Nothing can be inferred.
b. The smaller the family the more likely they are to own a microwave.
c. A lower proportion of large families (4 or more) own microwaves than small families.
d. Owning a microwave causes family size to increase.
e. Ownership of a microwave tends to increase as family size increases.
e 31. Which of the following is FALSE about cross tabulations?
a. Cross tabulations work equally well with continuous measures that have been recast as categorical measures.
b. Cross tabulations are used for studying the relationships between two (or more) categorical variables.
c. Recasting continuous measures into categories may result in lowered statistical power.
d. Cross tabulation seeks to investigate the influence of the independent variable on the dependent variable.
e. Recasting continuous measures into categories almost never results in the loss of information.
e 32. Consider the regression equation Y = 5 + 16X1 + 38X2 relating annual expenditures on a particular product Y to X1 and X2, where
X1 X2
__ __
If a person belongs to lower class 0 0
If a person belongs to middle class 1 0
If a person belongs to upper class 0 1
Which of the following is FALSE? The equation suggests
a. An upper class person could be expected on the average to spend $38 per year more than a lower class person on the product.
b. A middle class person could be expected on the average to spend $16 more per year on the product than a lower class person.
c. A lower class person could be expected on the average to spend $5 per year on the product.
d. An upper class person could be expected on the average to spend $22 more per year on the product than a middle class person.
e. An upper class person could be expected on the average to spend $38 per year on the product.
d 33. The upper limit of the Pearson chi-square test of independence is limited by
a. sample size.
b. the distribution of cases across the cells.
c. degrees of freedom.
d. Both a and b.
e. a, b, and c.
c 34. Which of the following concerning the Pearson chi-square test is FALSE?