Deck 20: Data Analysis: Analyzing Multiple Variables Simultaneously

Question 1

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.

Answer 1

C

Question 2

The value of the product-moment 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 ¥.

Answer 2

B

Question 3

Exhibit 20.1 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 (one-half 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 ( ),while those in rural areas use bank cards 10 times per month on average ( ).
Refer to Exhibit 20.1.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.

Answer 3

B

Question 4

Exhibit 20.2 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
Refer to Exhibit 20.2.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.

Question 5

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.

Question 6

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.

Question 7

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

Question 8

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.

Question 9

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 samples t-test.
D)chi-square goodness-of-fit test.
E)regression analysis.

Question 10

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.

Question 11

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.

Question 12

Exhibit 20.1 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 (one-half 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 ( ),while those in rural areas use bank cards 10 times per month on average ( ).
Refer to Exhibit 20.1.Which of the following is the null hypothesis that the researcher should use in comparing the usage rates?

A)
B)
C)
D)
E)

Question 13

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.

Question 14

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

Question 15

Exhibit 20.1 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 (one-half 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 ( ),while those in rural areas use bank cards 10 times per month on average ( ).
Refer to Exhibit 20.1.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.

Question 16

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.

Question 17

What conclusion(s)can you make from the following cross tabulation?

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.

Question 18

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)Chi-square goodness-of-fit test.
E)Regression analysis.

Question 19

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)Cross-sectional analysis
D)Cross tabulation
E)One-way tabulation

Question 20

Exhibit 20.2 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
Refer to Exhibit 20.2.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.

Question 21

A gas station wants to compare a group of consumers' overall perceptions of service with overall perceptions of service for a nearby competitor.This situation calls for the use of

A)paired sample t-test for means.
B)analysis of variance.
C)regression analysis.
D)independent samples t-test for means.
E)correlation analysis.

Question 22

Consider the regression equation Y = 5 + 16X₁ + 38X₂ relating annual expenditures on a particular product Y to X₁ and X₂,where 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.

Question 23

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.

Question 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.

Question 25

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.

Question 26

Exhibit 20.3 Refer to Exhibit 20.3.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.

Question 27

In ANOVA,the independent variables are typically called

A)treatments.
B)factors.
C)F-statistics.
D)causal variables.
E)tabulations.

Question 28

When using the z-test to compare proportions,the minimum cell size required is

A)10 per cell.
B)11 per cell.
C)20 per cell.
D)30 per cell.
E)70 per cell.

Question 29

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.

Question 30

Assuming the two predictors X₁ and X₂ are not correlated,the coefficients of partial regression, and ,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.

Question 31

A gum manufacturer wants to determine whether blue packaging or red packaging is preferred.The company performs a sales test by introducing red packages into a random sample of ten stores and blue packages are introduced in an independent,random sample of ten stores.The technique most appropriate for analyzing the data is

A)paired sample t-test for means.
B)Spearman rank-order correlation analysis.
C)regression analysis.
D)independent samples t-test for means.
E)correlation analysis.

Question 32

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.

Question 33

Exhibit 20.3 Refer to Exhibit 20.3.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.

Question 34

Exhibit 20.3 Refer to Exhibit 20.3.The above table is an example of

A)one-way classification.
B)cross tabulation.
C)one-way tabulation.
D)four-way classification.
E)three-way cross tabulation.

Question 35

Which of the following concerning the Pearson chi-square test is FALSE?

A)The Pearson chi-square test is conceptually similar to the chi-square goodness-of-fit test.
B)The Pearson chi-square test tests the null hypothesis that the variables are independent.
C)The Pearson chi-square test measures the degree of association between variables.
D)The Pearson chi-square test assesses the degree to which the two variables in a cross tabulation analysis are independent of one another.
E)All of the above statements concerning the Pearson chi-square test are true.

Question 36

Analysis of variance (ANOVA)is most applicable when there

A)are only two means being compared.
B)is exactly one categorical variable to be considered.
C)are more than two means being compared.
D)is the potential for a causal relationship between a continuous independent variable and a categorical dependent variable.
E)is a need to examine interjudge reliability.

Question 37

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.

Question 38

Cramer's V is scaled to range between

A)0.0 and 1.0.
B)-1.0 and 0.0.
C)-1.0 and 1.0.
D)0.0 to ¥.
E)-¥ to ¥.

Question 39

Exhibit 20.3 Refer to Exhibit 20.3.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

Question 40

A popular approach to measuring the strength of the relationship between two categorical variables is

A)cross tabulation.
B)Pearson chi-square test of independence.
C)Cramer's V.
D)regression analysis.
E)Kendall's coefficient of concordance.

Question 41

Which statistical technique should you use when you are attempting to answer the question: "Is there a significant relationship between the customers' disposable income (measured in dollars)and their repeat-buying behavior (measured by the number of rebuys in a twelve-month period)?"

A)Multiple regression analysis
B)Chi-Square test
C)Simple regression analysis
D)Pearson correlation coefficient
E)None of the above.

Question 42

The numerator in the Pearson product-moment correlation coefficient formula

A)is called the cross-products sum.
B)establishes the degree of covariation between two variables.
C)can range from -1.0 to +1.0.
D)Both a and b.
E)Both b and c.

Question 43

If we were comparing the difference between the mean number of sports drinks consumed by male vs.female athletes during a typical week and we calculated a z value of 4.33,we would conclude that the probability of support of the

A)null hypothesis of no difference is less than < 0.01 because 4.33 is greater than 2.58.
B)alternative hypothesis of no difference is less than < 0.01 because 4.33 is greater than 2.58.
C)null hypothesis of no difference is less than < 0.01 because 4.33 is less than 2.58.
D)alternative hypothesis of no difference is less than < 0.01 because 4.33 is less than 2.58.
E)None of the above.

Question 44

Let's assume we find in a study that the Pearson's correlation coefficient between number of years of education and cigarette smoking is -0.73.This means that as education level increases

A)smoking tends to increase.
B)smoking tends to decrease.
C)smoking changes 73%.
D)education and smoking are unrelated.
E)an educated person smokes 73 cigarettes a day.

Question 45

When a computed z-value (for a test for differences between two percentages),say 4.51,is larger than the standard z-value,say 1.96,then this amounts to

A)support for the null hypothesis;the two percentages are different.
B)no support for the null hypothesis;the two percentages are not different.
C)support for the null hypothesis,the two percentages is not different.
D)no support for the null hypothesis;the two percentages are different.
E)None of the above.

Question 46

When independent variables in a multiple regression equation are highly correlated among themselves,it indicates the existence of ____.The statistics used to measure if this exists is called VIF.

A)unstandardized coefficients
B)standardized coefficients
C)multicollinearity
D)standard error
E)standard deviation

Question 47

Let's assume there are sophomores,juniors,and seniors in your marketing research class and we want to know if their average GPAs differ.What is the proper statistical test?

A)t-test
B)z-test
C)Chi-square test
D)ANOVA
E)None of the above.

Question 48

Volvo cars,which have typically been positioned high on the safety attributes wants to know if people will respond favorably to proposed style changes.A sales manager wants to know if salespersons' morale is related to increases in recognition awards.These are questions that may be answered through

A)relationship analysis.
B)chi-square analysis.
C)associative analysis.
D)analysis of variance.
E)causal analysis.

Question 49

Multiple regression analysis is useful when there are ____ independent variable(s)and ____ dependent variable(s).

A)more than one,one
B)one,more than one
C)more than one,more than one
D)one,one
E)None of the above.

Question 50

In which of the following situations would it be useful to test for differences between two groups?

A)A retailer wishes to know if customer satisfaction is different between in-store v.online shoppers.
B)A beverage company wants to know if a new beverage concept differs between users v.nonusers of the current brand.
C)A department store wishes to know the differences between online catalogs vs.mail order catalog shoppers.
D)A state university ants to know is there is a significant difference in GPA between undergraduate and graduate students.
E)All of the above situations would benefit from tests for differences between two groups.

Question 51

If a = 0.152 and b = 1.32,the simple regression equation is

A)Y_i = 1.32 - 0.152 X_i
B)Y_i = 0.152 + 1.32 X_i
C)Y_i = 0.152 - 1.32 X_i
D)Y_i = 0.152/1.32 + X_i
E)None of the above.

Question 52

In ANOVA,a ____ allows a researcher to examine simultaneously the effects of two or more independent variables.

A)cross tabulation
B)scatter diagram
C)correlation coefficient
D)factorial design
E)coefficient of determination

Question 53

Assume that a researcher determines that a p-value of 0.01 or below determines significance.Listed below are several correlation coefficients and their respective significance levels.Which correlation coefficient demonstrates an association not likely due to chance (i.e. ,significant)?

A)0.22,0.06
B)0.75,0.00
C)-0.32,0.15
D)-0.76,0.95
E)0.26,0.10

Question 54

Suppose you were given an example of running a chi-square test using SPSS.The output shows a "Pearson Chi-Square" value of 82.123,df = 3 and the Asymp.Sig.= 0.000.This means

A)there is a significant association.
B)there is no significant association.
C)the difference is associative.
D)the means are not equal.
E)the variances are equal.

Question 55

Post-hoc test (e.g. ,LSD,Duncan's multiple comparison/range test)are used for determining the

A)significance of association among groups of related variables.
B)differences between means when ANOVA has produced a significant F-value.
C)differences between means when ANOVA has produced an insignificant F-value.
D)casual relationship between two nominal variables.
E)None of the above;none of these are statistical tests.

Question 56

If the null hypothesis of no differences across groups is true,

A)total variation should be equal to between-group variation.
B)between-group variation should be equal to within-group variation.
C)within-group variation should be equal to total variation.
D)Both a and b.
E)a,b,and c.

Question 57

A research study involving the research question: "On the basis of a survey of husband-wife households,is there a significant difference between the mean attitude score of husbands and that of wives toward our product?" will involve a

A)test for a single proportion.
B)test of two means when samples are independent.
C)test for a single mean.
D)test of two means when samples are dependent.
E)None of the above.

Question 58

Which statistical technique should you use to answer the question: "Is there a significant relationship between education level (a four-category ordinal variable)and whether or not consumers are aware that Firestone is a brand of tires?"

A)Multiple regression analysis
B)Pearson correlation coefficient
C)Chi-square test
D)Simple regression analysis
E)None of the above.

Question 59

If an organization selects two towns for a market study (one for the test and the other as a control)and measures the amount of trash in pounds per household,it must first determine the equality of the two towns using a

A)test of a single proportion.
B)test of a single mean.
C)test of two means.
D)test of two proportions.
E)None of the above.

Question 60

If a researcher were to take ten Asian countries where per capita income and automobile ownership by per capita were known,trying to find the overall picture of market size for the market could probably be done by using which of the following methods?

A)Analogy method
B)Latin square
C)Trade audit
D)Chain ratio method
E)Regression analysis

Question 61

The NFL office discovered data covering attendance at professional football games in the late 1940s and early 1950s.The game with the highest attendance was between the St.Louis Cardinals and the New York Giants.The office also found considerable information that someone had collected on each game day such as the level of GDP,the DOW,numbers of persons employed,number of new businesses formed during the week preceding the game,and the population.A student intern took the information and built a regression model to predict game attendance for the upcoming season.The model should

A)accurately predict game attendance.
B)NOT predict game attendance accurately because the variable levels of today (i.e. ,population,Dow,etc. )are out of range of those used to build the regression model.
C)predict game attendance accurately because the variable levels of today (i.e. ,population,Dow,etc. )are out of range of those used to build the regression model.
D)predict game attendance accurately because the variable levels (i.e. ,population,Dow,etc. )are within range of those used to build the regression model.
E)None of the above.

Question 62

The error term in the regression model represents all factors that determine criterion variable that are not part of the model.

Question 63

A statistic used to measure the strength of relationship between categorical variables is called a Cramer's V.

Question 64

Carters,a marketer of children appeal,knows that as girls increase in age,their dress size tends to get larger.This is an example of a causal type of relationship?

Question 65

The manager of New England Patriots conducted a large survey.He wanted to know if there was an association between fans being "season ticket holders" vs."non-season ticket holders" and whether they "bought" vs."didn't buy" team merchandise at the game.Since his survey included these measurements,he used SPSS to run a Pearson correlation coefficient that turned out to be 0.88 with a Sig.value of .001.This meant there is a significant relationship.

Question 66

All other variables held constant,a 95% confidence interval will give us a narrower range than will a 99% confidence interval.

Question 67

The magnitude of the Pearson correlation coefficient indicates the direction of association,while its sign indicates the strength of the association.

Question 68

A toy storeowner hypothesizes,at the 95% level of confidence,that parents spend less than $100 on toys per visit to her store.A sample is taken and the hypothesis test shows a z value of -1.65.We accept the hypothesis:

Question 69

In the chi-square analysis,the greater the differences between the observed frequencies and the expected frequencies,the less likely it is that there will be a statistically significant relationship.

Question 70

If the F-value in ANOVA produces a significantly high p-value (a.k.a."Sig." in SPSS)of 0.11 or more,then it is appropriate to proceed with a post-hoc test (e.g. ,Duncan).

Question 71

Olive Garden restaurants know that customers drink beverages for lunch and alcoholic drinks at supper.This is an example of an associative type of relationship?

Question 72

The coefficient of determination represents the relative proportion of the total variation in the outcome variable that can be accounted for by the predictor variable in the regression.

Question 73

Multicollinearity is said to be present in a regression problem if the criterion variables are independent.

Question 74

In multiple regression analysis,t tests are used to test for the statistical significance of betas.If a beta is insignificant,it means that its respective independent variable plays no meaningful role in predicting the dependent variable and the independent variable should be "removed" from the model.

Question 75

In a regression analysis,determining the statistical significance of the slope involves the use of the t-statistic.

Question 76

Percentages are always calculated in the direction of the causal variable.

Question 77

The simple regression technique in SPSS,not the researcher,specifies which variable should be the independent variable and which one should be the dependent variable.

Question 78

If you have a significant and very strong (e.g. ,> 0.90 correlation coefficient),you may assume there is a causal relationship between the two variables.

Question 79

The multiple R,also called the coefficient of determination,in multiple regression ranges from 0.00 to +1.00 and represents the amount of the dependent variable "explained" by the combined independent variables.

Question 80

Cross tabulation work equally will with continuous measures that have been recast as categorical measures.