Question 1

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

Accepted Answer

The coefficients of partial regression represent the average change in the criterion variable associated with a unit change in the appropriate predictor variable while holding the other predictor variable constant. This is because partial regression coefficients are calculated by controlling for the effects of other variables, meaning that the coefficient for a given predictor variable reflects its unique contribution to the criterion variable. Therefore, choice D correctly describes the interpretation of the partial regression coefficients in the context of the given assumption.

Question 2

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.

Accepted Answer

The answer of A popular approach to measuring the strength...

Question 3

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 these statements concerning the Pearson chi-square test are true.

Accepted Answer

The Pearson chi-square test does not measure the degree of association between variables; it tests whether there is a significant association or independence between categorical variables.

Question 4

Which statistical technique should you use to answer the question: "Is there a significant relation-ship 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 these are correct.

Accepted Answer

Chi-square tests are commonly used to test the relationship between two categorical variables, in this case, education level and awareness of Firestone as a brand of tires. The other options, such as multiple and simple regression analysis and Pearson correlation coefficient, are more appropriate when the variables are continuous or when examining the relationship between two continuous variables.

Question 5

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

Accepted Answer

The experiment involves two independent samples (red package group and blue package group) and the aim is to compare the preferences between the two groups. Therefore, an independent samples t-test for means is the most appropriate technique for analyzing the data. Choice A (paired sample t-test for means) is not suitable because the two groups are independent. Choice B (Spearman rank-order correlation analysis) and E (correlation analysis) are not suitable because the experiment is not looking for a relationship between two variables, but rather a difference between two groups. Choice C (regression analysis) is not suitable because there is only one independent variable (package color) and one dependent variable (sales preference).

Question 6

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)sample size and distribution of cases across the cells.
E)sample size and degrees of freedom.

Accepted Answer

The upper limit of the Pearson chi-square test of independence is influenced by both the sample size and the distribution of cases across the cells. A larger sample size and a more even distribution of cases can increase the power of the test, while a smaller sample size or a skewed distribution can limit it.

Question 7

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

Accepted Answer

Regression analysis is the best choice for this scenario as it allows the researcher to analyze the relationship between two variables and make predictions based on that relationship. In this case, the researcher can use regression analysis to determine how per capita income and automobile ownership relate to market size, allowing them to estimate market size in these ten Asian countries.

Question 8

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 these are correct.

Accepted Answer

The answer of Which statistical technique should you use when...

Question 9

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

Accepted Answer

The answer of A gas station wants to compare a...

Question 10

If a = 0.152 and b = 1.32,the simple regression equation is
A)Yi = 1.32 − 0.152 Xi
B)Yi = 0.152 + 1.32 Xi
C)Yi = 0.152 − 1.32 Xi
D)Yi = 0.152/1.32 + Xi
E)None of these are correct.

Accepted Answer

The simple regression equation is Y = a + bX, where Y is the dependent variable (in this case, Yi), X is the independent variable, a is the intercept (in this case, a = 0.152), and b is the slope (in this case, b = 1.32). Therefore, the equation would be Yi = 0.152 + 1.32 Xi.

Question 11

A research study involving the research question: "On the basis of a survey of husband-wife house-holds,is there a significant difference between the mean attitude score of husbands and that of wives toward our product?" will involve a test
A)for a single proportion.
B)of two means when samples are independent.
C)for a single mean.
D)of two means when samples are dependent.
E)None of these are correct.

Accepted Answer

This research question involves comparing the mean attitude scores of two related groups (husbands and wives within the same households), which means the samples are dependent, not independent. Therefore, a test of two means when samples are dependent is appropriate.

Question 12

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)None of these are correct.
E)All of these are correct.

Accepted Answer

The answer of If the null hypothesis of no differences...

Question 13

In ANOVA,the independent variables are typically called
A)treatments.
B)factors.
C)F-statistics.
D)causal variables.
E)tabulations.

Accepted Answer

In ANOVA, the independent variables are typically referred to as factors, as they represent the different categorical or continuous variables that are being tested for their effect on the dependent variable. The term "treatments" is also sometimes used interchangeably with factors, but it specifically refers to the different levels of a factor that are being compared. The terms "F-statistics," "causal variables," and "tabulations" are not typically used to describe the independent variables in ANOVA.

Question 14

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

Accepted Answer

A factorial design in ANOVA allows a researcher to examine the effects of two or more independent variables simultaneously. It involves manipulating two or more independent variables and observing how these variables affect the dependent variable. This design allows researchers to explore interactions between the independent variables as well. The other options listed are not relevant to ANOVA or do not involve examining multiple independent variables.

Question 15

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)is called the cross-products sum and establishes the degree of covariation between two variables.
E)is called the cross-product sum and can range from−1.0 to +1.0.

Accepted Answer

The numerator in the Pearson product-moment correlation coefficient formula is called the cross-products sum and establishes the degree of covariation between two variables. Additionally, it can range from −1.0 to +1.0.

Question 16

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 ∞.

Accepted Answer

Cramer's V is a measure of association between two nominal variables, giving a value between 0 and 1, where 0 means no association and 1 indicates a perfect association.

Question 17

When comparing the independent samples t-test for means and the paired sample t-test for means,one is for
A)univariate analysis while the other is for multivariate analysis.
B)small sample sizes while the other is for large sample sizes.
C)continuous variables while the other is for categorical variables.
D)measures from separate groups while the other is for measures from the same group.
E)All of these are correct.

Accepted Answer

The independent samples t-test is used to compare the means of two separate groups, while the paired sample t-test is used to compare the means of the same group at two different points in time or under two different conditions. Therefore, D is the correct choice as it accurately describes the difference between these two tests. Choices A, B, and C are not correct because they do not accurately describe the difference between these two tests.

Question 18

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 these are necessary assumptions.

Accepted Answer

The correct assumption necessary for the coefficients in a partial regression equation to be interpreted as described is that the predictor variables must be uncorrelated (D). This ensures that the change in the criterion variable can be attributed to the change in the predictor variable of interest, holding other variables constant, without the interference of multicollinearity.

Question 19

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 test of
A)a single proportion.
B)a single mean.
C)two means.
D)two proportions.
E)None of these are correct.

Accepted Answer

Since the measurement being taken is in pounds per household, it involves means. Also, since there are two towns being compared, the appropriate test would involve comparing the means of the two towns. Therefore, the correct choice would be a test of two means.

Question 20

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.

Accepted Answer

The answer of Which of the following is FALSE about...

Quiz 18: Analysis and Interpretation: Multiple Variables Simultaneously

Assuming the two predictors X1 and X2 are not correlated,the coefficients of partial regression can be interpreted as the

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

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

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

The upper limit of the Pearson chi-square test of independence is limited by

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?

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 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

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

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

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

In ANOVA,the independent variables are typically called

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

The numerator in the Pearson product-moment correlation coefficient formula

Cramer's V is scaled to range between

When comparing the independent samples t-test for means and the paired sample t-test for means,one is for

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?

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 test of

Which of the following is FALSE about cross tabulations?