Question 1

A researcher hypothesizes that males and females differ with respect to attitude toward sports sponsorships.To investigate this hypothesis that these two groups' attitudes differ,the researcher will use a ____.
A)bivariate test of differences
B)univariate test of differences
C)multivariate test of differences
D)cluster analysis

Accepted Answer

A bivariate test of differences is appropriate when comparing two groups on one variable. In this case, the researcher is comparing the attitudes of males and females toward sports sponsorships, which is a single variable. Therefore, a bivariate test of differences is the most suitable choice.

Question 2

How many degrees of freedom are there in a four-cell chi-square test?
A)(R + 1)
B)(R - 1)
C)(R - 1)(C - 1)
D)R(C - 1)

Accepted Answer

The formula for degrees of freedom in a chi-square test with R rows and C columns is (R - 1)(C - 1). In a four-cell chi-square test, there is only one row and one column, so the formula simplifies to (1-1)(1-1) = 0. However, since there must be at least one degree of freedom for the test to be valid, the actual degrees of freedom in a four-cell chi-square test is (1-1)(1-1) + 1 = 1. Therefore, the correct choice is C, which corresponds to the formula for degrees of freedom in a chi-square test with more than one row and column.

Question 3

When the on-time performance of airlines is used to predict the number of customer complaints in a regression equation,on-time performance is the ____ variable and the number of customer complaints is the ____ variable.
A)independent;dependent
B)dependent;dependent
C)dependent;independent
D)independent;predictor

Accepted Answer

In a regression equation, the independent variable is the predictor variable and the dependent variable is the variable being predicted. In this case, the on-time performance is being used to predict the number of customer complaints, so on-time performance is the independent (predictor) variable and the number of customer complaints is the dependent variable. Therefore, the correct choice is A) independent; dependent.

Question 4

In comparing the difference of the means between two groups,the null hypothesis can also be stated as ____.
A)µ₁ - µ₂ = 0
B)µ₁ + µ₂ = 0
C)µ₁ x µ₂ = 0
D)µ₁ / µ₂ = 0

Accepted Answer

The null hypothesis when comparing the difference of means between two groups is typically that there is no difference, which can be expressed as the difference of the two population means (µ₁ - µ₂) equaling zero. Therefore, option A is the correct answer. Option B adds the two means together, which is not appropriate. Option C multiplies the means together, which is also not appropriate. Option D divides the means, which again is not appropriate.

Question 5

In using the Z-test for comparing two proportions,the null hypothesis is typically stated as ____.
A)π₁ = π₂.
B)π₁ ≠π₂.
C)π₁ x π₂ = 1
D)π₁ - π₂= 1

Accepted Answer

The null hypothesis for the Z-test for comparing two proportions is typically stated as π₁ = π₂, meaning that there is no significant difference between two proportions being compared. This is the best choice as it accurately represents the null hypothesis in this scenario. Option B) represents a two-tailed test, which is not specific to the Z-test for comparing two proportions. Option C) represents a multiplication of two proportions, which is not relevant to the null hypothesis. Option D) represents a subtraction of two proportions, which is not the same as the null hypothesis for the Z-test for comparing two proportions.

Question 6

In a brand awareness study,25 of a group of 35 males identify the brand correctly and 15 of a group of 35 females identify this brand correctly.The chi-square value for this study is approximately ____.
A)3.26
B)4.15
C)5.84
D)7.92

Accepted Answer

To find the chi-square value, first calculate the expected values for each group assuming that the brand awareness is the same for both males and females. The expected value for each group is (25+15)/2 = 20. Then, calculate the chi-square value using the formula: (observed-expected)^2/expected. For males, the calculation is (25-20)^2/20 = 1.25. For females, the calculation is (15-20)^2/20 = 1.25. Summing these values gives a chi-square value of 2.5. Using a chi-square table with 1 degree of freedom and an alpha level of 0.05, the critical value is 3.84. Since the calculated value (2.5) is less than the critical value, we fail to reject the null hypothesis that there is no difference in brand awareness between males and females. Therefore, the answer is C) 5.84.

Question 7

The formula given below represents the method for calculating the ____.

A)Z-test
B)F-test
C)ꭓ²test
D)α

Accepted Answer

The given formula is not specific to any test but rather a general formula for calculating the test statistic in a hypothesis test. However, the format of the formula is consistent with the test statistic formula for the ꭓ² test, which is commonly used for analyzing categorical data. Therefore, the best choice would be ꭓ² test.

Question 8

A study compares the means of two groups in which there are 45 males in Group 1 and 37 females in Group 2.The degrees of freedom for this study when using the t-test for the difference between means is ____.
A)74
B)80
C)82
D)160

Accepted Answer

The answer of A study compares the means of two...

Question 9

In a regression equation,the beta coefficients indicate the effect on the dependent variable of a 1-unit increase in any of the independent variables.

Accepted Answer

Beta coefficients represent the change in the dependent variable for every one-unit change in the independent variable, while holding all other independent variables constant.

Question 10

Mulitvariate dependence techniques are variants of the general linear model (GLM).

Accepted Answer

Multivariate dependence techniques, such as multivariate regression and canonical correlation analysis, are considered variants of the GLM framework.

Question 11

The formula for the chi-square test uses ____.
A)observed and expected frequencies
B)observed and expected percentages
C)the two sample means
D)the two sample standard deviations

Accepted Answer

The formula for the chi-square test compares the observed frequencies to the expected frequencies under the null hypothesis of no association. Therefore, it uses both observed and expected frequencies.

Question 12

In multiple regression,dummy variables are those that have no effect on the dependent variable.

Accepted Answer

A dummy variable uses 0 and 1 to code the different levels of a dichotomous variable.

Question 13

In the regression equation,Y = a + βX,Y is the ____.
A)dependent variable
B)slope
C)independent variable
D)intercept

Accepted Answer

In the regression equation, Y is the dependent variable, which means that its value is dependent on the value of X. X, on the other hand, is the independent variable. The intercept (a) and slope (β) are the coefficients of the regression equation that help to predict the value of Y based on the value of X.

Question 14

In using the t-test to compare the means of two groups,the alternative hypothesis is typically stated as ____.
A)µ₁ ≠ µ₂
B)µ₁ = µ₂
C)µ₁ - µ₂ = 2
D)µ₁ + µ₂ = 1

Accepted Answer

The alternative hypothesis in a t-test should state that the means of the two groups being compared are not equal. Therefore, choice A is the correct alternative hypothesis as it states that the mean of the first group (µ₁) is not equal to the mean of the second group (µ₂).

Question 15

Several dummy variables can be included in a regression model.

Accepted Answer

Dummy variables are often used in regression models to represent categorical variables as numerical variables. They can be included in the model as separate predictor variables, with their values being either 0 or 1 to indicate the absence or presence of a particular category.

Question 16

What is another form of the alternative hypothesis when testing the difference between the means of the two groups?
A)µ₁ - µ₂ = 0
B)µ₁ - µ₂ 0
C)µ₁ - µ₂ = 2
D)µ₁ - µ₂ ≠ 2

Accepted Answer

The alternative hypothesis in testing the difference between the means of two groups often states that there is a difference, but does not specify the direction or magnitude. Therefore, "µ₁ - µ₂ ≠ 0" correctly represents an alternative hypothesis, indicating that the means of the two groups are not equal. The symbol "≠" is used to denote "not equal to," but due to a typographical error, it appears as "0" in option B. Understanding the context, option B is intended to mean "µ₁ - µ₂ ≠ 0".

Question 17

In regression analysis,the symbol X is commonly used for the ____ variable,and the symbol Y is commonly used for the ____ variable.
A)dependent;moderating
B)independent;dependent
C)dependent;independent
D)independent;moderating

Accepted Answer

In regression analysis, the independent variable is the one being manipulated or controlled by the researcher and is denoted by X, while the dependent variable is the one being measured or predicted by the regression equation and is denoted by Y. Therefore, B is the correct choice as it matches these definitions.

Question 18

Suppose that you are using a 9-point rating scale to compare men who have an annual income over $50,000 (Group 1)with men who have an annual income less than or equal to $50,000 (Group 2)with regard to their assessment of a new product.There are forty men in Group 1 and they have a mean of 7 and a standard deviation of 2.5,while the 35 men in Group 2 have a mean of 5 and a standard deviation of 1.4.What is the approximate value of t using the t-test?
A)3.43
B)4.19
C)5.64
D)There is not enough information to determine this.

Accepted Answer

To calculate the t-value, we use the formula:
t = (mean1 - mean2) / [sqrt((s1^2/n1)+(s2^2/n2))]
where mean1 = 7, mean2 = 5, s1 = 2.5, s2 = 1.4, n1 = 40, and n2 = 35.
Plugging in these values, we get:
t = (7-5) / [sqrt((2.5^2/40)+(1.4^2/35))] = 4.19
Therefore, the approximate value of t using the t-test is 4.19, and the best choice is B.

Question 19

In the regression equation,Y = a + βX , is the ____.
A)y-intercept
B)independent variable
C)slope of the regression line
D)dependent variable

Accepted Answer

The answer of In the regression equation,Y = a +...

Question 20

Multiple regression analysis includes a single independent variable but several dependent variables.

Accepted Answer

Multiple regression analysis is an extension of simple regression analysis allowing a metric dependent variable to be predicted by multiple independent variables.

Quiz 15: Testing for Differences Between Groups and for Predictive Relationships

A researcher hypothesizes that males and females differ with respect to attitude toward sports sponsorships.To investigate this hypothesis that these two groups' attitudes differ,the researcher will use a ____.

How many degrees of freedom are there in a four-cell chi-square test?

When the on-time performance of airlines is used to predict the number of customer complaints in a regression equation,on-time performance is the variable and the number of customer complaints is the variable.

In comparing the difference of the means between two groups,the null hypothesis can also be stated as ____.

In using the Z-test for comparing two proportions,the null hypothesis is typically stated as ____.

In a brand awareness study,25 of a group of 35 males identify the brand correctly and 15 of a group of 35 females identify this brand correctly.The chi-square value for this study is approximately ____.

The formula given below represents the method for calculating the ____.

A study compares the means of two groups in which there are 45 males in Group 1 and 37 females in Group 2.The degrees of freedom for this study when using the t-test for the difference between means is ____.

In a regression equation,the beta coefficients indicate the effect on the dependent variable of a 1-unit increase in any of the independent variables.

Mulitvariate dependence techniques are variants of the general linear model (GLM).

The formula for the chi-square test uses ____.

In multiple regression,dummy variables are those that have no effect on the dependent variable.

In the regression equation,Y = a + βX,Y is the ____.

In using the t-test to compare the means of two groups,the alternative hypothesis is typically stated as ____.

Several dummy variables can be included in a regression model.

What is another form of the alternative hypothesis when testing the difference between the means of the two groups?

In regression analysis,the symbol X is commonly used for the variable,and the symbol Y is commonly used for the variable.

In the regression equation,Y = a + βX , is the ____.

Multiple regression analysis includes a single independent variable but several dependent variables.