Question 1

In a study comparing 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) 84
B) 80
C) 82
D) 160

Accepted Answer

The degrees of freedom for the t-test for the difference between means formula is calculated as (n1 - 1) + (n2 - 1), where n1 and n2 are the sample sizes of the two groups. Plugging in the values, we get (45-1) + (37-1) = 80. Therefore, the correct answer is B.

Question 2

The Z-test for comparing two proportions is appropriate with which null hypothesis (H₀)?
A) π₁ = π₂.
B) π₁ ≠ π₂.
C) π₁ x π₂ = 1
D) π₁ - π₂ = 1

Accepted Answer

The null hypothesis (H₀) for the Z-test for comparing two proportions is always that the two population proportions are equal, which is represented as π₁ = π₂. Therefore, choice A is the correct answer.

Question 3

Which test is appropriate for comparing the scores of two interval variables drawn from related populations?
A) ANOVA
B) relative t-test
C) relative x² test
D) pair-samples t-test

Accepted Answer

The pair-samples t-test is appropriate for comparing the scores of two interval variables drawn from related populations, where the same individuals are measured twice (e.g. before and after a treatment, or under two different conditions). This test compares the means of the two sets of scores and is useful when the assumption of normality is met. ANOVA, relative t-test, and relative x² test are not appropriate for comparing two interval variables drawn from related populations.

Question 4

The F-distribution is a function of _____.
A) SSB - SSE
B) SSE - SSB
C) SSB/SSE
D) SSE/SSB

Accepted Answer

The F-distribution is calculated as the ratio of two variance estimates. Specifically, it is the ratio of the variance between groups (SSB) to the variance within groups (SSE), which is represented as SSB/SSE. Therefore, the best choice is C.

Question 5

The key statistical test for an ANOVA model is the _____.
A) x² test
B) t-test
C) F-test
D) Z-test

Accepted Answer

The F-test is used to determine if there is significant variance between the means of multiple groups in an ANOVA model.

Question 6

Which of the following is a requirement for using the Z-test for differences of proportions?
A) common sample
B) degrees of freedom of at least 50
C) sample size greater than 30
D) ratio measurement of all variables

Accepted Answer

The requirement for using the Z-test for differences of proportions is a sample size greater than 30. Therefore, option C is the correct choice. The other options, including a common sample, degrees of freedom of at least 50, and ratio measurement of all variables, are not related to the requirement for using the Z-test for differences of proportions.

Question 7

Multivariate dependence techniques are variants of the _____,which is a way of modeling some process based on how different variables cause fluctuations from the average dependent variable.
A) ordinary linear model (OLM)
B) weighted average model (WAM)
C) general linear model (GLM)
D) metric scaling model (MSM)

Accepted Answer

Multivariate dependence techniques are variants of the general linear model (GLM), which allows for the modeling of a dependent variable based on multiple independent variables. The GLM is a widely used statistical model that can accommodate both continuous and categorical predictor variables.

Question 8

In the regression equation,Y =α+ β X,Y is the _____.
A) dependent variable
B) slope
C) independent variable
D) y-intercept

Accepted Answer

In the regression equation, Y is the dependent variable as it is the variable being predicted or estimated based on the independent variable X. The slope (β) and y-intercept (α) are the parameters of the equation that determine the relationship between X and Y. The independent variable (X) is the variable that is believed to be the cause or predictor of changes in the dependent variable (Y).

Question 9

The mean of a variable over all observations is called the _____.
A) master mean
B) average mean
C) grand mean
D) ANOVA mean

Accepted Answer

The mean calculated over all observations is referred to as the grand mean. Option A is not a statistical term, option B is redundant, and option D is not accurate as ANOVA does not necessarily provide a mean.

Question 10

When a researcher is attempting to predict sales volume by using building permits,amount of advertising,and the income levels of residents,the researcher is using _____.
A) univariate analysis
B) a chi-square analysis
C) multiple regression analysis
D) factor analysis

Accepted Answer

The researcher is using multiple regression analysis since they are attempting to predict sales volume using multiple independent variables. Univariate analysis focuses on analyzing one variable at a time, chi-square analysis is used to determine if there is a significant association between two categorical variables, and factor analysis is used to identify underlying factors that explain the correlation between multiple variables.

Question 11

The sum of the differences between observed values and the group mean for a given set of observations is known as the _____.
A) within-group error
B) between-groups variance
C) F-ratio
D) g statistic

Accepted Answer

The sum of the differences between observed values and the group mean is the within-group error, also known as the residual error or variation. This measures how much variability there is within each group and is an important component in determining the overall significance of group differences. The between-groups variance is the variation between group means, while the F-ratio is a statistic used to test for significant differences between group means. The g statistic is not a relevant concept in this context.

Question 12

Practically speaking,what is the first thing a researcher should do when interpreting ANOVA results?
A) examine the actual means for each group
B) determine the between-groups variance
C) examine the total variance
D) check whether or not the overall model F is significant

Accepted Answer

Checking whether or not the overall model F is significant is the first step in interpreting ANOVA results as it determines if there is a statistically significant difference between the groups. Once this is established, the researcher can then examine the means and variances to further investigate the source of the difference.

Question 13

Which should be used when comparing the means of three groups to see if they are significantly different from one another?
A) One-group t-test
B) ANOVA
C) Three-group t-test
D) Chi-square test

Accepted Answer

ANOVA (Analysis of Variance) should be used when comparing the means of three or more groups to determine if there is a significant difference between them. A one-group t-test is only used to compare the mean of one group to a known value or hypothesized mean. A three-group t-test is not a valid statistical test. A chi-square test is used for categorical data and not for comparing means.

Question 14

Suppose that you used a 9-point rating scale and that you wanted to compare men who had an annual income over $50,000 (Group 1)with men who had an annual income less than or equal to $50,000 (Group 2)on their liking of a new product.If you studied 40 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) 2.64
D) not enough information to determine

Accepted Answer

To calculate t, we need to use the formula:

t = (x1 - x2) / √(s1^2/n1 + s2^2/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values from the problem, we get:

t = (7 - 5) / √(2.5^2/40 + 1.4^2/35)
t = 2 / √(0.15625 + 0.055102)
t = 2 / √0.211352
t = 2 / 0.459632
t = 4.347

Rounding to two decimal places, the answer is choice B) 4.19.

Question 15

Supposed you used a 10-point rating scale to measure intention-to-buy (1 = definitely would not buy and 10 = definitely would buy).If a group of 40 males had a mean of 7 and a standard deviation of 2.5,while a group of 35 females had a mean of 5 and a standard deviation of 1.4,the standard error of the difference between the means would be approximately _____.
A) 0.48
B) 1.36
C) 2.45
D) not enough information to determine

Accepted Answer

The answer of Supposed you used a 10-point rating scale...

Question 16

Which of the following is the sum of differences between the group mean and the grand mean summed over all groups for a given set of observations?
A) between-groups variance
B) total error variance
C) F-statistic
D) x² value

Accepted Answer

The sum of differences between the group mean and the grand mean summed over all groups is referred to as the between-groups variance. In ANOVA, this variance is used to calculate the F-statistic, which is used to test the significance of the group means. Thus, (A) is the correct option. Total error variance refers to the sum of differences between the individual observations and their respective group mean, and x² value is typically used in contingency table analyses.

Question 17

In using the t-test to compare the means of two groups,the degrees of freedom are calculated as _____.
A) n₁ - n₂ - 2
B) n₁ + n₂ - 2
C) n₁ x n₂ -2
D) n₁ / n₂ - 2

Accepted Answer

The degrees of freedom for a t-test comparing the means of two independent groups is calculated as the sum of the sample sizes of both groups minus 2, which is n₁ + n₂ - 2.

Question 18

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(s) are represented by X and the dependent variable is represented by Y. Therefore, choice B is correct as it correctly identifies X as the independent variable and Y as the dependent variable.

Question 19

All of the following are software that researchers can use to perform statistical calculations EXCEPT _____.
A) Excel
B) SAS
C) ANOVA
D) JMP

Accepted Answer

ANOVA is not a software, but a statistical technique used to analyze variance among different groups. The other choices, Excel, SAS, and JMP, are all software commonly used for statistical calculations.

Question 20

In practice,what is the first step in interpreting the t-test when comparing two means?
A) compute the t-test value
B) find the p-value associated with the t and the corresponding degrees of freedom
C) examine the difference in means to find the "direction" of any difference
D) examine if there is a difference at the 50 percent confidence interval before examining the 95 percent confidence interval

Accepted Answer

The first step in interpreting the t-test when comparing two means is to examine the difference in means to determine the direction of any difference. This will inform us whether one mean is greater or less than the other, or if they are approximately equal. Only after understanding the direction can we move on to computing the t-test value, finding the p-value, and interpreting the results with a confidence interval.

Quiz 15: Testing for Differences Between Groups and for Relationships Among Variables

In a study comparing 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:

The Z-test for comparing two proportions is appropriate with which null hypothesis (H₀) ?

Which test is appropriate for comparing the scores of two interval variables drawn from related populations?

The F-distribution is a function of _____.

The key statistical test for an ANOVA model is the _____.

Which of the following is a requirement for using the Z-test for differences of proportions?

Multivariate dependence techniques are variants of the _____,which is a way of modeling some process based on how different variables cause fluctuations from the average dependent variable.

In the regression equation,Y =α+ β X,Y is the _____.

The mean of a variable over all observations is called the _____.

When a researcher is attempting to predict sales volume by using building permits,amount of advertising,and the income levels of residents,the researcher is using _____.

The sum of the differences between observed values and the group mean for a given set of observations is known as the _____.

Practically speaking,what is the first thing a researcher should do when interpreting ANOVA results?

Which should be used when comparing the means of three groups to see if they are significantly different from one another?

Which of the following is the sum of differences between the group mean and the grand mean summed over all groups for a given set of observations?

In using the t-test to compare the means of two groups,the degrees of freedom are calculated as _____.

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

All of the following are software that researchers can use to perform statistical calculations EXCEPT _____.

In practice,what is the first step in interpreting the t-test when comparing two means?