MATH 110 Exam 8 Statistics Questions and Answers -
Portage Learning (2026/2027)
Advanced Statistical Inference & Regression | Key Domains: Multiple Regression Analysis, Analysis
of Variance (ANOVA), Chi-Square Tests for Goodness-of-Fit & Independence, Nonparametric
Statistics (e.g., Mann-Whitney U), and Advanced Probability Distributions | Expert-Aligned Structure
| Multiple-Choice Exam Format
Introduction
This structured MATH 110 Exam 8 for Portage Learning (2026/2027) provides 45 multiple-choice
questions with correct answers and rationales. It covers advanced topics in statistical inference,
focusing on the application of multivariable analysis, tests for categorical data, and methods for data
that do not meet parametric assumptions.
Exam Structure:
● Exam 8: Advanced Statistics: (45 MULTIPLE-CHOICE QUESTIONS)
Answer Format
All correct answers and analytical conclusions must appear in bold and cyan blue, accompanied by
concise rationales explaining the interpretation of regression output (e.g., the meaning of a
coefficient in multiple regression), the correct setup and calculation for an ANOVA F-test, the
application of a Chi-square test to a contingency table, the conditions for using a nonparametric
test, and why the alternative multiple-choice options misapply advanced statistical models,
misinterpret p-values in complex settings, or violate key assumptions of the tests.
Exam 8: Advanced Statistics (45 Multiple-Choice Questions)
1. In a multiple regression model, what does the coefficient of a predictor variable
represent?
, A. The correlation between the predictor and the response
B. The change in the response variable for a one-unit increase in the predictor, holding other
predictors constant
C. The total effect of the predictor on the response
D. The p-value for the predictor's significance
B. The change in the response variable for a one-unit increase in the predictor, holding other
predictors constant
Rationale: In multiple regression, coefficients are partial slopes—measuring the unique contribution of
each predictor while controlling for others. Option A describes simple correlation; C ignores
confounding; D confuses coefficient with p-value.
2. Which condition is required for valid inference in multiple regression?
A. All predictors must be categorical
B. Residuals must be normally distributed with constant variance
C. The sample size must be less than 30
D. Predictors must be uncorrelated with each other
B. Residuals must be normally distributed with constant variance
Rationale: Key assumptions include linearity, independence, homoscedasticity (constant variance), and
normality of residuals. Predictors can be quantitative or categorical (A); n ≥ 30 is often sufficient (C);
some correlation among predictors is acceptable (D)—only severe multicollinearity is problematic.
3. In a one-way ANOVA with 4 groups and total n = 40, what are the degrees of freedom for
the F-test?
A. df₁ = 3, df₂ = 36
B. df₁ = 4, df₂ = 36
C. df₁ = 3, df₂ = 40
D. df₁ = 4, df₂ = 39
A. df₁ = 3, df₂ = 36
, Rationale: dfbetween = k - 1 = 4 - 1 = 3; dfwithin = n - k = 40 - 4 = 36. The F-statistic has (k-1, n-k) degrees of
freedom.
4. A chi-square test of independence is performed on a 3×4 contingency table. What are the
degrees of freedom?
A. 6
B. 12
C. 7
D. 11
A. 6
Rationale: df = (rows - 1)(columns - 1) = (3-1)(4-1) = 2×3 = 6. This accounts for constraints in row and
column totals.
5. Which nonparametric test is used to compare two independent samples when the data is
ordinal?
A. Wilcoxon signed-rank test
B. Kruskal-Wallis test
C. Mann-Whitney U test
D. Friedman test
C. Mann-Whitney U test
Rationale: Mann-Whitney U (Wilcoxon rank-sum) tests for differences in central tendency between two
independent groups with ordinal or non-normal data. Wilcoxon signed-rank (A) is for paired data;
Kruskal-Wallis (B) for >2 groups; Friedman (D) for repeated measures.
6. In multiple regression, a high VIF (Variance Inflation Factor) for a predictor indicates:
A. The predictor is highly significant
B. The predictor is multicollinear with other predictors
C. The residual variance is low
D. The model has high R²
Portage Learning (2026/2027)
Advanced Statistical Inference & Regression | Key Domains: Multiple Regression Analysis, Analysis
of Variance (ANOVA), Chi-Square Tests for Goodness-of-Fit & Independence, Nonparametric
Statistics (e.g., Mann-Whitney U), and Advanced Probability Distributions | Expert-Aligned Structure
| Multiple-Choice Exam Format
Introduction
This structured MATH 110 Exam 8 for Portage Learning (2026/2027) provides 45 multiple-choice
questions with correct answers and rationales. It covers advanced topics in statistical inference,
focusing on the application of multivariable analysis, tests for categorical data, and methods for data
that do not meet parametric assumptions.
Exam Structure:
● Exam 8: Advanced Statistics: (45 MULTIPLE-CHOICE QUESTIONS)
Answer Format
All correct answers and analytical conclusions must appear in bold and cyan blue, accompanied by
concise rationales explaining the interpretation of regression output (e.g., the meaning of a
coefficient in multiple regression), the correct setup and calculation for an ANOVA F-test, the
application of a Chi-square test to a contingency table, the conditions for using a nonparametric
test, and why the alternative multiple-choice options misapply advanced statistical models,
misinterpret p-values in complex settings, or violate key assumptions of the tests.
Exam 8: Advanced Statistics (45 Multiple-Choice Questions)
1. In a multiple regression model, what does the coefficient of a predictor variable
represent?
, A. The correlation between the predictor and the response
B. The change in the response variable for a one-unit increase in the predictor, holding other
predictors constant
C. The total effect of the predictor on the response
D. The p-value for the predictor's significance
B. The change in the response variable for a one-unit increase in the predictor, holding other
predictors constant
Rationale: In multiple regression, coefficients are partial slopes—measuring the unique contribution of
each predictor while controlling for others. Option A describes simple correlation; C ignores
confounding; D confuses coefficient with p-value.
2. Which condition is required for valid inference in multiple regression?
A. All predictors must be categorical
B. Residuals must be normally distributed with constant variance
C. The sample size must be less than 30
D. Predictors must be uncorrelated with each other
B. Residuals must be normally distributed with constant variance
Rationale: Key assumptions include linearity, independence, homoscedasticity (constant variance), and
normality of residuals. Predictors can be quantitative or categorical (A); n ≥ 30 is often sufficient (C);
some correlation among predictors is acceptable (D)—only severe multicollinearity is problematic.
3. In a one-way ANOVA with 4 groups and total n = 40, what are the degrees of freedom for
the F-test?
A. df₁ = 3, df₂ = 36
B. df₁ = 4, df₂ = 36
C. df₁ = 3, df₂ = 40
D. df₁ = 4, df₂ = 39
A. df₁ = 3, df₂ = 36
, Rationale: dfbetween = k - 1 = 4 - 1 = 3; dfwithin = n - k = 40 - 4 = 36. The F-statistic has (k-1, n-k) degrees of
freedom.
4. A chi-square test of independence is performed on a 3×4 contingency table. What are the
degrees of freedom?
A. 6
B. 12
C. 7
D. 11
A. 6
Rationale: df = (rows - 1)(columns - 1) = (3-1)(4-1) = 2×3 = 6. This accounts for constraints in row and
column totals.
5. Which nonparametric test is used to compare two independent samples when the data is
ordinal?
A. Wilcoxon signed-rank test
B. Kruskal-Wallis test
C. Mann-Whitney U test
D. Friedman test
C. Mann-Whitney U test
Rationale: Mann-Whitney U (Wilcoxon rank-sum) tests for differences in central tendency between two
independent groups with ordinal or non-normal data. Wilcoxon signed-rank (A) is for paired data;
Kruskal-Wallis (B) for >2 groups; Friedman (D) for repeated measures.
6. In multiple regression, a high VIF (Variance Inflation Factor) for a predictor indicates:
A. The predictor is highly significant
B. The predictor is multicollinear with other predictors
C. The residual variance is low
D. The model has high R²
