MATH 110 Statistics Module 9 Exam | Latest
2025/2026 | Portage Learning | Verified
Questions and Answers | A+ Graded
Section 1: Introduction
This document provides the verified exam content for Module 9 of MATH 110 – Statistics
from Portage Learning, fully updated for the 2025/2026 academic year. It includes 100%
correct answers to questions covering chi-square tests, goodness-of-fit, and contingency
tables. Graded A+ and aligned with Portage Learning’s online curriculum, this guide offers
essential support for success in introductory statistical coursework.
Section 2: Exam Questions and Answers
Format: Multiple-choice and problem-based questions
Four answer choices per question (A–D)
Correct answer highlighted
Includes brief explanations for key terms and concepts
Question 1
Question: What is a chi-square test used for?
A) Testing means
B) Testing relationships between categorical variables
C) Estimating regression slopes
D) Calculating correlations
B) Testing relationships between categorical variables
Explanation: Assesses independence or goodness-of-fit.
Question 2
Question: What does a chi-square goodness-of-fit test evaluate?
A) Differences between means
B) Fit of observed frequencies to expected frequencies
C) Linear relationships
D) Variance equality
B) Fit of observed frequencies to expected frequencies
Explanation: Compares observed vs. expected distributions.
Question 3
Question: What is the null hypothesis in a chi-square test of independence?
A) Variables are dependent
B) Variables are independent
C) Observed equals expected
D) Sample size is sufficient
, B) Variables are independent
Explanation: H₀ assumes no association.
Question 4
Question: If the chi-square statistic is 10 and critical value is 9.21, what is the decision at α =
0.05?
A) Fail to reject H₀
B) Reject H₀
C) Accept H₀
D) No decision
B) Reject H₀
Explanation: Statistic > critical value.
Question 5
Question: What is the degrees of freedom for a 2x3 contingency table?
A) 2
B) 3
C) 5
D) 6
A) 2
Explanation: DF = (r-1)(c-1) = (2-1)(3-1) = 2.
Question 6
Question: What is the expected frequency in a cell if row total is 50, column total is 100, and
grand total is 200?
A) 10
B) 25
C) 50
D) 100
B) 25
Explanation: Expected = (50 × 100) / 200 = 25.
Question 7
Question: If the p-value is 0.01 and α = 0.05, what is the conclusion?
A) Fail to reject H₀
B) Reject H₀
C) Accept H₀
D) Increase α
B) Reject H₀
Explanation: p < α, so reject.
Question 8
Question: What is the chi-square critical value for α = 0.01 and DF = 2?
A) 4.61
2025/2026 | Portage Learning | Verified
Questions and Answers | A+ Graded
Section 1: Introduction
This document provides the verified exam content for Module 9 of MATH 110 – Statistics
from Portage Learning, fully updated for the 2025/2026 academic year. It includes 100%
correct answers to questions covering chi-square tests, goodness-of-fit, and contingency
tables. Graded A+ and aligned with Portage Learning’s online curriculum, this guide offers
essential support for success in introductory statistical coursework.
Section 2: Exam Questions and Answers
Format: Multiple-choice and problem-based questions
Four answer choices per question (A–D)
Correct answer highlighted
Includes brief explanations for key terms and concepts
Question 1
Question: What is a chi-square test used for?
A) Testing means
B) Testing relationships between categorical variables
C) Estimating regression slopes
D) Calculating correlations
B) Testing relationships between categorical variables
Explanation: Assesses independence or goodness-of-fit.
Question 2
Question: What does a chi-square goodness-of-fit test evaluate?
A) Differences between means
B) Fit of observed frequencies to expected frequencies
C) Linear relationships
D) Variance equality
B) Fit of observed frequencies to expected frequencies
Explanation: Compares observed vs. expected distributions.
Question 3
Question: What is the null hypothesis in a chi-square test of independence?
A) Variables are dependent
B) Variables are independent
C) Observed equals expected
D) Sample size is sufficient
, B) Variables are independent
Explanation: H₀ assumes no association.
Question 4
Question: If the chi-square statistic is 10 and critical value is 9.21, what is the decision at α =
0.05?
A) Fail to reject H₀
B) Reject H₀
C) Accept H₀
D) No decision
B) Reject H₀
Explanation: Statistic > critical value.
Question 5
Question: What is the degrees of freedom for a 2x3 contingency table?
A) 2
B) 3
C) 5
D) 6
A) 2
Explanation: DF = (r-1)(c-1) = (2-1)(3-1) = 2.
Question 6
Question: What is the expected frequency in a cell if row total is 50, column total is 100, and
grand total is 200?
A) 10
B) 25
C) 50
D) 100
B) 25
Explanation: Expected = (50 × 100) / 200 = 25.
Question 7
Question: If the p-value is 0.01 and α = 0.05, what is the conclusion?
A) Fail to reject H₀
B) Reject H₀
C) Accept H₀
D) Increase α
B) Reject H₀
Explanation: p < α, so reject.
Question 8
Question: What is the chi-square critical value for α = 0.01 and DF = 2?
A) 4.61
