MATH 110 MODULE 8 EXAM (LATEST 2026) | MATH110 INTRODUCTION TO
STATISTICS – PORTAGE LEARNING COMPLETE PRACTICE EXAM QUESTIONS AND
ANSWERS | VERIFIED SOLUTIONS | COMPREHENSIVE STUDY GUIDE | UPDATED
2026/2027
Examiner/Administrator: Portage Learning
━━━━━━━━━━━━━━━━━━━━━━━━━━━━
MATH110 INTRODUCTION TO STATISTICS – MODULE 8 EXAM
2026/2027 EDITION
━━━━━━━━━━━━━━━━━━━━━━━━━━━━
COMPLETE PRACTICE EXAM
100+ MULTIPLE-CHOICE QUESTIONS
PASSING SCORE: 70%
TESTING TIME: 120 MINUTES
━━━━━━━━━━━━━━━━━━━━━━━━━━━━
TABLE OF CONTENTS
Confidence Intervals
Sampling Distributions
Population Mean Estimation
Population Proportion Estimation
Margin of Error
Critical Values and Confidence Levels
Hypothesis Testing Fundamentals
Statistical Decision-Making
Interpretation of Statistical Results
Applied Statistical Problem Solving
PORTAGE LEARNING || ALIGNED WITH CURRENT STATISTICS COURSE BLUEPRINTS ||
INTRODUCTION TO STATISTICS MODULE 8 || PROFESSIONAL STUDY GUIDE || 100%
VERIFIED | GRADED A+ || COMPREHENSIVE EXAM PREPARATION || PREPARED FOR
ACADEMIC ASSESSMENT USE || PROFESSIONAL EXAMINATION USE
━━━━━━━━━━━━━━━━━━━━━━━━━━━━
,Confidence Intervals and Sampling Distributions
Q1. A researcher selects a random sample of 64 observations from a normally
distributed population with known standard deviation of 24. The sample mean is 180.
What is the standard error of the mean?
A. 2
B. 3
C. 4
D. 6
Correct Answer: 🔴 B. 3
Explanation: 🔹 The standard error is calculated as σ/√n = 24/√64 = 24/8 = 3. The
standard error measures the variability of sample means across repeated samples.
Options A, C, and D result from incorrect calculations of the denominator or
standard deviation.
Q2. A 95% confidence interval for a population mean is constructed. Which
interpretation is correct?
A. There is a 95% probability that the population mean changes over time.
B. Ninety-five percent of sample values fall inside the interval.
C. The method used will capture the true population mean in about 95% of repeated
samples.
D. The population mean has a 95% chance of being any value.
Correct Answer: 🔴 C. The method used will capture the true population mean in
about 95% of repeated samples.
Explanation: 🔹 Confidence intervals refer to the reliability of the estimation
procedure, not the probability of the fixed population parameter being inside the
interval. Options A, B, and D incorrectly interpret confidence levels.
Q3. A sample mean of 52 is obtained from a sample of 100 observations. The
population standard deviation is known to be 10. What is the margin of error for a
95% confidence interval?
,A. 1.96
B. 0.98
C. 2.45
D. 3.92
Correct Answer: 🔴 A. 1.96
Explanation: 🔹 Margin of error = z(σ/√n) = 1.96(10/10) = 1.96. This value represents
the maximum expected estimation error at the 95% confidence level. Other choices
result from computational errors.
Q4. Which factor will decrease the width of a confidence interval?
A. Increasing the confidence level
B. Increasing population variability
C. Increasing sample size
D. Using a smaller critical value incorrectly
Correct Answer: 🔴 C. Increasing sample size
Explanation: 🔹 Larger samples reduce standard error and narrow confidence
intervals. Increasing confidence level or variability widens intervals. Option D
describes an incorrect statistical procedure rather than a legitimate factor.
Q5. A confidence interval is reported as (42.5, 47.5). What is the point estimate?
A. 45.0
B. 42.5
C. 47.5
D. 5.0
Correct Answer: 🔴 A. 45.0
Explanation: 🔹 The point estimate is the midpoint of the interval: (42.5 + 47.5)/2 =
45.0. The endpoints are interval limits, and 5.0 is merely the interval width.
, Q6. Which statement best describes a sampling distribution?
A. Distribution of all observations in a population
B. Distribution of sample means from repeated samples
C. Distribution of confidence intervals
D. Distribution of measurement errors only
Correct Answer: 🔴 B. Distribution of sample means from repeated samples
Explanation: 🔹 Sampling distributions describe how a statistic varies across
repeated random samples. This concept forms the foundation of confidence intervals
and hypothesis testing.
Q7. As sample size increases, the standard error of the mean:
A. Increases
B. Remains constant
C. Approaches infinity
D. Decreases
Correct Answer: 🔴 D. Decreases
Explanation: 🔹 Standard error equals σ/√n. As n grows larger, the denominator
increases, causing standard error to shrink. This leads to more precise estimates.
Q8. A 99% confidence interval is generally:
A. Narrower than a 95% interval
B. Wider than a 95% interval
C. Identical to a 95% interval
D. Independent of confidence level
Correct Answer: 🔴 B. Wider than a 95% interval
Explanation: 🔹 Higher confidence requires a larger critical value and therefore a
wider interval to ensure greater certainty of capturing the population parameter.
STATISTICS – PORTAGE LEARNING COMPLETE PRACTICE EXAM QUESTIONS AND
ANSWERS | VERIFIED SOLUTIONS | COMPREHENSIVE STUDY GUIDE | UPDATED
2026/2027
Examiner/Administrator: Portage Learning
━━━━━━━━━━━━━━━━━━━━━━━━━━━━
MATH110 INTRODUCTION TO STATISTICS – MODULE 8 EXAM
2026/2027 EDITION
━━━━━━━━━━━━━━━━━━━━━━━━━━━━
COMPLETE PRACTICE EXAM
100+ MULTIPLE-CHOICE QUESTIONS
PASSING SCORE: 70%
TESTING TIME: 120 MINUTES
━━━━━━━━━━━━━━━━━━━━━━━━━━━━
TABLE OF CONTENTS
Confidence Intervals
Sampling Distributions
Population Mean Estimation
Population Proportion Estimation
Margin of Error
Critical Values and Confidence Levels
Hypothesis Testing Fundamentals
Statistical Decision-Making
Interpretation of Statistical Results
Applied Statistical Problem Solving
PORTAGE LEARNING || ALIGNED WITH CURRENT STATISTICS COURSE BLUEPRINTS ||
INTRODUCTION TO STATISTICS MODULE 8 || PROFESSIONAL STUDY GUIDE || 100%
VERIFIED | GRADED A+ || COMPREHENSIVE EXAM PREPARATION || PREPARED FOR
ACADEMIC ASSESSMENT USE || PROFESSIONAL EXAMINATION USE
━━━━━━━━━━━━━━━━━━━━━━━━━━━━
,Confidence Intervals and Sampling Distributions
Q1. A researcher selects a random sample of 64 observations from a normally
distributed population with known standard deviation of 24. The sample mean is 180.
What is the standard error of the mean?
A. 2
B. 3
C. 4
D. 6
Correct Answer: 🔴 B. 3
Explanation: 🔹 The standard error is calculated as σ/√n = 24/√64 = 24/8 = 3. The
standard error measures the variability of sample means across repeated samples.
Options A, C, and D result from incorrect calculations of the denominator or
standard deviation.
Q2. A 95% confidence interval for a population mean is constructed. Which
interpretation is correct?
A. There is a 95% probability that the population mean changes over time.
B. Ninety-five percent of sample values fall inside the interval.
C. The method used will capture the true population mean in about 95% of repeated
samples.
D. The population mean has a 95% chance of being any value.
Correct Answer: 🔴 C. The method used will capture the true population mean in
about 95% of repeated samples.
Explanation: 🔹 Confidence intervals refer to the reliability of the estimation
procedure, not the probability of the fixed population parameter being inside the
interval. Options A, B, and D incorrectly interpret confidence levels.
Q3. A sample mean of 52 is obtained from a sample of 100 observations. The
population standard deviation is known to be 10. What is the margin of error for a
95% confidence interval?
,A. 1.96
B. 0.98
C. 2.45
D. 3.92
Correct Answer: 🔴 A. 1.96
Explanation: 🔹 Margin of error = z(σ/√n) = 1.96(10/10) = 1.96. This value represents
the maximum expected estimation error at the 95% confidence level. Other choices
result from computational errors.
Q4. Which factor will decrease the width of a confidence interval?
A. Increasing the confidence level
B. Increasing population variability
C. Increasing sample size
D. Using a smaller critical value incorrectly
Correct Answer: 🔴 C. Increasing sample size
Explanation: 🔹 Larger samples reduce standard error and narrow confidence
intervals. Increasing confidence level or variability widens intervals. Option D
describes an incorrect statistical procedure rather than a legitimate factor.
Q5. A confidence interval is reported as (42.5, 47.5). What is the point estimate?
A. 45.0
B. 42.5
C. 47.5
D. 5.0
Correct Answer: 🔴 A. 45.0
Explanation: 🔹 The point estimate is the midpoint of the interval: (42.5 + 47.5)/2 =
45.0. The endpoints are interval limits, and 5.0 is merely the interval width.
, Q6. Which statement best describes a sampling distribution?
A. Distribution of all observations in a population
B. Distribution of sample means from repeated samples
C. Distribution of confidence intervals
D. Distribution of measurement errors only
Correct Answer: 🔴 B. Distribution of sample means from repeated samples
Explanation: 🔹 Sampling distributions describe how a statistic varies across
repeated random samples. This concept forms the foundation of confidence intervals
and hypothesis testing.
Q7. As sample size increases, the standard error of the mean:
A. Increases
B. Remains constant
C. Approaches infinity
D. Decreases
Correct Answer: 🔴 D. Decreases
Explanation: 🔹 Standard error equals σ/√n. As n grows larger, the denominator
increases, causing standard error to shrink. This leads to more precise estimates.
Q8. A 99% confidence interval is generally:
A. Narrower than a 95% interval
B. Wider than a 95% interval
C. Identical to a 95% interval
D. Independent of confidence level
Correct Answer: 🔴 B. Wider than a 95% interval
Explanation: 🔹 Higher confidence requires a larger critical value and therefore a
wider interval to ensure greater certainty of capturing the population parameter.
