,MATH 110 Module 8 | Practice Q&A | 2026/2027 | Statistics | Portage
Learning | 100% PASS
1. According to the Portage Learning MATH 110 course outline, Module 8
focuses primarily on:
A) Descriptive statistics and data visualization
B) Comparisons involving means and proportions
C) Probability and discrete random variables
D) Correlation and regression analysis
Correct Answer: Comparisons involving means and proportions
Rationale: Module 8 focuses on comparisons involving means and
proportions, including independent samples, dependent samples (paired
data), hypothesis testing for differences between means, confidence
intervals for differences between means, and hypothesis testing for
differences between proportions.
2. Which of the following is the key distinction between independent samples
and dependent samples?
A) Independent samples use the same subjects; dependent samples use
different subjects
B) Independent samples use different subjects; dependent samples use the
same or matched subjects
C) Independent samples are always larger than dependent samples
D) There is no difference between independent and dependent samples
Correct Answer: Independent samples use different subjects; dependent
samples use the same or matched subjects
,Rationale: Independent samples are drawn from two different populations
(different subjects), while dependent samples (paired/matched data) use the
same subjects measured twice or subjects that are matched in pairs.
3. A researcher wants to compare the mean test scores of two independent
groups of students. Which statistical method should be used?
A) One-sample t-test
B) Paired samples t-test
C) Independent samples t-test
D) Chi-square test
Correct Answer: Independent samples t-test
Rationale: An independent samples t-test is used to compare the means of
two independent groups (different subjects). A paired samples t-test is used
for dependent or matched samples.
4. A researcher wants to compare the mean blood pressure of the same
patients before and after a treatment. Which statistical method should be
used?
A) One-sample t-test
B) Paired samples t-test
C) Independent samples t-test
D) Z-test for proportions
Correct Answer: Paired samples t-test
Rationale: A paired samples t-test is used when the same subjects are
measured twice (before and after) or when subjects are matched in pairs.
This accounts for the correlation between the paired measurements.
, 5. A researcher wants to compare the proportion of voters who support a
candidate in two different cities. Which statistical method should be used?
A) One-sample t-test
B) Paired samples t-test
C) Independent samples t-test
D) Hypothesis test for difference in proportions
Correct Answer: Hypothesis test for difference in proportions
Rationale: When comparing proportions from two independent populations, a
hypothesis test for the difference in proportions is used. This is appropriate
for categorical data with two groups.
6. The standard error of the mean is calculated as:
A) σ / n
B) σ / √n
C) s / n
D) √(σ/n)
Correct Answer: σ / √n
Rationale: The standard error of the mean is σ / √n, where σ is the population
standard deviation and n is the sample size. It measures the variability of
sample means across repeated samples.
7. A researcher selects a random sample of 64 observations from a
population with a known standard deviation of 24. The sample mean is 180.
What is the standard error of the mean?
Learning | 100% PASS
1. According to the Portage Learning MATH 110 course outline, Module 8
focuses primarily on:
A) Descriptive statistics and data visualization
B) Comparisons involving means and proportions
C) Probability and discrete random variables
D) Correlation and regression analysis
Correct Answer: Comparisons involving means and proportions
Rationale: Module 8 focuses on comparisons involving means and
proportions, including independent samples, dependent samples (paired
data), hypothesis testing for differences between means, confidence
intervals for differences between means, and hypothesis testing for
differences between proportions.
2. Which of the following is the key distinction between independent samples
and dependent samples?
A) Independent samples use the same subjects; dependent samples use
different subjects
B) Independent samples use different subjects; dependent samples use the
same or matched subjects
C) Independent samples are always larger than dependent samples
D) There is no difference between independent and dependent samples
Correct Answer: Independent samples use different subjects; dependent
samples use the same or matched subjects
,Rationale: Independent samples are drawn from two different populations
(different subjects), while dependent samples (paired/matched data) use the
same subjects measured twice or subjects that are matched in pairs.
3. A researcher wants to compare the mean test scores of two independent
groups of students. Which statistical method should be used?
A) One-sample t-test
B) Paired samples t-test
C) Independent samples t-test
D) Chi-square test
Correct Answer: Independent samples t-test
Rationale: An independent samples t-test is used to compare the means of
two independent groups (different subjects). A paired samples t-test is used
for dependent or matched samples.
4. A researcher wants to compare the mean blood pressure of the same
patients before and after a treatment. Which statistical method should be
used?
A) One-sample t-test
B) Paired samples t-test
C) Independent samples t-test
D) Z-test for proportions
Correct Answer: Paired samples t-test
Rationale: A paired samples t-test is used when the same subjects are
measured twice (before and after) or when subjects are matched in pairs.
This accounts for the correlation between the paired measurements.
, 5. A researcher wants to compare the proportion of voters who support a
candidate in two different cities. Which statistical method should be used?
A) One-sample t-test
B) Paired samples t-test
C) Independent samples t-test
D) Hypothesis test for difference in proportions
Correct Answer: Hypothesis test for difference in proportions
Rationale: When comparing proportions from two independent populations, a
hypothesis test for the difference in proportions is used. This is appropriate
for categorical data with two groups.
6. The standard error of the mean is calculated as:
A) σ / n
B) σ / √n
C) s / n
D) √(σ/n)
Correct Answer: σ / √n
Rationale: The standard error of the mean is σ / √n, where σ is the population
standard deviation and n is the sample size. It measures the variability of
sample means across repeated samples.
7. A researcher selects a random sample of 64 observations from a
population with a known standard deviation of 24. The sample mean is 180.
What is the standard error of the mean?
