, BUSI 230 — EXAM 3
Introduction to Probability and Statistics
Liberty University
100-Question Independent Practice Examination
2026/2027 Edition
This independent practice assessment emphasizes inference, estimation, chi-square tests and regression, with
supporting foundations.
Sampling and design
1. A researcher samples every 25th invoice after a random starting point. Which sampling design was
used?
A) Cluster sampling
B) Systematic random sampling
C) Stratified sampling
D) Convenience sampling
Correct Answer: B) Systematic random sampling
Rationale: A random start followed by a fixed selection interval is systematic sampling. A cluster design chooses intact
groups, whereas stratification samples within defined subgroups; convenience sampling has no probability-based
selection rule.
2. A survey of only customers who respond to a voluntary online poll is most vulnerable to which
problem?
A) Finite-population correction
B) Voluntary-response bias
C) Perfect stratification
D) Random assignment
Correct Answer: B) Voluntary-response bias
Rationale: People with strong views are more likely to respond, so the respondents may differ systematically from the
full customer population. Making a survey larger does not remove voluntary-response bias.
3. A study labels store locations by region and randomly selects stores from each region. What purpose
does this design chiefly serve?
A) Representation of every defined region
B) Guaranteeing equal sales
C) Removing all measurement error
D) Turning observational data into a randomized experiment
Correct Answer: A) Representation of every defined region
Rationale: Stratified sampling ensures the chosen regions contribute observations. It can improve precision when
strata differ; it cannot make measurement perfect or randomly assign treatments.
4. To assess whether a new script causes higher sales, managers randomly assign the script to some
sales teams. What is the key strength of the random assignment?
BUSI 230 | Exam 3 | Independent Practice | 2026/2027 1
, A) It reduces systematic confounding between groups
B) It removes every source of nonresponse
C) It makes samples representative of every industry
D) It guarantees a significant result
Correct Answer: A) It reduces systematic confounding between groups
Rationale: Random assignment tends to balance measured and unmeasured confounders between treatment and
control groups, supporting causal interpretation. It does not guarantee significance or representativeness outside the
study.
Estimation
5. A 95% confidence interval for mean delivery time is reported as 28 to 34 minutes. Which interpretation
is best?
A) There is a 95% chance each delivery takes 28 to 34 minutes
B) The sample mean changes between 28 and 34 each minute
C) 95% of observed deliveries were in this interval
D) The method captures the fixed population mean in about 95% of repeated samples
Correct Answer: D) The method captures the fixed population mean in about 95% of repeated samples
Rationale: Coverage refers to the repeated-sampling performance of the interval procedure, not to probability assigned
to an already fixed parameter. It is not a prediction interval for individual deliveries.
6. Holding confidence level and population variability fixed, increasing sample size typically has what
effect on a mean confidence interval?
A) It changes the confidence level automatically
B) It narrows the interval
C) It makes the mean equal the median
D) It widens the interval
Correct Answer: B) It narrows the interval
Rationale: The standard error of the sample mean is proportional to 1/sqrt(n). A larger n reduces estimation uncertainty
while the stated confidence level stays unchanged.
7. Which condition particularly supports use of a t critical value rather than z for a mean interval?
A) The sample size is always one million
B) The population contains exactly two values
C) The sample median is zero
D) Population standard deviation is unknown and estimated from the sample
Correct Answer: D) Population standard deviation is unknown and estimated from the sample
Rationale: The t distribution accounts for uncertainty from estimating the population standard deviation. The t degrees
of freedom are normally n-1 for a one-sample mean analysis.
8. What changes when a two-sided confidence interval uses 99% rather than 95% confidence, all else
equal?
A) The interval becomes wider
B) The interval becomes narrower
C) The sample standard deviation becomes zero
BUSI 230 | Exam 3 | Independent Practice | 2026/2027 2
Introduction to Probability and Statistics
Liberty University
100-Question Independent Practice Examination
2026/2027 Edition
This independent practice assessment emphasizes inference, estimation, chi-square tests and regression, with
supporting foundations.
Sampling and design
1. A researcher samples every 25th invoice after a random starting point. Which sampling design was
used?
A) Cluster sampling
B) Systematic random sampling
C) Stratified sampling
D) Convenience sampling
Correct Answer: B) Systematic random sampling
Rationale: A random start followed by a fixed selection interval is systematic sampling. A cluster design chooses intact
groups, whereas stratification samples within defined subgroups; convenience sampling has no probability-based
selection rule.
2. A survey of only customers who respond to a voluntary online poll is most vulnerable to which
problem?
A) Finite-population correction
B) Voluntary-response bias
C) Perfect stratification
D) Random assignment
Correct Answer: B) Voluntary-response bias
Rationale: People with strong views are more likely to respond, so the respondents may differ systematically from the
full customer population. Making a survey larger does not remove voluntary-response bias.
3. A study labels store locations by region and randomly selects stores from each region. What purpose
does this design chiefly serve?
A) Representation of every defined region
B) Guaranteeing equal sales
C) Removing all measurement error
D) Turning observational data into a randomized experiment
Correct Answer: A) Representation of every defined region
Rationale: Stratified sampling ensures the chosen regions contribute observations. It can improve precision when
strata differ; it cannot make measurement perfect or randomly assign treatments.
4. To assess whether a new script causes higher sales, managers randomly assign the script to some
sales teams. What is the key strength of the random assignment?
BUSI 230 | Exam 3 | Independent Practice | 2026/2027 1
, A) It reduces systematic confounding between groups
B) It removes every source of nonresponse
C) It makes samples representative of every industry
D) It guarantees a significant result
Correct Answer: A) It reduces systematic confounding between groups
Rationale: Random assignment tends to balance measured and unmeasured confounders between treatment and
control groups, supporting causal interpretation. It does not guarantee significance or representativeness outside the
study.
Estimation
5. A 95% confidence interval for mean delivery time is reported as 28 to 34 minutes. Which interpretation
is best?
A) There is a 95% chance each delivery takes 28 to 34 minutes
B) The sample mean changes between 28 and 34 each minute
C) 95% of observed deliveries were in this interval
D) The method captures the fixed population mean in about 95% of repeated samples
Correct Answer: D) The method captures the fixed population mean in about 95% of repeated samples
Rationale: Coverage refers to the repeated-sampling performance of the interval procedure, not to probability assigned
to an already fixed parameter. It is not a prediction interval for individual deliveries.
6. Holding confidence level and population variability fixed, increasing sample size typically has what
effect on a mean confidence interval?
A) It changes the confidence level automatically
B) It narrows the interval
C) It makes the mean equal the median
D) It widens the interval
Correct Answer: B) It narrows the interval
Rationale: The standard error of the sample mean is proportional to 1/sqrt(n). A larger n reduces estimation uncertainty
while the stated confidence level stays unchanged.
7. Which condition particularly supports use of a t critical value rather than z for a mean interval?
A) The sample size is always one million
B) The population contains exactly two values
C) The sample median is zero
D) Population standard deviation is unknown and estimated from the sample
Correct Answer: D) Population standard deviation is unknown and estimated from the sample
Rationale: The t distribution accounts for uncertainty from estimating the population standard deviation. The t degrees
of freedom are normally n-1 for a one-sample mean analysis.
8. What changes when a two-sided confidence interval uses 99% rather than 95% confidence, all else
equal?
A) The interval becomes wider
B) The interval becomes narrower
C) The sample standard deviation becomes zero
BUSI 230 | Exam 3 | Independent Practice | 2026/2027 2
