Lean Six Sigma Green Belt Statistical Analysis & Process
Control Certification Exam | Complete Exam Prep & Verified
Answers 2026/2027
QUESTION 1
What does the standard deviation (𝜎) measure in a dataset?
• A. The central tendency or average value of the data.
• B. The dispersion or spread of data points around the mean.
• C. The exact midpoint separating the higher and lower halves of
data.
• D. The difference between the maximum and minimum values.
Correct Answer: B. The dispersion or spread of data points around the
mean.
Detailed Rationale: Standard deviation quantifies how much individual
data values vary or deviate from the arithmetic mean of the
distribution.
QUESTION 2
According to the Empirical Rule (68-95-99.7 rule) for a normal
distribution, approximately what percentage of data falls within ±2
standard deviations of the mean?
• A. 68%
• B. 95%
• C. 99.7%
, • D. 50%
Correct Answer: B. 95%
Detailed Rationale: The Empirical Rule states that approximately 68%
of data falls within ±1𝜎, 95% within ±2𝜎, and 99.7% within ±3𝜎 of
the mean in a normal distribution.
QUESTION 3
What does the Central Limit Theorem state regarding the distribution of
sample means?
• A. The distribution of sample means always follows a uniform
distribution.
• B. As sample size increases (𝑛 ≥ 30), the distribution of sample
means approaches a normal distribution regardless of the
underlying population distribution shape.
• C. Sample means have a higher standard deviation than the
original population.
• D. Sample means can only be calculated if the population is
perfectly skewed.
Correct Answer: B. As sample size increases (𝑛 ≥ 30), the distribution
of sample means approaches a normal distribution regardless of the
underlying population distribution shape.
Detailed Rationale: The Central Limit Theorem is fundamental to
inferential statistics, allowing Green Belts to use normal distribution
models for hypothesis testing on means when sample sizes are
sufficiently large.
,QUESTION 4
In hypothesis testing, what does a Type I error (𝛼) represent?
• A. Rejecting the null hypothesis when it is actually true (a false
positive).
• B. Failing to reject the null hypothesis when it is actually false (a
false negative).
• C. Correctly rejecting the null hypothesis.
• D. Correctly accepting the null hypothesis.
Correct Answer: A. Rejecting the null hypothesis when it is actually true
(a false positive).
Detailed Rationale: A Type I error occurs when a team concludes there
is a significant difference or improvement when, in reality, no true
change occurred and the result was due to random chance.
QUESTION 5
If a calculated 𝑝-value in a hypothesis test is 0.03 and the significance
level (𝛼) is set at 0.05, what is the correct statistical decision?
• A. Fail to reject the null hypothesis because 𝑝 < 𝛼.
• B. Reject the null hypothesis because 𝑝 < 𝛼.
• C. Accept the null hypothesis as absolutely proven.
• D. Redo the test with a larger sample size.
Correct Answer: B. Reject the null hypothesis because 𝑝 < 𝛼.
, Detailed Rationale: When the 𝑝-value is less than the significance level
(𝛼), there is sufficient statistical evidence to reject the null hypothesis in
favor of the alternative hypothesis.
QUESTION 6
When should a One-Sample 𝑡-test be used instead of a One-Sample 𝑍-
test?
• A. When the population standard deviation (𝜎) is known and
sample size is large.
• B. When the population standard deviation (𝜎) is unknown and
must be estimated using the sample standard deviation (𝑠).
• C. When analyzing categorical pass/fail attribute data.
• D. When comparing three or more independent population
means.
Correct Answer: B. When the population standard deviation (𝜎) is
unknown and must be estimated using the sample standard deviation
(𝑠).
Detailed Rationale: In most practical scenarios, the true population
standard deviation is unknown, requiring the use of the 𝑡-distribution
rather than the standard normal 𝑍-distribution.
QUESTION 7
What is the primary purpose of a Paired 𝑡-test?
• A. To compare the means of two independent groups measured
under different conditions.
Control Certification Exam | Complete Exam Prep & Verified
Answers 2026/2027
QUESTION 1
What does the standard deviation (𝜎) measure in a dataset?
• A. The central tendency or average value of the data.
• B. The dispersion or spread of data points around the mean.
• C. The exact midpoint separating the higher and lower halves of
data.
• D. The difference between the maximum and minimum values.
Correct Answer: B. The dispersion or spread of data points around the
mean.
Detailed Rationale: Standard deviation quantifies how much individual
data values vary or deviate from the arithmetic mean of the
distribution.
QUESTION 2
According to the Empirical Rule (68-95-99.7 rule) for a normal
distribution, approximately what percentage of data falls within ±2
standard deviations of the mean?
• A. 68%
• B. 95%
• C. 99.7%
, • D. 50%
Correct Answer: B. 95%
Detailed Rationale: The Empirical Rule states that approximately 68%
of data falls within ±1𝜎, 95% within ±2𝜎, and 99.7% within ±3𝜎 of
the mean in a normal distribution.
QUESTION 3
What does the Central Limit Theorem state regarding the distribution of
sample means?
• A. The distribution of sample means always follows a uniform
distribution.
• B. As sample size increases (𝑛 ≥ 30), the distribution of sample
means approaches a normal distribution regardless of the
underlying population distribution shape.
• C. Sample means have a higher standard deviation than the
original population.
• D. Sample means can only be calculated if the population is
perfectly skewed.
Correct Answer: B. As sample size increases (𝑛 ≥ 30), the distribution
of sample means approaches a normal distribution regardless of the
underlying population distribution shape.
Detailed Rationale: The Central Limit Theorem is fundamental to
inferential statistics, allowing Green Belts to use normal distribution
models for hypothesis testing on means when sample sizes are
sufficiently large.
,QUESTION 4
In hypothesis testing, what does a Type I error (𝛼) represent?
• A. Rejecting the null hypothesis when it is actually true (a false
positive).
• B. Failing to reject the null hypothesis when it is actually false (a
false negative).
• C. Correctly rejecting the null hypothesis.
• D. Correctly accepting the null hypothesis.
Correct Answer: A. Rejecting the null hypothesis when it is actually true
(a false positive).
Detailed Rationale: A Type I error occurs when a team concludes there
is a significant difference or improvement when, in reality, no true
change occurred and the result was due to random chance.
QUESTION 5
If a calculated 𝑝-value in a hypothesis test is 0.03 and the significance
level (𝛼) is set at 0.05, what is the correct statistical decision?
• A. Fail to reject the null hypothesis because 𝑝 < 𝛼.
• B. Reject the null hypothesis because 𝑝 < 𝛼.
• C. Accept the null hypothesis as absolutely proven.
• D. Redo the test with a larger sample size.
Correct Answer: B. Reject the null hypothesis because 𝑝 < 𝛼.
, Detailed Rationale: When the 𝑝-value is less than the significance level
(𝛼), there is sufficient statistical evidence to reject the null hypothesis in
favor of the alternative hypothesis.
QUESTION 6
When should a One-Sample 𝑡-test be used instead of a One-Sample 𝑍-
test?
• A. When the population standard deviation (𝜎) is known and
sample size is large.
• B. When the population standard deviation (𝜎) is unknown and
must be estimated using the sample standard deviation (𝑠).
• C. When analyzing categorical pass/fail attribute data.
• D. When comparing three or more independent population
means.
Correct Answer: B. When the population standard deviation (𝜎) is
unknown and must be estimated using the sample standard deviation
(𝑠).
Detailed Rationale: In most practical scenarios, the true population
standard deviation is unknown, requiring the use of the 𝑡-distribution
rather than the standard normal 𝑍-distribution.
QUESTION 7
What is the primary purpose of a Paired 𝑡-test?
• A. To compare the means of two independent groups measured
under different conditions.
