Module 6 Exam (Latest-2026/2027) / Module 6 Exam / Statistics Module 6 Exam | Portage Learning 2026/2027 -
2026/2027 Official Exam
OBJECTIVE ASSESSMENT - EXAM
Module 6 Exam (Latest-2026/2027) / Module 6 Exam / Statistics Module 6
Exam | Portage Learning 2026/2027 - 2026/2027 Official Exam
50 100% 2026/2027
QUESTIONS VERIFIED ANSWERS EDITION
TOPICS COVERED
Sampling Distributions Estimation & Margin of Error
Central Limit Theorem Sample Size Determination
Confidence Intervals
COVER PAGE - 1
, SECTION 1 | Sampling Distributions & Central Limit Theorem | Q1-Q10
Module 6 Exam (Latest-2026/2027) / Module 6 Exam / Statistics Module 6 Exam | Portage Learning 2026/2027 2026/2027
Q1 Question 1 of 50
A researcher draws all possible samples of size 36 from a population with mean 72 and standard
deviation 12, and computes the sample mean for each. The distribution formed by these sample means
is being analyzed. What is the expected standard deviation of this distribution?
2.0, calculated as the population standard deviation divided by the sample size
2.0, calculated as the population standard deviation divided by the square root of sample size
12.0, equal to the population standard deviation since sample size is large
0.33, calculated as the sample size divided by the population standard deviation
Correct Answer: B
Rationale:
The standard error of the mean equals sigma divided by the square root of n, giving 12 divided by 6 which
equals 2.0. Option A incorrectly divides by n rather than the square root of n, while option B ignores the
reduction in variability that averaging produces.
Q2 Question 2 of 50
An instructor states that as sample size increases, the sampling distribution of the sample mean
becomes approximately normal regardless of the population shape. A student asks which theorem this
describes. Which theorem is the instructor referencing?
Law of Large Numbers, which guarantees convergence to the population mean
Central Limit Theorem, which states sample means approach normality as n grows
Chebyshev Theorem, which bounds the proportion of values within k standard deviations
Empirical Rule, which applies only when the population is already normal
Correct Answer: B
Rationale:
The Central Limit Theorem states that for sufficiently large sample sizes, the sampling distribution of the
sample mean approaches a normal distribution regardless of the underlying population shape. The Law of
Large Numbers addresses convergence to the mean, not distributional shape.
Module 6 Exam (Latest-2026/2027) / Module 6 Exam / Statistics Module 6 Exam | Portage Learning 2026/2027 - 2026/2027 | Passing Score: 80% | Page 2 of 27
, SECTION 1 | Sampling Distributions & Central Limit Theorem | Q1-Q10
Module 6 Exam (Latest-2026/2027) / Module 6 Exam / Statistics Module 6 Exam | Portage Learning 2026/2027 2026/2027
Q3 Question 3 of 50
A quality control engineer samples 25 light bulbs from a population that is strongly right-skewed with
mean life 800 hours and standard deviation 100 hours. The engineer wants to compute probabilities
about the sample mean. Which statement is most appropriate regarding the sampling distribution?
The sampling distribution is normal because the population standard deviation is known
The sampling distribution cannot be assumed normal because n is less than 30 and the
population is skewed
The sampling distribution is normal because the sample was randomly selected
The sampling distribution follows a t-distribution with 24 degrees of freedom
Correct Answer: B
Rationale:
When the sample size is below 30 and the population is not normally distributed, the Central Limit Theorem
cannot be safely applied, so the sampling distribution cannot be assumed normal. Random sampling alone
or a known standard deviation does not justify normality in this case.
Q4 Question 4 of 50
A population has mean 50 and standard deviation 8. Samples of size 64 are drawn and the sample
mean is computed. Within what range will approximately 95 percent of sample means fall, according to
the empirical rule?
46 to 54, which is plus or minus two standard errors of the mean
48 to 52, which is plus or minus one standard error of the mean
42 to 58, which is plus or minus three standard errors of the mean
34 to 66, which is plus or minus two population standard deviations
Correct Answer: A
Rationale:
The standard error is 8 divided by the square root of 64 which equals 1. Approximately 95 percent of sample
means fall within two standard errors of the population mean, giving 50 plus or minus 2, or 48 to 52. Option D
incorrectly uses the population standard deviation rather than the standard error.
Module 6 Exam (Latest-2026/2027) / Module 6 Exam / Statistics Module 6 Exam | Portage Learning 2026/2027 - 2026/2027 | Passing Score: 80% | Page 3 of 27
2026/2027 Official Exam
OBJECTIVE ASSESSMENT - EXAM
Module 6 Exam (Latest-2026/2027) / Module 6 Exam / Statistics Module 6
Exam | Portage Learning 2026/2027 - 2026/2027 Official Exam
50 100% 2026/2027
QUESTIONS VERIFIED ANSWERS EDITION
TOPICS COVERED
Sampling Distributions Estimation & Margin of Error
Central Limit Theorem Sample Size Determination
Confidence Intervals
COVER PAGE - 1
, SECTION 1 | Sampling Distributions & Central Limit Theorem | Q1-Q10
Module 6 Exam (Latest-2026/2027) / Module 6 Exam / Statistics Module 6 Exam | Portage Learning 2026/2027 2026/2027
Q1 Question 1 of 50
A researcher draws all possible samples of size 36 from a population with mean 72 and standard
deviation 12, and computes the sample mean for each. The distribution formed by these sample means
is being analyzed. What is the expected standard deviation of this distribution?
2.0, calculated as the population standard deviation divided by the sample size
2.0, calculated as the population standard deviation divided by the square root of sample size
12.0, equal to the population standard deviation since sample size is large
0.33, calculated as the sample size divided by the population standard deviation
Correct Answer: B
Rationale:
The standard error of the mean equals sigma divided by the square root of n, giving 12 divided by 6 which
equals 2.0. Option A incorrectly divides by n rather than the square root of n, while option B ignores the
reduction in variability that averaging produces.
Q2 Question 2 of 50
An instructor states that as sample size increases, the sampling distribution of the sample mean
becomes approximately normal regardless of the population shape. A student asks which theorem this
describes. Which theorem is the instructor referencing?
Law of Large Numbers, which guarantees convergence to the population mean
Central Limit Theorem, which states sample means approach normality as n grows
Chebyshev Theorem, which bounds the proportion of values within k standard deviations
Empirical Rule, which applies only when the population is already normal
Correct Answer: B
Rationale:
The Central Limit Theorem states that for sufficiently large sample sizes, the sampling distribution of the
sample mean approaches a normal distribution regardless of the underlying population shape. The Law of
Large Numbers addresses convergence to the mean, not distributional shape.
Module 6 Exam (Latest-2026/2027) / Module 6 Exam / Statistics Module 6 Exam | Portage Learning 2026/2027 - 2026/2027 | Passing Score: 80% | Page 2 of 27
, SECTION 1 | Sampling Distributions & Central Limit Theorem | Q1-Q10
Module 6 Exam (Latest-2026/2027) / Module 6 Exam / Statistics Module 6 Exam | Portage Learning 2026/2027 2026/2027
Q3 Question 3 of 50
A quality control engineer samples 25 light bulbs from a population that is strongly right-skewed with
mean life 800 hours and standard deviation 100 hours. The engineer wants to compute probabilities
about the sample mean. Which statement is most appropriate regarding the sampling distribution?
The sampling distribution is normal because the population standard deviation is known
The sampling distribution cannot be assumed normal because n is less than 30 and the
population is skewed
The sampling distribution is normal because the sample was randomly selected
The sampling distribution follows a t-distribution with 24 degrees of freedom
Correct Answer: B
Rationale:
When the sample size is below 30 and the population is not normally distributed, the Central Limit Theorem
cannot be safely applied, so the sampling distribution cannot be assumed normal. Random sampling alone
or a known standard deviation does not justify normality in this case.
Q4 Question 4 of 50
A population has mean 50 and standard deviation 8. Samples of size 64 are drawn and the sample
mean is computed. Within what range will approximately 95 percent of sample means fall, according to
the empirical rule?
46 to 54, which is plus or minus two standard errors of the mean
48 to 52, which is plus or minus one standard error of the mean
42 to 58, which is plus or minus three standard errors of the mean
34 to 66, which is plus or minus two population standard deviations
Correct Answer: A
Rationale:
The standard error is 8 divided by the square root of 64 which equals 1. Approximately 95 percent of sample
means fall within two standard errors of the population mean, giving 50 plus or minus 2, or 48 to 52. Option D
incorrectly uses the population standard deviation rather than the standard error.
Module 6 Exam (Latest-2026/2027) / Module 6 Exam / Statistics Module 6 Exam | Portage Learning 2026/2027 - 2026/2027 | Passing Score: 80% | Page 3 of 27
