,Liberty University PSYC 354 Quiz 5 | Statistics for the
Social Sciences (2026) Q&A
1. Which of the following best describes a sampling distribution?
A) The distribution of all individual scores in a population
B) The distribution of a statistic (such as the mean) calculated from all possible samples of
the same size from a population
C) The distribution of scores from a single sample
D) The distribution of raw scores after they have been transformed into z-scores
Correct Answer: The distribution of a statistic (such as the mean) calculated from all
possible samples of the same size from a population
Rationale: A sampling distribution is the theoretical distribution of a statistic (like the mean)
that would be obtained if all possible samples of a given size were drawn from a population.
It is a foundational concept in inferential statistics, allowing researchers to determine
probabilities associated with sample statistics.
2. According to the central limit theorem, as sample size increases, the distribution of sample
means approaches which type of distribution?
A) A positively skewed distribution
B) A negatively skewed distribution
C) A normal distribution
D) A uniform distribution
Correct Answer: A normal distribution
Rationale: The central limit theorem states that regardless of the shape of the population
distribution, the distribution of sample means will approach a normal distribution as the
sample size becomes sufficiently large (typically n ≥ 30). This theorem is critical because it
allows researchers to use normal-curve probabilities for hypothesis testing.
,3. What is the standard error of the mean?
A) The standard deviation of the raw scores in the population
B) The standard deviation of the sampling distribution of the mean
C) The difference between the sample mean and the population mean
D) The variance of the sample data
Correct Answer: The standard deviation of the sampling distribution of the mean
Rationale: The standard error of the mean (SEM) is the standard deviation of the sampling
distribution of the mean. It measures the average distance between a sample mean and the
population mean. It is calculated as σ / √n, where σ is the population standard deviation and n
is the sample size.
4. How does increasing the sample size affect the standard error of the mean?
A) It increases the standard error
B) It decreases the standard error
C) It has no effect on the standard error
D) It makes the standard error equal to the population standard deviation
Correct Answer: It decreases the standard error
Rationale: The standard error of the mean is calculated as σ / √n. Because the sample size (n)
is in the denominator, increasing n decreases the standard error. This means that larger
samples provide more precise estimates of the population mean.
5. A researcher draws a sample of n = 25 from a population with μ = 50 and σ = 10. What is
the standard error of the mean?
A) 0.4
B) 2.0
C) 10
D) 25
, Correct Answer: 2.0
Rationale: The standard error of the mean is calculated as σ / √n = 10 / √25 = = 2.0.
This value represents the average distance between sample means and the population mean
for samples of this size.
6. A researcher draws a sample of n = 100 from a population with μ = 80 and σ = 20. What is
the standard error of the mean?
A) 0.2
B) 2.0
C) 8.0
D) 20
Correct Answer: 2.0
Rationale: The standard error of the mean is σ / √n = 20 / √100 = = 2.0. Increasing
the sample size from 25 to 100 (as in the previous question) decreased the standard error from
2.0 to 2.0 in this case because the standard deviation is also different.
7. What is the relationship between sample size and the shape of the sampling distribution of
the mean?
A) The shape becomes more skewed as sample size increases
B) The shape becomes closer to normal as sample size increases
C) The shape becomes bimodal as sample size increases
D) The shape is unrelated to sample size
Correct Answer: The shape becomes closer to normal as sample size increases
Rationale: According to the central limit theorem, the sampling distribution of the mean
becomes increasingly normal as sample size increases, regardless of the shape of the
population distribution. This is true even when the population is heavily skewed.
Social Sciences (2026) Q&A
1. Which of the following best describes a sampling distribution?
A) The distribution of all individual scores in a population
B) The distribution of a statistic (such as the mean) calculated from all possible samples of
the same size from a population
C) The distribution of scores from a single sample
D) The distribution of raw scores after they have been transformed into z-scores
Correct Answer: The distribution of a statistic (such as the mean) calculated from all
possible samples of the same size from a population
Rationale: A sampling distribution is the theoretical distribution of a statistic (like the mean)
that would be obtained if all possible samples of a given size were drawn from a population.
It is a foundational concept in inferential statistics, allowing researchers to determine
probabilities associated with sample statistics.
2. According to the central limit theorem, as sample size increases, the distribution of sample
means approaches which type of distribution?
A) A positively skewed distribution
B) A negatively skewed distribution
C) A normal distribution
D) A uniform distribution
Correct Answer: A normal distribution
Rationale: The central limit theorem states that regardless of the shape of the population
distribution, the distribution of sample means will approach a normal distribution as the
sample size becomes sufficiently large (typically n ≥ 30). This theorem is critical because it
allows researchers to use normal-curve probabilities for hypothesis testing.
,3. What is the standard error of the mean?
A) The standard deviation of the raw scores in the population
B) The standard deviation of the sampling distribution of the mean
C) The difference between the sample mean and the population mean
D) The variance of the sample data
Correct Answer: The standard deviation of the sampling distribution of the mean
Rationale: The standard error of the mean (SEM) is the standard deviation of the sampling
distribution of the mean. It measures the average distance between a sample mean and the
population mean. It is calculated as σ / √n, where σ is the population standard deviation and n
is the sample size.
4. How does increasing the sample size affect the standard error of the mean?
A) It increases the standard error
B) It decreases the standard error
C) It has no effect on the standard error
D) It makes the standard error equal to the population standard deviation
Correct Answer: It decreases the standard error
Rationale: The standard error of the mean is calculated as σ / √n. Because the sample size (n)
is in the denominator, increasing n decreases the standard error. This means that larger
samples provide more precise estimates of the population mean.
5. A researcher draws a sample of n = 25 from a population with μ = 50 and σ = 10. What is
the standard error of the mean?
A) 0.4
B) 2.0
C) 10
D) 25
, Correct Answer: 2.0
Rationale: The standard error of the mean is calculated as σ / √n = 10 / √25 = = 2.0.
This value represents the average distance between sample means and the population mean
for samples of this size.
6. A researcher draws a sample of n = 100 from a population with μ = 80 and σ = 20. What is
the standard error of the mean?
A) 0.2
B) 2.0
C) 8.0
D) 20
Correct Answer: 2.0
Rationale: The standard error of the mean is σ / √n = 20 / √100 = = 2.0. Increasing
the sample size from 25 to 100 (as in the previous question) decreased the standard error from
2.0 to 2.0 in this case because the standard deviation is also different.
7. What is the relationship between sample size and the shape of the sampling distribution of
the mean?
A) The shape becomes more skewed as sample size increases
B) The shape becomes closer to normal as sample size increases
C) The shape becomes bimodal as sample size increases
D) The shape is unrelated to sample size
Correct Answer: The shape becomes closer to normal as sample size increases
Rationale: According to the central limit theorem, the sampling distribution of the mean
becomes increasingly normal as sample size increases, regardless of the shape of the
population distribution. This is true even when the population is heavily skewed.
