,Liberty University PSYC 354 Quiz 6 | Statistics for the
Social Sciences (2026) Q&A
1. Which of the following best describes the purpose of a t-test in statistical analysis?
A) To compare the means of three or more groups
B) To determine whether a sample mean differs from a population mean when the population
standard deviation is unknown
C) To examine the relationship between two categorical variables
D) To calculate the correlation coefficient between two continuous variables
Correct Answer: To determine whether a sample mean differs from a population mean when
the population standard deviation is unknown
Rationale: The t-test is used when the population standard deviation (σ) is unknown, and the
sample standard deviation (s) is used to estimate it. This is the primary difference between a
t-test and a z-test. The t-distribution is used instead of the normal distribution to account for
the additional uncertainty introduced by estimating σ.
2. What is the primary difference between a z-test and a t-test?
A) The z-test is used for small samples, while the t-test is used for large samples
B) The z-test requires the population standard deviation to be known, while the t-test does not
C) The z-test is used for correlation, while the t-test is used for mean differences
D) There is no difference between the two tests
Correct Answer: The z-test requires the population standard deviation to be known, while
the t-test does not
Rationale: The key distinction is that the z-test requires knowledge of the population
standard deviation (σ), while the t-test uses the sample standard deviation (s) to estimate σ.
As sample size increases, the t-distribution approaches the z-distribution.
,3. Which of the following is a parametric test?
A) Chi-square test
B) Mann-Whitney U test
C) One-sample t-test
D) Wilcoxon signed-rank test
Correct Answer: One-sample t-test
Rationale: The one-sample t-test is a parametric test, meaning it is based on assumptions
about the population, such as normality and homogeneity of variance. The chi-square test,
Mann-Whitney U test, and Wilcoxon signed-rank test are non-parametric tests.
4. When is a one-sample t-test most appropriate?
A) When comparing the means of two independent groups
B) When comparing a sample mean to a known population mean and the population standard
deviation is unknown
C) When comparing the means of three or more groups
D) When examining the relationship between two continuous variables
Correct Answer: When comparing a sample mean to a known population mean and the
population standard deviation is unknown
Rationale: The one-sample t-test is specifically designed to compare a single sample mean to
a known population mean when σ is unknown. This is the appropriate test when the
researcher has one group of participants and wants to determine if their mean differs from a
known value.
5. What is the formula for the t-test statistic for a one-sample t-test?
A) t = (M – μ) / σ
B) t = (M – μ) / (s / √n)
C) t = (X – μ) / s
, D) t = (M – μ) / SEM
Correct Answer: t = (M – μ) / (s / √n)
Rationale: The one-sample t-test statistic is calculated as t = (M – μ) / (s / √n), where M is
the sample mean, μ is the population mean, s is the sample standard deviation, and n is the
sample size. The denominator is the estimated standard error of the mean.
6. What are degrees of freedom (df) for a one-sample t-test?
A) n
B) n – 1
C) n – 2
D) n + 1
Correct Answer: n – 1
Rationale: Degrees of freedom for a one-sample t-test are calculated as n – 1, where n is the
sample size. This reflects the number of scores that are free to vary after the mean has been
calculated. The df value is used to determine the critical t-value from the t-distribution table.
7. A researcher conducts a one-sample t-test with a sample size of n = 16. What are the
degrees of freedom for this test?
A) 15
B) 16
C) 17
D) 14
Correct Answer: 15
Social Sciences (2026) Q&A
1. Which of the following best describes the purpose of a t-test in statistical analysis?
A) To compare the means of three or more groups
B) To determine whether a sample mean differs from a population mean when the population
standard deviation is unknown
C) To examine the relationship between two categorical variables
D) To calculate the correlation coefficient between two continuous variables
Correct Answer: To determine whether a sample mean differs from a population mean when
the population standard deviation is unknown
Rationale: The t-test is used when the population standard deviation (σ) is unknown, and the
sample standard deviation (s) is used to estimate it. This is the primary difference between a
t-test and a z-test. The t-distribution is used instead of the normal distribution to account for
the additional uncertainty introduced by estimating σ.
2. What is the primary difference between a z-test and a t-test?
A) The z-test is used for small samples, while the t-test is used for large samples
B) The z-test requires the population standard deviation to be known, while the t-test does not
C) The z-test is used for correlation, while the t-test is used for mean differences
D) There is no difference between the two tests
Correct Answer: The z-test requires the population standard deviation to be known, while
the t-test does not
Rationale: The key distinction is that the z-test requires knowledge of the population
standard deviation (σ), while the t-test uses the sample standard deviation (s) to estimate σ.
As sample size increases, the t-distribution approaches the z-distribution.
,3. Which of the following is a parametric test?
A) Chi-square test
B) Mann-Whitney U test
C) One-sample t-test
D) Wilcoxon signed-rank test
Correct Answer: One-sample t-test
Rationale: The one-sample t-test is a parametric test, meaning it is based on assumptions
about the population, such as normality and homogeneity of variance. The chi-square test,
Mann-Whitney U test, and Wilcoxon signed-rank test are non-parametric tests.
4. When is a one-sample t-test most appropriate?
A) When comparing the means of two independent groups
B) When comparing a sample mean to a known population mean and the population standard
deviation is unknown
C) When comparing the means of three or more groups
D) When examining the relationship between two continuous variables
Correct Answer: When comparing a sample mean to a known population mean and the
population standard deviation is unknown
Rationale: The one-sample t-test is specifically designed to compare a single sample mean to
a known population mean when σ is unknown. This is the appropriate test when the
researcher has one group of participants and wants to determine if their mean differs from a
known value.
5. What is the formula for the t-test statistic for a one-sample t-test?
A) t = (M – μ) / σ
B) t = (M – μ) / (s / √n)
C) t = (X – μ) / s
, D) t = (M – μ) / SEM
Correct Answer: t = (M – μ) / (s / √n)
Rationale: The one-sample t-test statistic is calculated as t = (M – μ) / (s / √n), where M is
the sample mean, μ is the population mean, s is the sample standard deviation, and n is the
sample size. The denominator is the estimated standard error of the mean.
6. What are degrees of freedom (df) for a one-sample t-test?
A) n
B) n – 1
C) n – 2
D) n + 1
Correct Answer: n – 1
Rationale: Degrees of freedom for a one-sample t-test are calculated as n – 1, where n is the
sample size. This reflects the number of scores that are free to vary after the mean has been
calculated. The df value is used to determine the critical t-value from the t-distribution table.
7. A researcher conducts a one-sample t-test with a sample size of n = 16. What are the
degrees of freedom for this test?
A) 15
B) 16
C) 17
D) 14
Correct Answer: 15
