THE T-TEST COMPREHENSIVE EXAM
(CNSL 503) QUESTIONS AND ANSWERS
1. What is the primary reason for using a t-test instead of a z-test in most behavioral science
research?
A. The population mean is unknown.
B. The population standard deviation is unknown.
C. The sample size is too large for a z-test.
D. The data is not normally distributed.
Answer: B
Conceptual Explanation: A t-test is used when the population standard deviation is
unknown and must be estimated using the sample standard deviation.
2. Which of the following describes the relationship between the t-distribution and the
normal distribution?
A. The t-distribution is taller and narrower.
B. The t-distribution is skewed to the right.
C. The t-distribution is identical regardless of sample size.
,D. The t-distribution has thicker tails and lower peaks.
Answer: D
Conceptual Explanation: The t-distribution has more probability in its tails (thicker tails)
and a flatter peak than the normal distribution, though it approaches normality as degrees
of freedom increase.
3. In a one-sample t-test, what does the degrees of freedom (df) represent?
A. n + 1
B. n / 2
C. n - 1
D. n - 2
Answer: C
Conceptual Explanation: For a one-sample t-test, degrees of freedom is calculated as the
sample size minus one (n - 1).
4. An independent-samples t-test is used to compare means between:
A. Two unrelated groups on the same dependent variable.
B. The same group at two different time points.
C. A single group against a known population mean.
D. Three or more groups simultaneously.
, Answer: A
Conceptual Explanation: Independent-samples t-tests compare the means of two distinct,
unrelated groups.
5. What is the null hypothesis for a non-directional independent-samples t-test?
A. Mean 1 is greater than Mean 2.
B. There is no difference between the two population means.
C. Mean 1 is less than Mean 2.
D. The variances of the two groups are unequal.
Answer: B
Conceptual Explanation: The null hypothesis (H0) states that there is no significant
difference between the population means being compared.
6. What is the formula for the degrees of freedom in an independent-samples t-test
(assuming equal variances)?
A. n1 + n2 - 1
B. n1 + n2 - 2
C. n1 - 1
D. (n1 + n2) / 2
Answer: B
(CNSL 503) QUESTIONS AND ANSWERS
1. What is the primary reason for using a t-test instead of a z-test in most behavioral science
research?
A. The population mean is unknown.
B. The population standard deviation is unknown.
C. The sample size is too large for a z-test.
D. The data is not normally distributed.
Answer: B
Conceptual Explanation: A t-test is used when the population standard deviation is
unknown and must be estimated using the sample standard deviation.
2. Which of the following describes the relationship between the t-distribution and the
normal distribution?
A. The t-distribution is taller and narrower.
B. The t-distribution is skewed to the right.
C. The t-distribution is identical regardless of sample size.
,D. The t-distribution has thicker tails and lower peaks.
Answer: D
Conceptual Explanation: The t-distribution has more probability in its tails (thicker tails)
and a flatter peak than the normal distribution, though it approaches normality as degrees
of freedom increase.
3. In a one-sample t-test, what does the degrees of freedom (df) represent?
A. n + 1
B. n / 2
C. n - 1
D. n - 2
Answer: C
Conceptual Explanation: For a one-sample t-test, degrees of freedom is calculated as the
sample size minus one (n - 1).
4. An independent-samples t-test is used to compare means between:
A. Two unrelated groups on the same dependent variable.
B. The same group at two different time points.
C. A single group against a known population mean.
D. Three or more groups simultaneously.
, Answer: A
Conceptual Explanation: Independent-samples t-tests compare the means of two distinct,
unrelated groups.
5. What is the null hypothesis for a non-directional independent-samples t-test?
A. Mean 1 is greater than Mean 2.
B. There is no difference between the two population means.
C. Mean 1 is less than Mean 2.
D. The variances of the two groups are unequal.
Answer: B
Conceptual Explanation: The null hypothesis (H0) states that there is no significant
difference between the population means being compared.
6. What is the formula for the degrees of freedom in an independent-samples t-test
(assuming equal variances)?
A. n1 + n2 - 1
B. n1 + n2 - 2
C. n1 - 1
D. (n1 + n2) / 2
Answer: B
