COMPREHENSIVE EXAM ON THE T-
TEST (CNSL 503) QUESTIONS AND
ANSWERS
1. When conducting a one-sample t-test, what is the primary reason the t-distribution is used
instead of the standard normal z-distribution?
A. The population standard deviation is unknown.
B. The population mean is unknown.
C. The sample size is always smaller than 30.
D. The data are not normally distributed.
Answer: A
Conceptual Explanation: The t-test is specifically designed for situations where the
population standard deviation is unknown and must be estimated from sample data.
2. Which of the following defines the ‘degrees of freedom’ for a single-sample t-test?
A. Square root of n
B. n - 2
C. n1 + n2 - 2
,D. n - 1
Answer: D
Conceptual Explanation: For a one-sample t-test, the degrees of freedom represent the
number of scores in a sample that are free to vary, calculated as n - 1.
3. How does the shape of the t-distribution change as the degrees of freedom increase?
A. It becomes flatter with thicker tails.
B. It becomes skewed to the right.
C. It becomes narrower and more leptokurtic than a z-distribution.
D. It approaches the shape of a normal distribution.
Answer: D
Conceptual Explanation: As sample size (and thus df) increases, the t-distribution
converges toward the standard normal z-distribution because the sample variance
becomes a better estimate of population variance.
4. In an independent-measures t-test, what is the null hypothesis?
A. M1 - M2 = 0
B. M1 = μ1
C. μ1 - μ2 = 0
D. σ1 = σ2
, Answer: C
Conceptual Explanation: The null hypothesis for an independent-measures t-test states
that there is no difference between the population means (μ1 - μ2 = 0).
5. What is the calculated value of df for an independent-measures study with n1 = 15 and n2
= 15?
A. 28
B. 29
C. 30
D. 14
Answer: A
Conceptual Explanation: The df for independent measures is (n1 - 1) + (n2 - 1), which is
14 + 14 = 28.
6. If a researcher reports a t-statistic with df = 20 for a repeated-measures study, how many
individuals participated in the study?
A. 21
B. 20
C. 22
D. 40
Answer: A
TEST (CNSL 503) QUESTIONS AND
ANSWERS
1. When conducting a one-sample t-test, what is the primary reason the t-distribution is used
instead of the standard normal z-distribution?
A. The population standard deviation is unknown.
B. The population mean is unknown.
C. The sample size is always smaller than 30.
D. The data are not normally distributed.
Answer: A
Conceptual Explanation: The t-test is specifically designed for situations where the
population standard deviation is unknown and must be estimated from sample data.
2. Which of the following defines the ‘degrees of freedom’ for a single-sample t-test?
A. Square root of n
B. n - 2
C. n1 + n2 - 2
,D. n - 1
Answer: D
Conceptual Explanation: For a one-sample t-test, the degrees of freedom represent the
number of scores in a sample that are free to vary, calculated as n - 1.
3. How does the shape of the t-distribution change as the degrees of freedom increase?
A. It becomes flatter with thicker tails.
B. It becomes skewed to the right.
C. It becomes narrower and more leptokurtic than a z-distribution.
D. It approaches the shape of a normal distribution.
Answer: D
Conceptual Explanation: As sample size (and thus df) increases, the t-distribution
converges toward the standard normal z-distribution because the sample variance
becomes a better estimate of population variance.
4. In an independent-measures t-test, what is the null hypothesis?
A. M1 - M2 = 0
B. M1 = μ1
C. μ1 - μ2 = 0
D. σ1 = σ2
, Answer: C
Conceptual Explanation: The null hypothesis for an independent-measures t-test states
that there is no difference between the population means (μ1 - μ2 = 0).
5. What is the calculated value of df for an independent-measures study with n1 = 15 and n2
= 15?
A. 28
B. 29
C. 30
D. 14
Answer: A
Conceptual Explanation: The df for independent measures is (n1 - 1) + (n2 - 1), which is
14 + 14 = 28.
6. If a researcher reports a t-statistic with df = 20 for a repeated-measures study, how many
individuals participated in the study?
A. 21
B. 20
C. 22
D. 40
Answer: A
