MODULE 5: THE T-TEST
COMPREHENSIVE ASSESSMENT
QUESTIONS AND ANSWERS
1. When is it appropriate to use a t-test instead of a z-test?
A. When the population mean is unknown.
B. When the sample size is greater than 100.
C. When the data is measured on a nominal scale.
D. When the population standard deviation is unknown.
Answer: D
Conceptual Explanation: A t-test is used when the population standard deviation is
unknown, requiring the use of the sample standard deviation as an estimate.
2. In a one-sample t-test, what does the degrees of freedom (df) represent?
A. N - 1
B. N - 2
C. (n1 + n2) - 2
,D. N
Answer: A
Conceptual Explanation: For a one-sample t-test, the degrees of freedom is calculated as
the sample size minus one (N - 1).
3. Which of the following describes the shape of the t-distribution compared to the normal
distribution?
A. The t-distribution is taller and narrower.
B. The t-distribution is identical regardless of sample size.
C. The t-distribution is skewed to the right.
D. The t-distribution has thicker tails and is flatter in the center.
Answer: D
Conceptual Explanation: The t-distribution is more spread out (platykurtic) with thicker
tails than the normal distribution, though it approaches normality as sample size increases.
4. An independent samples t-test is specifically designed to compare:
A. The mean of one group against a known population constant.
B. The means of two different, unrelated groups.
C. The same group of participants at two different time points.
D. The variances of three or more groups.
, Answer: B
Conceptual Explanation: Independent samples t-tests compare the means of two distinct,
unrelated groups (between-subjects design).
5. What is the null hypothesis (H0) for a non-directional independent samples t-test?
A. μ1 > μ2
B. μ1 = μ2
C. μ1 < μ2
D. μ1 ≠ μ2
Answer: B
Conceptual Explanation: The null hypothesis states that there is no difference between
the population means (μ1 = μ2).
6. If a researcher calculates an independent samples t-test with n1 = 15 and n2 = 15, what are
the degrees of freedom?
A. 28
B. 29
C. 30
D. 14
Answer: A
COMPREHENSIVE ASSESSMENT
QUESTIONS AND ANSWERS
1. When is it appropriate to use a t-test instead of a z-test?
A. When the population mean is unknown.
B. When the sample size is greater than 100.
C. When the data is measured on a nominal scale.
D. When the population standard deviation is unknown.
Answer: D
Conceptual Explanation: A t-test is used when the population standard deviation is
unknown, requiring the use of the sample standard deviation as an estimate.
2. In a one-sample t-test, what does the degrees of freedom (df) represent?
A. N - 1
B. N - 2
C. (n1 + n2) - 2
,D. N
Answer: A
Conceptual Explanation: For a one-sample t-test, the degrees of freedom is calculated as
the sample size minus one (N - 1).
3. Which of the following describes the shape of the t-distribution compared to the normal
distribution?
A. The t-distribution is taller and narrower.
B. The t-distribution is identical regardless of sample size.
C. The t-distribution is skewed to the right.
D. The t-distribution has thicker tails and is flatter in the center.
Answer: D
Conceptual Explanation: The t-distribution is more spread out (platykurtic) with thicker
tails than the normal distribution, though it approaches normality as sample size increases.
4. An independent samples t-test is specifically designed to compare:
A. The mean of one group against a known population constant.
B. The means of two different, unrelated groups.
C. The same group of participants at two different time points.
D. The variances of three or more groups.
, Answer: B
Conceptual Explanation: Independent samples t-tests compare the means of two distinct,
unrelated groups (between-subjects design).
5. What is the null hypothesis (H0) for a non-directional independent samples t-test?
A. μ1 > μ2
B. μ1 = μ2
C. μ1 < μ2
D. μ1 ≠ μ2
Answer: B
Conceptual Explanation: The null hypothesis states that there is no difference between
the population means (μ1 = μ2).
6. If a researcher calculates an independent samples t-test with n1 = 15 and n2 = 15, what are
the degrees of freedom?
A. 28
B. 29
C. 30
D. 14
Answer: A
