ADVANCED STATISTICS QUIZ: THE T-
TEST (CNSL 503) QUESTIONS AND
ANSWERS
1. When is it more appropriate to use a t-test instead of a z-test?
A. When the population standard deviation is unknown
B. When the population mean is unknown
C. When the sample size is greater than 100
D. When the data is measured on a nominal scale
Answer: A
Conceptual Explanation: The t-test is specifically used when the population standard
deviation is unknown and must be estimated using the sample standard deviation.
2. Which of the following describes the shape of the t-distribution as the degrees of freedom
increase?
A. It approaches the shape of the standard normal distribution
B. It becomes flatter with thicker tails
C. It becomes more skewed to the right
D. It becomes increasingly narrow and tall compared to the z-distribution
,Answer: A
Conceptual Explanation: As sample size (and thus degrees of freedom) increases, the t-
distribution converges toward the standard normal (z) distribution.
3. What is the degrees of freedom formula for a one-sample t-test?
A. N - 1
B. N - 2
C. (n1 - 1) + (n2 - 1)
D. N
Answer: A
Conceptual Explanation: For a one-sample t-test, the degrees of freedom are calculated as
the total number of observations minus one.
4. In an independent samples t-test, what does the null hypothesis usually state?
A. The population means are equal
B. The sample means are significantly different
C. The variance of the two groups is different
D. The effect size is large
Answer: A
, Conceptual Explanation: The null hypothesis (H0) typically posits that there is no
difference between the population means of the two groups being compared.
5. A researcher reports t(24) = 2.50, p < .05. How many participants were in this one-sample
study?
A. 24
B. 23
C. 25
D. 26
Answer: C
Conceptual Explanation: Since df = N - 1 for a one-sample test, if df = 24, then N = 24 + 1 =
25.
6. Which test is most appropriate for a pre-test/post-test design involving the same
participants?
A. Independent samples t-test
B. One-sample t-test
C. Chi-square test
D. Dependent (paired) samples t-test
Answer: D
TEST (CNSL 503) QUESTIONS AND
ANSWERS
1. When is it more appropriate to use a t-test instead of a z-test?
A. When the population standard deviation is unknown
B. When the population mean is unknown
C. When the sample size is greater than 100
D. When the data is measured on a nominal scale
Answer: A
Conceptual Explanation: The t-test is specifically used when the population standard
deviation is unknown and must be estimated using the sample standard deviation.
2. Which of the following describes the shape of the t-distribution as the degrees of freedom
increase?
A. It approaches the shape of the standard normal distribution
B. It becomes flatter with thicker tails
C. It becomes more skewed to the right
D. It becomes increasingly narrow and tall compared to the z-distribution
,Answer: A
Conceptual Explanation: As sample size (and thus degrees of freedom) increases, the t-
distribution converges toward the standard normal (z) distribution.
3. What is the degrees of freedom formula for a one-sample t-test?
A. N - 1
B. N - 2
C. (n1 - 1) + (n2 - 1)
D. N
Answer: A
Conceptual Explanation: For a one-sample t-test, the degrees of freedom are calculated as
the total number of observations minus one.
4. In an independent samples t-test, what does the null hypothesis usually state?
A. The population means are equal
B. The sample means are significantly different
C. The variance of the two groups is different
D. The effect size is large
Answer: A
, Conceptual Explanation: The null hypothesis (H0) typically posits that there is no
difference between the population means of the two groups being compared.
5. A researcher reports t(24) = 2.50, p < .05. How many participants were in this one-sample
study?
A. 24
B. 23
C. 25
D. 26
Answer: C
Conceptual Explanation: Since df = N - 1 for a one-sample test, if df = 24, then N = 24 + 1 =
25.
6. Which test is most appropriate for a pre-test/post-test design involving the same
participants?
A. Independent samples t-test
B. One-sample t-test
C. Chi-square test
D. Dependent (paired) samples t-test
Answer: D
