ADVANCED T-TEST CONCEPTS IN
CNSL 503 QUESTIONS AND ANSWERS
1. When conducting an independent samples t-test, which assumption is violated if the
variance of one group is significantly larger than the other?
A. Independence of observations
B. Normality of the sampling distribution
C. Homogeneity of variance
D. Linearity of the means
Answer: C
Conceptual Explanation: Homogeneity of variance, often tested by Levene’s test, assumes
that the groups being compared have roughly the same variance.
2. In a paired-samples t-test with 25 pairs of participants, what are the degrees of freedom
(df)?
A. 49
B. 48
C. 25
,D. 24
Answer: D
Conceptual Explanation: For a paired-samples t-test, df = n - 1, where n is the number of
pairs. Thus, 25 - 1 = 24.
3. Which of the following would increase the likelihood of rejecting the null hypothesis in a t-
test?
A. Decreasing the sample size
B. Increasing the difference between group means
C. Increasing the standard deviation within groups
D. Using a two-tailed test instead of a one-tailed test
Answer: B
Conceptual Explanation: A larger difference between means increases the numerator of
the t-statistic, leading to a higher t-value and a lower p-value.
4. What does Cohen’s d measure in the context of a t-test?
A. The probability that the null hypothesis is true
B. The ratio of between-group variance to within-group variance
C. The degrees of freedom of the test
D. The standardized difference between two means
, Answer: D
Conceptual Explanation: Cohen’s d is a measure of effect size that indicates how many
standard deviations the means differ by.
5. If a researcher performs a one-sample t-test and calculates a t-statistic of 0, what can be
concluded about the sample mean?
A. The p-value is 0
B. The sample size was too small to calculate a difference
C. The variance of the sample is zero
D. The sample mean is equal to the population mean specified in the null hypothesis
Answer: D
Conceptual Explanation: The numerator of the t-statistic formula is (Sample Mean -
Population Mean). If t = 0, the difference must be zero.
6. Which test is most appropriate for comparing the test scores of the same group of students
before and after a training module?
A. Dependent (Paired) samples t-test
B. One-sample t-test
C. Independent samples t-test
D. Z-test
Answer: A
CNSL 503 QUESTIONS AND ANSWERS
1. When conducting an independent samples t-test, which assumption is violated if the
variance of one group is significantly larger than the other?
A. Independence of observations
B. Normality of the sampling distribution
C. Homogeneity of variance
D. Linearity of the means
Answer: C
Conceptual Explanation: Homogeneity of variance, often tested by Levene’s test, assumes
that the groups being compared have roughly the same variance.
2. In a paired-samples t-test with 25 pairs of participants, what are the degrees of freedom
(df)?
A. 49
B. 48
C. 25
,D. 24
Answer: D
Conceptual Explanation: For a paired-samples t-test, df = n - 1, where n is the number of
pairs. Thus, 25 - 1 = 24.
3. Which of the following would increase the likelihood of rejecting the null hypothesis in a t-
test?
A. Decreasing the sample size
B. Increasing the difference between group means
C. Increasing the standard deviation within groups
D. Using a two-tailed test instead of a one-tailed test
Answer: B
Conceptual Explanation: A larger difference between means increases the numerator of
the t-statistic, leading to a higher t-value and a lower p-value.
4. What does Cohen’s d measure in the context of a t-test?
A. The probability that the null hypothesis is true
B. The ratio of between-group variance to within-group variance
C. The degrees of freedom of the test
D. The standardized difference between two means
, Answer: D
Conceptual Explanation: Cohen’s d is a measure of effect size that indicates how many
standard deviations the means differ by.
5. If a researcher performs a one-sample t-test and calculates a t-statistic of 0, what can be
concluded about the sample mean?
A. The p-value is 0
B. The sample size was too small to calculate a difference
C. The variance of the sample is zero
D. The sample mean is equal to the population mean specified in the null hypothesis
Answer: D
Conceptual Explanation: The numerator of the t-statistic formula is (Sample Mean -
Population Mean). If t = 0, the difference must be zero.
6. Which test is most appropriate for comparing the test scores of the same group of students
before and after a training module?
A. Dependent (Paired) samples t-test
B. One-sample t-test
C. Independent samples t-test
D. Z-test
Answer: A
