COMPREHENSIVE EXAM: THE T-TEST
(CNSL 503) QUESTIONS AND ANSWERS
1. Which of the following conditions must be met to justify the use of a t-test instead of a Z-
test?
A. The population standard deviation is unknown
B. The population mean is unknown
C. The sample size is greater than 100
D. The data follows a binomial distribution
Answer: A
Conceptual Explanation: A t-test is used specifically when the population standard
deviation is unknown and must be estimated using the sample standard deviation.
2. In an independent samples t-test, what does ‘degrees of freedom’ represent?
A. The total number of observations minus two
B. The number of groups being compared
C. The total number of observations minus one
,D. The square root of the variance
Answer: A
Conceptual Explanation: For an independent samples t-test, df = (n1 - 1) + (n2 - 1), which
simplifies to N - 2.
3. What is the primary objective of a paired-samples t-test?
A. To compare the means of two unrelated groups
B. To determine the correlation between three variables
C. To predict the value of a dependent variable
D. To compare the means of the same group at two different times
Answer: D
Conceptual Explanation: Paired-samples t-tests (or repeated measures) are used to
compare means from the same subjects under different conditions or times.
4. Which assumption states that the variance in one group is approximately equal to the
variance in the other group?
A. Homogeneity of variance
B. Independence of observations
C. Linearity
D. Normality
, Answer: A
Conceptual Explanation: Homogeneity of variance assumes that the spread of data points
is similar across the groups being compared.
5. If a researcher calculates a p-value of 0.03 and the alpha level is set at 0.05, what is the
appropriate conclusion?
A. Fail to reject the null hypothesis
B. Accept the null hypothesis
C. Reject the null hypothesis
D. The test is inconclusive
Answer: C
Conceptual Explanation: If the p-value is less than or equal to the alpha level (0.03 <
0.05), the results are statistically significant, and the null hypothesis is rejected.
6. Cohen’s d is a measure of:
A. Statistical significance
B. Effect size
C. Probability of Type II error
D. Degrees of freedom
Answer: B
(CNSL 503) QUESTIONS AND ANSWERS
1. Which of the following conditions must be met to justify the use of a t-test instead of a Z-
test?
A. The population standard deviation is unknown
B. The population mean is unknown
C. The sample size is greater than 100
D. The data follows a binomial distribution
Answer: A
Conceptual Explanation: A t-test is used specifically when the population standard
deviation is unknown and must be estimated using the sample standard deviation.
2. In an independent samples t-test, what does ‘degrees of freedom’ represent?
A. The total number of observations minus two
B. The number of groups being compared
C. The total number of observations minus one
,D. The square root of the variance
Answer: A
Conceptual Explanation: For an independent samples t-test, df = (n1 - 1) + (n2 - 1), which
simplifies to N - 2.
3. What is the primary objective of a paired-samples t-test?
A. To compare the means of two unrelated groups
B. To determine the correlation between three variables
C. To predict the value of a dependent variable
D. To compare the means of the same group at two different times
Answer: D
Conceptual Explanation: Paired-samples t-tests (or repeated measures) are used to
compare means from the same subjects under different conditions or times.
4. Which assumption states that the variance in one group is approximately equal to the
variance in the other group?
A. Homogeneity of variance
B. Independence of observations
C. Linearity
D. Normality
, Answer: A
Conceptual Explanation: Homogeneity of variance assumes that the spread of data points
is similar across the groups being compared.
5. If a researcher calculates a p-value of 0.03 and the alpha level is set at 0.05, what is the
appropriate conclusion?
A. Fail to reject the null hypothesis
B. Accept the null hypothesis
C. Reject the null hypothesis
D. The test is inconclusive
Answer: C
Conceptual Explanation: If the p-value is less than or equal to the alpha level (0.03 <
0.05), the results are statistically significant, and the null hypothesis is rejected.
6. Cohen’s d is a measure of:
A. Statistical significance
B. Effect size
C. Probability of Type II error
D. Degrees of freedom
Answer: B
