CNSL 503 STATISTICS: THE T-TEST
COMPREHENSIVE FINAL EXAM
QUESTIONS AND ANSWERS
1. Which of the following is a primary assumption required to conduct an independent
samples t-test?
A. The dependent variable must be categorical.
B. The populations from which the samples are drawn must be approximately normally
distributed.
C. The observations within each group must be dependent.
D. The sample sizes of the two groups must be exactly equal.
Answer: B
Conceptual Explanation: An independent samples t-test assumes that the dependent
variable is normally distributed in both populations, especially with smaller sample sizes.
2. In a one-sample t-test, what does the null hypothesis usually state?
A. The sample mean is significantly different from the population mean.
B. The population variance is unknown.
,C. The sample mean is equal to a specific hypothesized population mean.
D. The sample distribution is skewed.
Answer: C
Conceptual Explanation: The null hypothesis (H0) typically predicts no difference, stating
the sample mean equals the population mean.
3. When should a paired-samples t-test be utilized instead of an independent-samples t-test?
A. When participants are measured twice, such as in a pre-test and post-test design.
B. When the dependent variable is measured on a nominal scale.
C. When comparing two groups that have no relationship to each other.
D. When the sample size is greater than 100.
Answer: A
Conceptual Explanation: Paired-samples t-tests are used for dependent observations,
such as the same subjects measured at two different time points.
4. What is the formula for degrees of freedom in a standard independent-samples t-test with
two groups (n1 and n2)?
A. n1 + n2 - 1
B. (n1 - 1) + (n2 - 1)
C. n1 + n2
, D. n1 - n2
Answer: B
Conceptual Explanation: The degrees of freedom for an independent samples t-test is
calculated by summing the df of both groups: (n1-1) + (n2-1), which simplifies to n1 + n2 -
2.
5. If a researcher decreases the alpha level from 0.05 to 0.01, what happens to the risk of a
Type I error?
A. It increases.
B. It stays the same.
C. It decreases.
D. It becomes zero.
Answer: C
Conceptual Explanation: The alpha level represents the probability of a Type I error
(rejecting a true null hypothesis); lowering it reduces this risk.
6. What does ‘Homogeneity of Variance’ imply in the context of a t-test?
A. The standard deviations of the two populations are approximately equal.
B. The means of the two groups are equal.
C. The sample sizes must be identical.
D. The data is perfectly symmetrical.
COMPREHENSIVE FINAL EXAM
QUESTIONS AND ANSWERS
1. Which of the following is a primary assumption required to conduct an independent
samples t-test?
A. The dependent variable must be categorical.
B. The populations from which the samples are drawn must be approximately normally
distributed.
C. The observations within each group must be dependent.
D. The sample sizes of the two groups must be exactly equal.
Answer: B
Conceptual Explanation: An independent samples t-test assumes that the dependent
variable is normally distributed in both populations, especially with smaller sample sizes.
2. In a one-sample t-test, what does the null hypothesis usually state?
A. The sample mean is significantly different from the population mean.
B. The population variance is unknown.
,C. The sample mean is equal to a specific hypothesized population mean.
D. The sample distribution is skewed.
Answer: C
Conceptual Explanation: The null hypothesis (H0) typically predicts no difference, stating
the sample mean equals the population mean.
3. When should a paired-samples t-test be utilized instead of an independent-samples t-test?
A. When participants are measured twice, such as in a pre-test and post-test design.
B. When the dependent variable is measured on a nominal scale.
C. When comparing two groups that have no relationship to each other.
D. When the sample size is greater than 100.
Answer: A
Conceptual Explanation: Paired-samples t-tests are used for dependent observations,
such as the same subjects measured at two different time points.
4. What is the formula for degrees of freedom in a standard independent-samples t-test with
two groups (n1 and n2)?
A. n1 + n2 - 1
B. (n1 - 1) + (n2 - 1)
C. n1 + n2
, D. n1 - n2
Answer: B
Conceptual Explanation: The degrees of freedom for an independent samples t-test is
calculated by summing the df of both groups: (n1-1) + (n2-1), which simplifies to n1 + n2 -
2.
5. If a researcher decreases the alpha level from 0.05 to 0.01, what happens to the risk of a
Type I error?
A. It increases.
B. It stays the same.
C. It decreases.
D. It becomes zero.
Answer: C
Conceptual Explanation: The alpha level represents the probability of a Type I error
(rejecting a true null hypothesis); lowering it reduces this risk.
6. What does ‘Homogeneity of Variance’ imply in the context of a t-test?
A. The standard deviations of the two populations are approximately equal.
B. The means of the two groups are equal.
C. The sample sizes must be identical.
D. The data is perfectly symmetrical.
