THE T-TEST (CNSL 503 STATISTICS)
COMPREHENSIVE FINAL EXAM
QUESTIONS AND ANSWERS
1. When conducting a one-sample t-test, what is the null hypothesis typically testing?
A. The sample mean is significantly different from the population mean.
B. The sample mean is equal to the population mean.
C. The sample variance is equal to the population variance.
D. The population mean is unknown and estimated by the sample mean.
Answer: B
Conceptual Explanation: The null hypothesis in a one-sample t-test states that there is no
significant difference between the sample mean and the known or hypothesized population
mean.
2. Which of the following is a primary requirement for using a t-test instead of a z-test?
A. The population standard deviation is unknown.
B. The sample size is greater than 100.
C. The population standard deviation is known.
,D. The data is measured on a nominal scale.
Answer: A
Conceptual Explanation: A t-test is used when the population standard deviation is
unknown and must be estimated using the sample standard deviation.
3. In an independent samples t-test, what does the term ‘pooled variance’ refer to?
A. The sum of the variances of both groups.
B. The average of the two sample means.
C. The variance of the difference scores between pairs.
D. A weighted average of the two sample variances based on degrees of freedom.
Answer: D
Conceptual Explanation: Pooled variance is a method for estimating a single common
variance when assuming that two independent populations have equal variances.
4. Which assumption is violated if the variances of two groups in an independent t-test are
significantly different?
A. Homogeneity of variance
B. Independence of observations
C. Normality
D. Linearly of data
, Answer: A
Conceptual Explanation: Homogeneity of variance assumes that the populations from
which the samples are drawn have the same variance.
5. What is the degrees of freedom formula for a paired samples t-test with n pairs of
observations?
A. n - 1
B. n1 + n2 - 2
C. n - 2
D. (n - 1) + (n - 1)
Answer: A
Conceptual Explanation: For paired samples, the test is performed on the difference
scores, so the degrees of freedom are the number of pairs minus one.
6. A researcher reports a result as t(24) = 2.50, p < .05. How many participants were in this
one-sample study?
A. 24
B. 25
C. 23
D. 26
Answer: B
COMPREHENSIVE FINAL EXAM
QUESTIONS AND ANSWERS
1. When conducting a one-sample t-test, what is the null hypothesis typically testing?
A. The sample mean is significantly different from the population mean.
B. The sample mean is equal to the population mean.
C. The sample variance is equal to the population variance.
D. The population mean is unknown and estimated by the sample mean.
Answer: B
Conceptual Explanation: The null hypothesis in a one-sample t-test states that there is no
significant difference between the sample mean and the known or hypothesized population
mean.
2. Which of the following is a primary requirement for using a t-test instead of a z-test?
A. The population standard deviation is unknown.
B. The sample size is greater than 100.
C. The population standard deviation is known.
,D. The data is measured on a nominal scale.
Answer: A
Conceptual Explanation: A t-test is used when the population standard deviation is
unknown and must be estimated using the sample standard deviation.
3. In an independent samples t-test, what does the term ‘pooled variance’ refer to?
A. The sum of the variances of both groups.
B. The average of the two sample means.
C. The variance of the difference scores between pairs.
D. A weighted average of the two sample variances based on degrees of freedom.
Answer: D
Conceptual Explanation: Pooled variance is a method for estimating a single common
variance when assuming that two independent populations have equal variances.
4. Which assumption is violated if the variances of two groups in an independent t-test are
significantly different?
A. Homogeneity of variance
B. Independence of observations
C. Normality
D. Linearly of data
, Answer: A
Conceptual Explanation: Homogeneity of variance assumes that the populations from
which the samples are drawn have the same variance.
5. What is the degrees of freedom formula for a paired samples t-test with n pairs of
observations?
A. n - 1
B. n1 + n2 - 2
C. n - 2
D. (n - 1) + (n - 1)
Answer: A
Conceptual Explanation: For paired samples, the test is performed on the difference
scores, so the degrees of freedom are the number of pairs minus one.
6. A researcher reports a result as t(24) = 2.50, p < .05. How many participants were in this
one-sample study?
A. 24
B. 25
C. 23
D. 26
Answer: B
