CNSL 503: THE T-TEST ADVANCED
COMPREHENSIVE EXAM QUESTIONS
AND ANSWERS
1. When conducting an independent-samples t-test, what is the specific purpose of Levene’s
Test?
A. To determine if the sample means are significantly different from the population mean.
B. To check if the data follows a perfectly normal distribution.
C. To calculate the effect size using Cohen’s d.
D. To verify the assumption that the variances of the two groups are equal.
Answer: D
Conceptual Explanation: Levene’s Test is used to assess the equality of variances
(homogeneity of variance) for a variable calculated for two or more groups. If the p-value is
significant, the assumption is violated.
2. In a one-sample t-test, what does the ‘degrees of freedom’ (df) represent?
A. The total number of samples minus the number of groups.
B. The number of independent values that can vary in an analysis, calculated as n - 1.
,C. The probability of making a Type I error.
D. The standard deviation divided by the square root of the sample size.
Answer: B
Conceptual Explanation: For a one-sample t-test, the degrees of freedom represent the
number of values in the final calculation of a statistic that are free to vary, which is the
sample size minus one (n-1).
3. Which of the following scenarios would necessitate the use of a paired-samples
(dependent) t-test?
A. Comparing the mean test scores of two different classes taught by different teachers.
B. Comparing the average salary of men versus women in a specific industry.
C. Comparing the mean weight of a group of participants before and after a six-week diet
program.
D. Comparing the mean height of a sample to a known national average.
Answer: C
Conceptual Explanation: A paired-samples t-test is used when the same subjects are
measured twice (pre-test/post-test) or when subjects are matched in pairs.
4. What is the primary difference between a z-test and a t-test?
A. The z-test is used for small samples, while the t-test is for large samples.
, B. The t-test is used when the population standard deviation is unknown and must be
estimated from the sample.
C. The t-test requires the population standard deviation, while the z-test does not.
D. The z-test is only used for qualitative data.
Answer: B
Conceptual Explanation: We use a t-test when the population standard deviation is
unknown. The t-distribution accounts for the extra uncertainty of estimating the standard
deviation from a sample.
5. If a researcher reports a t-value of 2.50 with a p-value of 0.02, and the alpha level is set at
0.05, what is the appropriate conclusion?
A. Accept the null hypothesis.
B. Reject the null hypothesis; the results are statistically significant.
C. Fail to reject the null hypothesis; the results are not significant.
D. The test is invalid because the t-value is higher than the p-value.
Answer: B
Conceptual Explanation: Since the p-value (0.02) is less than the alpha level (0.05), we
reject the null hypothesis and conclude there is a statistically significant difference.
6. What happens to the t-distribution as the degrees of freedom increase?
A. It becomes flatter and more spread out.
COMPREHENSIVE EXAM QUESTIONS
AND ANSWERS
1. When conducting an independent-samples t-test, what is the specific purpose of Levene’s
Test?
A. To determine if the sample means are significantly different from the population mean.
B. To check if the data follows a perfectly normal distribution.
C. To calculate the effect size using Cohen’s d.
D. To verify the assumption that the variances of the two groups are equal.
Answer: D
Conceptual Explanation: Levene’s Test is used to assess the equality of variances
(homogeneity of variance) for a variable calculated for two or more groups. If the p-value is
significant, the assumption is violated.
2. In a one-sample t-test, what does the ‘degrees of freedom’ (df) represent?
A. The total number of samples minus the number of groups.
B. The number of independent values that can vary in an analysis, calculated as n - 1.
,C. The probability of making a Type I error.
D. The standard deviation divided by the square root of the sample size.
Answer: B
Conceptual Explanation: For a one-sample t-test, the degrees of freedom represent the
number of values in the final calculation of a statistic that are free to vary, which is the
sample size minus one (n-1).
3. Which of the following scenarios would necessitate the use of a paired-samples
(dependent) t-test?
A. Comparing the mean test scores of two different classes taught by different teachers.
B. Comparing the average salary of men versus women in a specific industry.
C. Comparing the mean weight of a group of participants before and after a six-week diet
program.
D. Comparing the mean height of a sample to a known national average.
Answer: C
Conceptual Explanation: A paired-samples t-test is used when the same subjects are
measured twice (pre-test/post-test) or when subjects are matched in pairs.
4. What is the primary difference between a z-test and a t-test?
A. The z-test is used for small samples, while the t-test is for large samples.
, B. The t-test is used when the population standard deviation is unknown and must be
estimated from the sample.
C. The t-test requires the population standard deviation, while the z-test does not.
D. The z-test is only used for qualitative data.
Answer: B
Conceptual Explanation: We use a t-test when the population standard deviation is
unknown. The t-distribution accounts for the extra uncertainty of estimating the standard
deviation from a sample.
5. If a researcher reports a t-value of 2.50 with a p-value of 0.02, and the alpha level is set at
0.05, what is the appropriate conclusion?
A. Accept the null hypothesis.
B. Reject the null hypothesis; the results are statistically significant.
C. Fail to reject the null hypothesis; the results are not significant.
D. The test is invalid because the t-value is higher than the p-value.
Answer: B
Conceptual Explanation: Since the p-value (0.02) is less than the alpha level (0.05), we
reject the null hypothesis and conclude there is a statistically significant difference.
6. What happens to the t-distribution as the degrees of freedom increase?
A. It becomes flatter and more spread out.
