MODULE 5: THE T-TEST (PORTAGE LEARNING STATISTICS CNSL 503, THE T-TEST) QUESTIONS AND CORRECT
ANSWERS (VERIFIED ANSWERS) PLUS RATIONALES 2026 Q&A |LATEST EXAM UPDATE 2026/2027
SECTION ONE: QUESTIONS 1-100
Question 1
What is the primary purpose of a t-test?
A. To compare the means of two groups on a continuous dependent variable.
B. To examine the relationship between two categorical variables.
C. To predict the value of a dependent variable based on an independent variable.
D. To compare the variances of three or more groups.
🟢 A. To compare the means of two groups on a continuous dependent variable.
🔴 RATIONALE: The t-test is specifically designed to determine if there is a statistically significant difference
between the means of two groups. Options B, C, and D describe chi-square tests, regression, and ANOVA,
respectively.
Question 2
A researcher wants to compare the test scores of the same group of students before and after a teaching
intervention. Which type of t-test is appropriate?
A. Independent samples t-test
B. One-sample t-test
C. Paired samples t-test
D. Welch's t-test
🟢 C. Paired samples t-test
🔴 RATIONALE: A paired samples t-test is used when the same subjects are measured twice (e.g., pre-test and
post-test). This design controls for individual differences, making it the correct choice.
,Question 3
For an independent samples t-test, what is the assumption regarding the scale of measurement of the
dependent variable?
A. It must be nominal.
B. It must be ordinal.
C. It must be continuous (interval or ratio).
D. It must be dichotomous.
🟢 C. It must be continuous (interval or ratio).
🔴 RATIONALE: The dependent variable in a t-test must be measured on a continuous scale (interval or ratio) to
compute a meaningful mean, which is the core metric being compared between the two groups.
Question 4
The assumption of homogeneity of variance refers to:
A. The variances within each of the two groups being approximately equal.
B. The means of the two groups being equal.
C. The sample sizes of the two groups being equal.
D. The data being normally distributed in the population.
🟢 A. The variances within each of the two groups being approximately equal.
🔴 RATIONALE: Homogeneity of variance (or homoscedasticity) is a key assumption for the independent
samples t-test, requiring that the variance of scores is similar in both groups being compared. Violating this
assumption can lead to inaccurate results.
Question 5
Which of the following is the null hypothesis for an independent samples t-test?
A. H₀: μ₁ = μ₂
B. H₀: μ₁ ≠ μ₂
,C. H₀: μ₁ > μ₂
D. H₀: x̄ ₁ = x̄ ₂
🟢 A. H₀: μ₁ = μ₂
🔴 RATIONALE: The null hypothesis (H₀) for any t-test always states there is no difference between the
population means (μ). The alternative hypothesis is that they are not equal (H₁: μ₁ ≠ μ₂).
Question 6
A researcher finds a t-statistic of 2.45 with 18 degrees of freedom. The critical value for a two-tailed test at α =
.05 is 2.101. What should the researcher conclude?
A. Fail to reject the null hypothesis.
B. Reject the null hypothesis.
C. Accept the alternative hypothesis with certainty.
D. Conclude the study is flawed.
🟢 B. Reject the null hypothesis.
🔴 RATIONALE: When the calculated t-statistic (2.45) exceeds the critical value (2.101), it falls in the rejection
region. Therefore, the null hypothesis is rejected, and the result is statistically significant.
Question 7
In a t-test, what does 'degrees of freedom' (df) primarily represent?
A. The number of participants in the study.
B. The number of independent variables.
C. The number of scores that are free to vary when estimating a parameter.
D. The maximum value the t-statistic can attain.
🟢 C. The number of scores that are free to vary when estimating a parameter.
🔴 RATIONALE: Degrees of freedom represent the amount of independent information available to estimate a
parameter. For an independent samples t-test, df = (n₁ - 1) + (n₂ - 1), which is the number of scores free to vary.
, Question 8
Which of the following scenarios would most likely violate the assumption of independence of observations for
a t-test?
A. Randomly assigning 50 participants to either a treatment or control group.
B. Measuring the same participant's anxiety level once.
C. Using data from participants in the same family who influence each other.
D. Comparing the test scores of two different classes of students.
🟢 C. Using data from participants in the same family who influence each other.
🔴 RATIONALE: Independence of observations means scores from one participant should not influence another.
Using data from the same family violates this because their scores are likely correlated due to shared
environment and genetics.
Question 9
What is the effect of using a one-tailed test instead of a two-tailed test?
A. It reduces the critical value needed for significance.
B. It increases the critical value needed for significance.
C. It has no effect on the critical value.
D. It makes the test more conservative.
🟢 A. It reduces the critical value needed for significance.
🔴 RATIONALE: A one-tailed test concentrates all of the alpha level (e.g., .05) into one tail of the distribution.
This makes it easier to reach significance in that specific direction compared to a two-tailed test, which splits
alpha between two tails.
Question 10
A counseling psychologist wants to know if mindfulness therapy is more effective than cognitive-behavioral
therapy (CBT) for reducing depression scores. Two separate groups of participants are used. This is an example
ANSWERS (VERIFIED ANSWERS) PLUS RATIONALES 2026 Q&A |LATEST EXAM UPDATE 2026/2027
SECTION ONE: QUESTIONS 1-100
Question 1
What is the primary purpose of a t-test?
A. To compare the means of two groups on a continuous dependent variable.
B. To examine the relationship between two categorical variables.
C. To predict the value of a dependent variable based on an independent variable.
D. To compare the variances of three or more groups.
🟢 A. To compare the means of two groups on a continuous dependent variable.
🔴 RATIONALE: The t-test is specifically designed to determine if there is a statistically significant difference
between the means of two groups. Options B, C, and D describe chi-square tests, regression, and ANOVA,
respectively.
Question 2
A researcher wants to compare the test scores of the same group of students before and after a teaching
intervention. Which type of t-test is appropriate?
A. Independent samples t-test
B. One-sample t-test
C. Paired samples t-test
D. Welch's t-test
🟢 C. Paired samples t-test
🔴 RATIONALE: A paired samples t-test is used when the same subjects are measured twice (e.g., pre-test and
post-test). This design controls for individual differences, making it the correct choice.
,Question 3
For an independent samples t-test, what is the assumption regarding the scale of measurement of the
dependent variable?
A. It must be nominal.
B. It must be ordinal.
C. It must be continuous (interval or ratio).
D. It must be dichotomous.
🟢 C. It must be continuous (interval or ratio).
🔴 RATIONALE: The dependent variable in a t-test must be measured on a continuous scale (interval or ratio) to
compute a meaningful mean, which is the core metric being compared between the two groups.
Question 4
The assumption of homogeneity of variance refers to:
A. The variances within each of the two groups being approximately equal.
B. The means of the two groups being equal.
C. The sample sizes of the two groups being equal.
D. The data being normally distributed in the population.
🟢 A. The variances within each of the two groups being approximately equal.
🔴 RATIONALE: Homogeneity of variance (or homoscedasticity) is a key assumption for the independent
samples t-test, requiring that the variance of scores is similar in both groups being compared. Violating this
assumption can lead to inaccurate results.
Question 5
Which of the following is the null hypothesis for an independent samples t-test?
A. H₀: μ₁ = μ₂
B. H₀: μ₁ ≠ μ₂
,C. H₀: μ₁ > μ₂
D. H₀: x̄ ₁ = x̄ ₂
🟢 A. H₀: μ₁ = μ₂
🔴 RATIONALE: The null hypothesis (H₀) for any t-test always states there is no difference between the
population means (μ). The alternative hypothesis is that they are not equal (H₁: μ₁ ≠ μ₂).
Question 6
A researcher finds a t-statistic of 2.45 with 18 degrees of freedom. The critical value for a two-tailed test at α =
.05 is 2.101. What should the researcher conclude?
A. Fail to reject the null hypothesis.
B. Reject the null hypothesis.
C. Accept the alternative hypothesis with certainty.
D. Conclude the study is flawed.
🟢 B. Reject the null hypothesis.
🔴 RATIONALE: When the calculated t-statistic (2.45) exceeds the critical value (2.101), it falls in the rejection
region. Therefore, the null hypothesis is rejected, and the result is statistically significant.
Question 7
In a t-test, what does 'degrees of freedom' (df) primarily represent?
A. The number of participants in the study.
B. The number of independent variables.
C. The number of scores that are free to vary when estimating a parameter.
D. The maximum value the t-statistic can attain.
🟢 C. The number of scores that are free to vary when estimating a parameter.
🔴 RATIONALE: Degrees of freedom represent the amount of independent information available to estimate a
parameter. For an independent samples t-test, df = (n₁ - 1) + (n₂ - 1), which is the number of scores free to vary.
, Question 8
Which of the following scenarios would most likely violate the assumption of independence of observations for
a t-test?
A. Randomly assigning 50 participants to either a treatment or control group.
B. Measuring the same participant's anxiety level once.
C. Using data from participants in the same family who influence each other.
D. Comparing the test scores of two different classes of students.
🟢 C. Using data from participants in the same family who influence each other.
🔴 RATIONALE: Independence of observations means scores from one participant should not influence another.
Using data from the same family violates this because their scores are likely correlated due to shared
environment and genetics.
Question 9
What is the effect of using a one-tailed test instead of a two-tailed test?
A. It reduces the critical value needed for significance.
B. It increases the critical value needed for significance.
C. It has no effect on the critical value.
D. It makes the test more conservative.
🟢 A. It reduces the critical value needed for significance.
🔴 RATIONALE: A one-tailed test concentrates all of the alpha level (e.g., .05) into one tail of the distribution.
This makes it easier to reach significance in that specific direction compared to a two-tailed test, which splits
alpha between two tails.
Question 10
A counseling psychologist wants to know if mindfulness therapy is more effective than cognitive-behavioral
therapy (CBT) for reducing depression scores. Two separate groups of participants are used. This is an example
