Module 5: The T-Test (Portage Learning Statistics CNSL 503) –
Verified Questions and Correct Answers 2025/2026
Description: Portage Learning CNSL 503 Module 5 covers The T-Test with verified questions and
correct answers, updated for 2025/2026. Focuses on hypothesis testing, statistical significance,
and data interpretation for counseling and research statistics students.
Keywords: Portage Learning CNSL 503 t-test statistics module hypothesis testing data analysis
Section 1: T-Test Fundamentals & Assumptions
1. What is the primary purpose of a t-test?
To determine if there is a statistically significant difference between the means of two
groups.
2. The t-test is specifically used when the population standard deviation is...
Unknown and must be estimated from the sample data.
3. What is the key difference between a z-test and a t-test?
A z-test uses the population standard deviation (σ), while a t-test uses the sample
standard deviation (s) to estimate the standard error.
4. The shape of the t-distribution is influenced by what?
The degrees of freedom (df).
5. As sample size increases, the t-distribution approaches the shape of what other
distribution?
The normal (z) distribution.
6. What are the three main types of t-tests covered in an introductory statistics course?
One-sample t-test, independent-samples t-test, and paired-samples t-test.
7. What is the null hypothesis (H₀) for an independent-samples t-test?
H₀: μ₁ = μ₂ (The means of the two populations are equal).
8. What is the alternative hypothesis (H₁) for a paired-samples t-test?
H₁: μ_D ≠ 0 (The mean of the difference scores is not equal to zero).
, 9. The assumption of normality in a t-test requires that...
The sampling distribution of the mean is normally distributed, which is generally met
with a large enough sample size (n > 30) due to the Central Limit Theorem.
10. What does the assumption of homogeneity of variance (homoscedasticity) mean?
That the variances in the populations from which the samples are drawn are
approximately equal.
11. Which test is commonly used to check the assumption of homogeneity of variance for
an independent-samples t-test?
Levene's Test.
12. If Levene's test is significant (p < .05), what does this indicate?
The assumption of homogeneity of variance has been violated, and you should use the
adjusted t-test output (e.g., "Equal variances not assumed" in SPSS).
13. For a one-sample t-test, the degrees of freedom (df) is calculated as...
df = n - 1, where n is the sample size.
14. For an independent-samples t-test, the degrees of freedom (df) is calculated as...
df = n₁ + n₂ - 2.
15. For a paired-samples t-test, the degrees of freedom (df) is calculated as...
df = n - 1, where n is the number of pairs of observations.
Section 2: One-Sample T-Test
16. A one-sample t-test compares the mean of a single sample to...
A known or hypothesized population mean (a test value).
17. A researcher wants to know if students in her school score above the national average
of 100 on an IQ test. What type of t-test should she use?
A one-sample t-test.
18. For the IQ example, what would the null hypothesis (H₀) be?
H₀: μ_school = 100.
19. For the IQ example, what would a non-directional (two-tailed) alternative hypothesis
(H₁) be?
H₁: μ_school ≠ 100.
20. You conduct a one-sample t-test with n=25. What are the degrees of freedom?
df = 25 - 1 = 24.
Verified Questions and Correct Answers 2025/2026
Description: Portage Learning CNSL 503 Module 5 covers The T-Test with verified questions and
correct answers, updated for 2025/2026. Focuses on hypothesis testing, statistical significance,
and data interpretation for counseling and research statistics students.
Keywords: Portage Learning CNSL 503 t-test statistics module hypothesis testing data analysis
Section 1: T-Test Fundamentals & Assumptions
1. What is the primary purpose of a t-test?
To determine if there is a statistically significant difference between the means of two
groups.
2. The t-test is specifically used when the population standard deviation is...
Unknown and must be estimated from the sample data.
3. What is the key difference between a z-test and a t-test?
A z-test uses the population standard deviation (σ), while a t-test uses the sample
standard deviation (s) to estimate the standard error.
4. The shape of the t-distribution is influenced by what?
The degrees of freedom (df).
5. As sample size increases, the t-distribution approaches the shape of what other
distribution?
The normal (z) distribution.
6. What are the three main types of t-tests covered in an introductory statistics course?
One-sample t-test, independent-samples t-test, and paired-samples t-test.
7. What is the null hypothesis (H₀) for an independent-samples t-test?
H₀: μ₁ = μ₂ (The means of the two populations are equal).
8. What is the alternative hypothesis (H₁) for a paired-samples t-test?
H₁: μ_D ≠ 0 (The mean of the difference scores is not equal to zero).
, 9. The assumption of normality in a t-test requires that...
The sampling distribution of the mean is normally distributed, which is generally met
with a large enough sample size (n > 30) due to the Central Limit Theorem.
10. What does the assumption of homogeneity of variance (homoscedasticity) mean?
That the variances in the populations from which the samples are drawn are
approximately equal.
11. Which test is commonly used to check the assumption of homogeneity of variance for
an independent-samples t-test?
Levene's Test.
12. If Levene's test is significant (p < .05), what does this indicate?
The assumption of homogeneity of variance has been violated, and you should use the
adjusted t-test output (e.g., "Equal variances not assumed" in SPSS).
13. For a one-sample t-test, the degrees of freedom (df) is calculated as...
df = n - 1, where n is the sample size.
14. For an independent-samples t-test, the degrees of freedom (df) is calculated as...
df = n₁ + n₂ - 2.
15. For a paired-samples t-test, the degrees of freedom (df) is calculated as...
df = n - 1, where n is the number of pairs of observations.
Section 2: One-Sample T-Test
16. A one-sample t-test compares the mean of a single sample to...
A known or hypothesized population mean (a test value).
17. A researcher wants to know if students in her school score above the national average
of 100 on an IQ test. What type of t-test should she use?
A one-sample t-test.
18. For the IQ example, what would the null hypothesis (H₀) be?
H₀: μ_school = 100.
19. For the IQ example, what would a non-directional (two-tailed) alternative hypothesis
(H₁) be?
H₁: μ_school ≠ 100.
20. You conduct a one-sample t-test with n=25. What are the degrees of freedom?
df = 25 - 1 = 24.
