1 | Page
MODULE 5: THE T-TEST (PORTAGE
LEARNING STATISTICS CNSL 503)
PRACTICE EXAM WITH VERIFIED
ANSWERS & COMPLETE
RATIONALES
## SECTION 1: FOUNDATIONS OF THE T-TEST
**1. When population standard deviation is known, the z-score
is used. When population standard deviation is unknown, the
__ is used.**
A. F-score
B. Chi-square score
C. t-score
D. p-score
**Correct answer:** t-score
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**Rationale:** A t-score is used when the population standard
deviation (σ) is unknown and must be estimated using the
sample standard deviation (s). The z-score is used when the
population standard deviation is known. This is the fundamental
distinction between z-tests and t-tests .
---
**2. True/False: Since t-scores are centered normally around
the mean and form a bell-shaped curve, probabilities can be
calculated to draw inferences about populations.**
A. True
B. False
**Correct answer:** True
**Rationale:** The t-distribution is symmetric and bell-shaped
like the normal distribution. This property allows researchers to
calculate probabilities and make statistical inferences about
population parameters, even when the population standard
deviation is unknown .
---
**3. What determines how well the t-distribution approximates
the normal distribution of the z-scores?**
,3 | Page
A. Sample mean
B. Degrees of freedom (df)
C. Population variance
D. Alpha level
**Correct answer:** Degrees of freedom (df)
**Rationale:** Degrees of freedom (df = n - 1) determine how
well the t-distribution approximates the normal distribution. As
sample size increases, the t-distribution becomes more like the
normal distribution. Smaller degrees of freedom produce a t-
distribution with heavier tails .
---
**4. A t-distribution approximately resembles a normal
distribution when n = ___.**
A. n = 5
B. n = 8
C. n = 12
D. n = 30
**Correct answer:** n = 12
, 4 | Page
**Rationale:** According to the Portage Learning CNSL 503
materials, a t-distribution approximately resembles a normal
distribution when n = 12. As sample size increases, the t-
distribution converges toward the standard normal distribution .
---
**5. T-testing for a one-sample test is used when ___.**
A. the population mean is unknown
B. the population mean is known
C. the sample size is small
D. the population standard deviation is known
**Correct answer:** the population mean is known
**Rationale:** A one-sample t-test is used when the population
mean (μ) is known and the researcher wants to compare a
sample mean to that population mean. The population standard
deviation is unknown .
---
MODULE 5: THE T-TEST (PORTAGE
LEARNING STATISTICS CNSL 503)
PRACTICE EXAM WITH VERIFIED
ANSWERS & COMPLETE
RATIONALES
## SECTION 1: FOUNDATIONS OF THE T-TEST
**1. When population standard deviation is known, the z-score
is used. When population standard deviation is unknown, the
__ is used.**
A. F-score
B. Chi-square score
C. t-score
D. p-score
**Correct answer:** t-score
,2 | Page
**Rationale:** A t-score is used when the population standard
deviation (σ) is unknown and must be estimated using the
sample standard deviation (s). The z-score is used when the
population standard deviation is known. This is the fundamental
distinction between z-tests and t-tests .
---
**2. True/False: Since t-scores are centered normally around
the mean and form a bell-shaped curve, probabilities can be
calculated to draw inferences about populations.**
A. True
B. False
**Correct answer:** True
**Rationale:** The t-distribution is symmetric and bell-shaped
like the normal distribution. This property allows researchers to
calculate probabilities and make statistical inferences about
population parameters, even when the population standard
deviation is unknown .
---
**3. What determines how well the t-distribution approximates
the normal distribution of the z-scores?**
,3 | Page
A. Sample mean
B. Degrees of freedom (df)
C. Population variance
D. Alpha level
**Correct answer:** Degrees of freedom (df)
**Rationale:** Degrees of freedom (df = n - 1) determine how
well the t-distribution approximates the normal distribution. As
sample size increases, the t-distribution becomes more like the
normal distribution. Smaller degrees of freedom produce a t-
distribution with heavier tails .
---
**4. A t-distribution approximately resembles a normal
distribution when n = ___.**
A. n = 5
B. n = 8
C. n = 12
D. n = 30
**Correct answer:** n = 12
, 4 | Page
**Rationale:** According to the Portage Learning CNSL 503
materials, a t-distribution approximately resembles a normal
distribution when n = 12. As sample size increases, the t-
distribution converges toward the standard normal distribution .
---
**5. T-testing for a one-sample test is used when ___.**
A. the population mean is unknown
B. the population mean is known
C. the sample size is small
D. the population standard deviation is known
**Correct answer:** the population mean is known
**Rationale:** A one-sample t-test is used when the population
mean (μ) is known and the researcher wants to compare a
sample mean to that population mean. The population standard
deviation is unknown .
---
