CNSL 503 Statistics Module 4 Exam
Portage Learning Actual 2026/2027
– Complete Questions with
Detailed Rationales | 100% Verified
Answers – Pass Guaranteed – A+
Graded INSTANT DOWNLOAD
QUESTION 1
The normal distribution is characterized by which of the
following?
A. Symmetrical bell shape
B. Unimodal curve
C. Mean = Median = Mode
D. All of the above
Answer: D. All of the above
Rationale: The normal distribution is a frequency distribution
shaped like a symmetrical bell, unimodal curve where the mean,
median, and mode all coincide at the center. This distribution is
foundational to inferential statistics because of these properties .
,QUESTION 2
For a normal distribution, approximately what percentage of
scores falls within ±1 standard deviation of the mean?
A. 50%
B. 68%
C. 95%
D. 99.7%
Answer: B. 68%
Rationale: In a normal distribution, approximately 68% of scores
fall within one standard deviation of the mean (±1σ), 95% within
±2σ, and 99.7% within ±3σ. This is known as the empirical rule or
68-95-99.7 rule.
QUESTION 3
Researchers wanted to compare sample data regarding social
media usage to the whole population. The population mean is
3.5 hours with a standard deviation of 0.5 hours. Calculate the
z-score for a value of 4 hours.
Answer: z = 1.00
Rationale: The z-score formula is z = (X - μ) / σ. Substituting the
values: z = (4 - 3.5) / 0.5 = 0..5 = 1.00. This indicates that 4
hours is exactly 1 standard deviation above the population mean .
,QUESTION 4
Using the same population data (μ = 3.5, σ = 0.5), calculate
the raw value (X) for a z-score of +2.00.
Answer: X = 4.5
Rationale: The raw value formula is X = (z)(σ) + μ. Substituting: X
= (2.00)(0.5) + 3.5 = 1.0 + 3.5 = 4.5 hours .
QUESTION 5
For the t-equation t₀ = (x̄ - μ) / (s/√n):
A. What goes in the denominator?
B. What goes in the numerator?
Answer:
A. The spread of the sample average
B. The location of the sample average (adjusted for mu)
Rationale: In the t-equation, the numerator (x̄ - μ) represents the
location of the sample average adjusted for the population mean
(distance from the null hypothesis value). The denominator (s/√n)
represents the spread (standard error) of the sample average. This
creates a standardized score that follows a t-distribution when the
population standard deviation is unknown .
, QUESTION 6
What is statistical power?
Answer: The probability of correctly rejecting a null hypothesis
that is false
Rationale: Statistical power is measured on a scale of 0 to 1 and
represents the likelihood that a test will detect an effect when one
truly exists. Higher power means greater probability of avoiding a
Type II error (failing to reject a false null hypothesis) .
QUESTION 7
Which of the following factors affect statistical power?
A. Sample size
B. Size of the effect
C. Significance level (α)
D. All of the above
Answer: D. All of the above
Rationale: Statistical power is influenced by: (1) Sample size –
larger samples increase power; (2) Effect size – larger effects are
easier to detect; (3) Significance level – a more lenient α (e.g., 0.05
vs. 0.01) increases power. All these factors work together in power
analysis .
Portage Learning Actual 2026/2027
– Complete Questions with
Detailed Rationales | 100% Verified
Answers – Pass Guaranteed – A+
Graded INSTANT DOWNLOAD
QUESTION 1
The normal distribution is characterized by which of the
following?
A. Symmetrical bell shape
B. Unimodal curve
C. Mean = Median = Mode
D. All of the above
Answer: D. All of the above
Rationale: The normal distribution is a frequency distribution
shaped like a symmetrical bell, unimodal curve where the mean,
median, and mode all coincide at the center. This distribution is
foundational to inferential statistics because of these properties .
,QUESTION 2
For a normal distribution, approximately what percentage of
scores falls within ±1 standard deviation of the mean?
A. 50%
B. 68%
C. 95%
D. 99.7%
Answer: B. 68%
Rationale: In a normal distribution, approximately 68% of scores
fall within one standard deviation of the mean (±1σ), 95% within
±2σ, and 99.7% within ±3σ. This is known as the empirical rule or
68-95-99.7 rule.
QUESTION 3
Researchers wanted to compare sample data regarding social
media usage to the whole population. The population mean is
3.5 hours with a standard deviation of 0.5 hours. Calculate the
z-score for a value of 4 hours.
Answer: z = 1.00
Rationale: The z-score formula is z = (X - μ) / σ. Substituting the
values: z = (4 - 3.5) / 0.5 = 0..5 = 1.00. This indicates that 4
hours is exactly 1 standard deviation above the population mean .
,QUESTION 4
Using the same population data (μ = 3.5, σ = 0.5), calculate
the raw value (X) for a z-score of +2.00.
Answer: X = 4.5
Rationale: The raw value formula is X = (z)(σ) + μ. Substituting: X
= (2.00)(0.5) + 3.5 = 1.0 + 3.5 = 4.5 hours .
QUESTION 5
For the t-equation t₀ = (x̄ - μ) / (s/√n):
A. What goes in the denominator?
B. What goes in the numerator?
Answer:
A. The spread of the sample average
B. The location of the sample average (adjusted for mu)
Rationale: In the t-equation, the numerator (x̄ - μ) represents the
location of the sample average adjusted for the population mean
(distance from the null hypothesis value). The denominator (s/√n)
represents the spread (standard error) of the sample average. This
creates a standardized score that follows a t-distribution when the
population standard deviation is unknown .
, QUESTION 6
What is statistical power?
Answer: The probability of correctly rejecting a null hypothesis
that is false
Rationale: Statistical power is measured on a scale of 0 to 1 and
represents the likelihood that a test will detect an effect when one
truly exists. Higher power means greater probability of avoiding a
Type II error (failing to reject a false null hypothesis) .
QUESTION 7
Which of the following factors affect statistical power?
A. Sample size
B. Size of the effect
C. Significance level (α)
D. All of the above
Answer: D. All of the above
Rationale: Statistical power is influenced by: (1) Sample size –
larger samples increase power; (2) Effect size – larger effects are
easier to detect; (3) Significance level – a more lenient α (e.g., 0.05
vs. 0.01) increases power. All these factors work together in power
analysis .
