CNSL 503 STATISTICS EXAM 2 ACTUAL
EXAM 2026/2027 | Graduate Counseling |
Frequency Distributions & Variability |
Comprehensive Practice Test | Verified
Q&A | Pass Guaranteed - A+ Graded
SECTION 1: HYPOTHESIS TESTING FUNDAMENTALS (15
Questions)
Q1: A counseling researcher is testing whether a new trauma therapy reduces PTSD
symptoms more than the current standard treatment. The researcher predicts the new
therapy will show lower symptom scores. What type of hypothesis is this?
A. Non-directional two-tailed hypothesis
B. Directional one-tailed hypothesis [CORRECT]
C. Null hypothesis only
D. Alternative hypothesis with no direction specified
Correct Answer: B
Rationale: This is a directional one-tailed hypothesis because the researcher specifically
predicts the direction of the effect (new therapy will produce lower scores). One-tailed tests
are used when theoretical or empirical evidence strongly suggests a specific direction. In
counseling research, directional hypotheses are appropriate when previous studies or theory
clearly indicate the expected outcome, but they require careful justification to avoid bias.
Q2: A researcher sets α = .05 and obtains p = .03 in their study comparing depression scores
between two therapy groups. What is the correct statistical decision?
A. Fail to reject H₀ because p > α
B. Reject H₀ because p < α [CORRECT]
C. Accept H₁ as proven true
D. Increase the alpha level to .10 to confirm significance
Correct Answer: B
,Rationale: When p (.03) is less than α (.05), we reject the null hypothesis, concluding there is
a statistically significant difference between groups. However, we never "accept" the
alternative hypothesis as absolute truth—statistical significance indicates evidence against
H₀, not proof of H₁. In counseling research, this significant result would suggest the therapy
difference warrants further investigation and potential clinical consideration.
Q3: In hypothesis testing, a Type II error occurs when:
A. We reject a true null hypothesis
B. We fail to reject a false null hypothesis [CORRECT]
C. We set alpha too high at .001
D. The effect size is larger than expected
Correct Answer: B
Rationale: A Type II error (β) occurs when we fail to reject a false null hypothesis, essentially
missing a true effect or difference. This is particularly problematic in counseling research
when an effective intervention is deemed ineffective due to insufficient power. Type I error (α)
is rejecting a true null. Counseling researchers must balance both errors, as missing effective
treatments (Type II) may deny clients beneficial interventions.
Q4: Which scenario represents a Type I error in counseling research?
A. Concluding a therapy is ineffective when it actually helps clients
B. Concluding a therapy helps clients when it actually has no effect [CORRECT]
C. Using a sample size that is too small to detect an effect
D. Failing to control for confounding variables in the research design
Correct Answer: B
Rationale: A Type I error occurs when we conclude there is a significant effect (rejecting H₀)
when no true effect exists in the population. In this case, concluding a therapy is effective
when it truly isn't could lead to implementing costly, ineffective treatments. The probability of
Type I error equals the alpha level (.05, .01, or .001). Counseling researchers use conservative
alphas when testing novel interventions to prevent adopting ineffective practices.
Q5: A researcher testing a new anxiety intervention obtains p = .08 with α = .05. What is the
most appropriate conclusion?
A. The intervention is clinically proven to work
B. There is insufficient evidence to reject the null hypothesis [CORRECT]
C. The null hypothesis is definitely true
,D. The effect size is necessarily zero
Correct Answer: B
Rationale: When p > α (.08 > .05), we fail to reject the null hypothesis, meaning there is
insufficient statistical evidence to conclude the intervention differs from control. This does
not prove the null is true or that there's zero effect—there may be a real effect that the study
lacked power to detect. In counseling research, this "trend" (p = .08) might warrant replication
with larger samples rather than abandoning a potentially effective treatment.
Q6: The critical value for a two-tailed z-test at α = .05 is:
A. ±1.645
B. ±1.96 [CORRECT]
C. ±2.33
D. ±2.58
Correct Answer: B
Rationale: For a two-tailed test at α = .05, the critical z-values are ±1.96, which captures the
central 95% of the standard normal distribution, leaving 2.5% in each tail. One-tailed tests at α
= .05 use 1.645. More stringent alphas (.01, .001) use higher critical values (2.576, 3.291).
Counseling researchers select alpha levels based on the consequences of errors, with .05
being standard for exploratory research and .01 for confirmatory studies.
Q7: A counseling researcher wants to test whether a mindfulness program changes stress
levels without predicting the direction of change. This requires:
A. A one-tailed test with α = .05 in the upper tail
B. A two-tailed test with α = .025 in each tail [CORRECT]
C. A one-tailed test with α = .10 split between tails
D. No hypothesis test, only descriptive statistics
Correct Answer: B
Rationale: A non-directional hypothesis requires a two-tailed test, splitting the alpha level
equally between both tails (.025 in each tail for α = .05 total). This approach detects effects in
either direction—increases or decreases in stress. Two-tailed tests are more conservative
and appropriate when researchers lack strong theoretical justification for predicting direction,
which is common in exploratory counseling research examining novel interventions.
Q8: In counseling research, statistical significance does NOT necessarily indicate:
, A. The p-value is less than alpha
B. The result is clinically meaningful [CORRECT]
C. The null hypothesis is rejected
D. The finding is unlikely due to chance alone
Correct Answer: B
Rationale: Statistical significance (p < α) indicates the result is unlikely due to sampling error,
but does not guarantee clinical significance or practical importance. A therapy might show
statistically significant improvement on a depression scale (p = .001) but with only 1-point
change on a 100-point scale—clinically meaningless. Counseling researchers must examine
effect sizes and clinical benchmarks alongside p-values to determine if statistically
significant results warrant implementation in practice.
Q9: The probability of correctly rejecting a false null hypothesis is called:
A. Alpha level
B. Statistical power [CORRECT]
C. Effect size
D. Confidence interval
Correct Answer: B
Rationale: Statistical power (1 - β) is the probability of detecting a true effect when it exists,
or correctly rejecting a false null hypothesis. Power of .80 means an 80% chance of finding a
significant effect if one truly exists. Adequate power (typically .80 or higher) is essential in
counseling research to avoid Type II errors that might dismiss effective treatments. Power
depends on sample size, effect size, and alpha level.
Q10: A researcher sets α = .01 instead of .05. What is the effect on Type I and Type II error
rates?
A. Type I error decreases; Type II error increases [CORRECT]
B. Type I error increases; Type II error decreases
C. Both error rates decrease
D. Both error rates remain unchanged
Correct Answer: B
Rationale: Decreasing alpha from .05 to .01 makes the criterion for significance more
stringent, reducing Type I error probability (fewer false positives) but increasing Type II error
probability (more false negatives) because the test becomes less sensitive. This trade-off is
EXAM 2026/2027 | Graduate Counseling |
Frequency Distributions & Variability |
Comprehensive Practice Test | Verified
Q&A | Pass Guaranteed - A+ Graded
SECTION 1: HYPOTHESIS TESTING FUNDAMENTALS (15
Questions)
Q1: A counseling researcher is testing whether a new trauma therapy reduces PTSD
symptoms more than the current standard treatment. The researcher predicts the new
therapy will show lower symptom scores. What type of hypothesis is this?
A. Non-directional two-tailed hypothesis
B. Directional one-tailed hypothesis [CORRECT]
C. Null hypothesis only
D. Alternative hypothesis with no direction specified
Correct Answer: B
Rationale: This is a directional one-tailed hypothesis because the researcher specifically
predicts the direction of the effect (new therapy will produce lower scores). One-tailed tests
are used when theoretical or empirical evidence strongly suggests a specific direction. In
counseling research, directional hypotheses are appropriate when previous studies or theory
clearly indicate the expected outcome, but they require careful justification to avoid bias.
Q2: A researcher sets α = .05 and obtains p = .03 in their study comparing depression scores
between two therapy groups. What is the correct statistical decision?
A. Fail to reject H₀ because p > α
B. Reject H₀ because p < α [CORRECT]
C. Accept H₁ as proven true
D. Increase the alpha level to .10 to confirm significance
Correct Answer: B
,Rationale: When p (.03) is less than α (.05), we reject the null hypothesis, concluding there is
a statistically significant difference between groups. However, we never "accept" the
alternative hypothesis as absolute truth—statistical significance indicates evidence against
H₀, not proof of H₁. In counseling research, this significant result would suggest the therapy
difference warrants further investigation and potential clinical consideration.
Q3: In hypothesis testing, a Type II error occurs when:
A. We reject a true null hypothesis
B. We fail to reject a false null hypothesis [CORRECT]
C. We set alpha too high at .001
D. The effect size is larger than expected
Correct Answer: B
Rationale: A Type II error (β) occurs when we fail to reject a false null hypothesis, essentially
missing a true effect or difference. This is particularly problematic in counseling research
when an effective intervention is deemed ineffective due to insufficient power. Type I error (α)
is rejecting a true null. Counseling researchers must balance both errors, as missing effective
treatments (Type II) may deny clients beneficial interventions.
Q4: Which scenario represents a Type I error in counseling research?
A. Concluding a therapy is ineffective when it actually helps clients
B. Concluding a therapy helps clients when it actually has no effect [CORRECT]
C. Using a sample size that is too small to detect an effect
D. Failing to control for confounding variables in the research design
Correct Answer: B
Rationale: A Type I error occurs when we conclude there is a significant effect (rejecting H₀)
when no true effect exists in the population. In this case, concluding a therapy is effective
when it truly isn't could lead to implementing costly, ineffective treatments. The probability of
Type I error equals the alpha level (.05, .01, or .001). Counseling researchers use conservative
alphas when testing novel interventions to prevent adopting ineffective practices.
Q5: A researcher testing a new anxiety intervention obtains p = .08 with α = .05. What is the
most appropriate conclusion?
A. The intervention is clinically proven to work
B. There is insufficient evidence to reject the null hypothesis [CORRECT]
C. The null hypothesis is definitely true
,D. The effect size is necessarily zero
Correct Answer: B
Rationale: When p > α (.08 > .05), we fail to reject the null hypothesis, meaning there is
insufficient statistical evidence to conclude the intervention differs from control. This does
not prove the null is true or that there's zero effect—there may be a real effect that the study
lacked power to detect. In counseling research, this "trend" (p = .08) might warrant replication
with larger samples rather than abandoning a potentially effective treatment.
Q6: The critical value for a two-tailed z-test at α = .05 is:
A. ±1.645
B. ±1.96 [CORRECT]
C. ±2.33
D. ±2.58
Correct Answer: B
Rationale: For a two-tailed test at α = .05, the critical z-values are ±1.96, which captures the
central 95% of the standard normal distribution, leaving 2.5% in each tail. One-tailed tests at α
= .05 use 1.645. More stringent alphas (.01, .001) use higher critical values (2.576, 3.291).
Counseling researchers select alpha levels based on the consequences of errors, with .05
being standard for exploratory research and .01 for confirmatory studies.
Q7: A counseling researcher wants to test whether a mindfulness program changes stress
levels without predicting the direction of change. This requires:
A. A one-tailed test with α = .05 in the upper tail
B. A two-tailed test with α = .025 in each tail [CORRECT]
C. A one-tailed test with α = .10 split between tails
D. No hypothesis test, only descriptive statistics
Correct Answer: B
Rationale: A non-directional hypothesis requires a two-tailed test, splitting the alpha level
equally between both tails (.025 in each tail for α = .05 total). This approach detects effects in
either direction—increases or decreases in stress. Two-tailed tests are more conservative
and appropriate when researchers lack strong theoretical justification for predicting direction,
which is common in exploratory counseling research examining novel interventions.
Q8: In counseling research, statistical significance does NOT necessarily indicate:
, A. The p-value is less than alpha
B. The result is clinically meaningful [CORRECT]
C. The null hypothesis is rejected
D. The finding is unlikely due to chance alone
Correct Answer: B
Rationale: Statistical significance (p < α) indicates the result is unlikely due to sampling error,
but does not guarantee clinical significance or practical importance. A therapy might show
statistically significant improvement on a depression scale (p = .001) but with only 1-point
change on a 100-point scale—clinically meaningless. Counseling researchers must examine
effect sizes and clinical benchmarks alongside p-values to determine if statistically
significant results warrant implementation in practice.
Q9: The probability of correctly rejecting a false null hypothesis is called:
A. Alpha level
B. Statistical power [CORRECT]
C. Effect size
D. Confidence interval
Correct Answer: B
Rationale: Statistical power (1 - β) is the probability of detecting a true effect when it exists,
or correctly rejecting a false null hypothesis. Power of .80 means an 80% chance of finding a
significant effect if one truly exists. Adequate power (typically .80 or higher) is essential in
counseling research to avoid Type II errors that might dismiss effective treatments. Power
depends on sample size, effect size, and alpha level.
Q10: A researcher sets α = .01 instead of .05. What is the effect on Type I and Type II error
rates?
A. Type I error decreases; Type II error increases [CORRECT]
B. Type I error increases; Type II error decreases
C. Both error rates decrease
D. Both error rates remain unchanged
Correct Answer: B
Rationale: Decreasing alpha from .05 to .01 makes the criterion for significance more
stringent, reducing Type I error probability (fewer false positives) but increasing Type II error
probability (more false negatives) because the test becomes less sensitive. This trade-off is
