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 investigates whether a new trauma-focused therapy reduces
PTSD symptoms compared to no treatment. The researcher predicts the therapy group will
show lower symptom scores. What type of hypothesis is this?
A. Non-directional (two-tailed) hypothesis because it only tests for any difference
B. Directional (one-tailed) hypothesis because it predicts the specific direction of effect
[CORRECT]
C. Null hypothesis because it states the expected outcome
D. Alternative hypothesis because it assumes no difference exists
Correct Answer: B
Rationale: This is a directional (one-tailed) hypothesis because the researcher specifically
predicts that the therapy group will have lower scores, not merely different scores.
Directional hypotheses are appropriate when theoretical or empirical evidence strongly
suggests a specific direction of effect, which is common in clinical intervention research
where treatments are expected to reduce pathology.
Q2: In counseling research, a Type I error occurs when:
A. The researcher fails to detect a true therapeutic effect that actually exists
,B. The researcher concludes a therapy is effective when it actually is not [CORRECT]
C. The sample size is too small to achieve adequate statistical power
D. The effect size is smaller than Cohen's d = 0.2
Correct Answer: B
Rationale: A Type I error (α) occurs when we reject a true null hypothesis, concluding that an
intervention has an effect when it actually does not. In counseling contexts, this is
particularly problematic as it may lead to implementing ineffective treatments, wasting
resources, and potentially causing harm through false hope or opportunity costs.
Q3: Which of the following represents the CORRECT sequence of steps in hypothesis testing?
A. State hypotheses → Set criteria → Collect data → Compute statistic → Make decision
[CORRECT]
B. Collect data → State hypotheses → Compute statistic → Set criteria → Make decision
C. Set criteria → State hypotheses → Collect data → Compute statistic → Make decision
D. State hypotheses → Collect data → Set criteria → Compute statistic → Make decision
Correct Answer: A
Rationale: The proper sequence requires stating hypotheses and establishing decision
criteria (α level, critical values) before data collection to prevent bias. This a priori approach
ensures scientific rigor and prevents "cherry-picking" data or changing significance levels
after seeing the results, which would violate fundamental research ethics in counseling
psychology.
Q4: A researcher sets α = .01 instead of the conventional .05. What is the effect on Type I and
Type II error rates?
A. Type I error decreases; Type II error decreases
B. Type I error decreases; Type II error increases [CORRECT]
C. Type I error increases; Type II error decreases
D. Type I error increases; Type II error increases
Correct Answer: B
,Rationale: Decreasing alpha from .05 to .01 makes the criterion for significance more
stringent, reducing the probability of Type I error (false positives). However, this
simultaneously increases Type II error probability (β) because we become more conservative
about rejecting the null hypothesis, potentially missing true effects. This trade-off is crucial in
counseling research where both false positives (ineffective treatments) and false negatives
(discarding helpful interventions) have serious consequences.
Q5: In a study examining whether mindfulness training affects anxiety levels, the researcher
obtains p = .03 with α = .05. What is the correct interpretation?
A. There is a 3% probability that the null hypothesis is true
B. There is a 97% probability that the alternative hypothesis is true
C. If the null hypothesis were true, there is a 3% probability of obtaining these results or more
extreme [CORRECT]
D. The probability that the results occurred by chance is 3%
Correct Answer: C
Rationale: The p-value represents the probability of obtaining the observed results (or more
extreme) assuming the null hypothesis is true , not the probability that the null hypothesis
itself is true. This frequentist interpretation is commonly misunderstood; p = .03 means that
if mindfulness had no true effect, we'd see results this extreme only 3% of the time due to
sampling error alone.
Q6: A counseling researcher finds a statistically significant difference (p < .05) between two
therapy approaches, but the effect size is Cohen's d = 0.15. What should the researcher
conclude?
A. The result is practically significant because it is statistically significant
B. The result is not practically significant despite statistical significance [CORRECT]
C. The sample size was too small to detect practical significance
D. The alpha level should be increased to .10 to achieve practical significance
Correct Answer: B
Rationale: Statistical significance (p < .05) indicates the result is unlikely due to chance, but
practical significance depends on effect size magnitude. With Cohen's d = 0.15 (below the
, "small" threshold of 0.2), the difference between therapies is negligible in real-world clinical
terms, even if statistically detectable with a large sample. Counseling researchers must
report both to avoid implementing interventions with trivial real-world impact.
Q7: Which of the following is TRUE regarding critical values and rejection regions?
A. For a two-tailed test with α = .05, the critical z-value is ±1.645
B. The rejection region represents values unlikely to occur if the null hypothesis is true
[CORRECT]
C. As sample size increases, critical t-values increase
D. The rejection region for a one-tailed test is always larger than for a two-tailed test at the
same α level
Correct Answer: B
Rationale: The rejection region contains extreme values that would be rare if the null
hypothesis were true, leading us to reject H₀. For α = .05 two-tailed, the critical z-value is
±1.96 (not 1.645, which is for one-tailed). As sample size increases, critical t-values decrease
approaching z-values. One-tailed tests concentrate all α in one tail, making the critical region
larger in that direction but nonexistent in the other.
Q8: A researcher testing a new depression intervention uses a one-tailed hypothesis
predicting improvement. The results show the intervention actually makes symptoms
significantly worse (p = .02 in the opposite direction). What should the researcher do?
A. Report the result as significant because p < .05
B. Fail to reject the null hypothesis and conclude no effect exists
C. Switch to a two-tailed test post-hoc to report the significant finding
D. Fail to reject the null hypothesis and consider the harmful effect in discussion [CORRECT]
Correct Answer: D
Rationale: With a one-tailed test predicting improvement, results in the opposite direction
cannot be declared "significant" regardless of p-value magnitude. The researcher must fail to
reject H₀ while acknowledging in the discussion that the intervention showed potential harm.
Switching to two-tailed post-hoc constitutes p-hacking, a serious ethical violation. This
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 investigates whether a new trauma-focused therapy reduces
PTSD symptoms compared to no treatment. The researcher predicts the therapy group will
show lower symptom scores. What type of hypothesis is this?
A. Non-directional (two-tailed) hypothesis because it only tests for any difference
B. Directional (one-tailed) hypothesis because it predicts the specific direction of effect
[CORRECT]
C. Null hypothesis because it states the expected outcome
D. Alternative hypothesis because it assumes no difference exists
Correct Answer: B
Rationale: This is a directional (one-tailed) hypothesis because the researcher specifically
predicts that the therapy group will have lower scores, not merely different scores.
Directional hypotheses are appropriate when theoretical or empirical evidence strongly
suggests a specific direction of effect, which is common in clinical intervention research
where treatments are expected to reduce pathology.
Q2: In counseling research, a Type I error occurs when:
A. The researcher fails to detect a true therapeutic effect that actually exists
,B. The researcher concludes a therapy is effective when it actually is not [CORRECT]
C. The sample size is too small to achieve adequate statistical power
D. The effect size is smaller than Cohen's d = 0.2
Correct Answer: B
Rationale: A Type I error (α) occurs when we reject a true null hypothesis, concluding that an
intervention has an effect when it actually does not. In counseling contexts, this is
particularly problematic as it may lead to implementing ineffective treatments, wasting
resources, and potentially causing harm through false hope or opportunity costs.
Q3: Which of the following represents the CORRECT sequence of steps in hypothesis testing?
A. State hypotheses → Set criteria → Collect data → Compute statistic → Make decision
[CORRECT]
B. Collect data → State hypotheses → Compute statistic → Set criteria → Make decision
C. Set criteria → State hypotheses → Collect data → Compute statistic → Make decision
D. State hypotheses → Collect data → Set criteria → Compute statistic → Make decision
Correct Answer: A
Rationale: The proper sequence requires stating hypotheses and establishing decision
criteria (α level, critical values) before data collection to prevent bias. This a priori approach
ensures scientific rigor and prevents "cherry-picking" data or changing significance levels
after seeing the results, which would violate fundamental research ethics in counseling
psychology.
Q4: A researcher sets α = .01 instead of the conventional .05. What is the effect on Type I and
Type II error rates?
A. Type I error decreases; Type II error decreases
B. Type I error decreases; Type II error increases [CORRECT]
C. Type I error increases; Type II error decreases
D. Type I error increases; Type II error increases
Correct Answer: B
,Rationale: Decreasing alpha from .05 to .01 makes the criterion for significance more
stringent, reducing the probability of Type I error (false positives). However, this
simultaneously increases Type II error probability (β) because we become more conservative
about rejecting the null hypothesis, potentially missing true effects. This trade-off is crucial in
counseling research where both false positives (ineffective treatments) and false negatives
(discarding helpful interventions) have serious consequences.
Q5: In a study examining whether mindfulness training affects anxiety levels, the researcher
obtains p = .03 with α = .05. What is the correct interpretation?
A. There is a 3% probability that the null hypothesis is true
B. There is a 97% probability that the alternative hypothesis is true
C. If the null hypothesis were true, there is a 3% probability of obtaining these results or more
extreme [CORRECT]
D. The probability that the results occurred by chance is 3%
Correct Answer: C
Rationale: The p-value represents the probability of obtaining the observed results (or more
extreme) assuming the null hypothesis is true , not the probability that the null hypothesis
itself is true. This frequentist interpretation is commonly misunderstood; p = .03 means that
if mindfulness had no true effect, we'd see results this extreme only 3% of the time due to
sampling error alone.
Q6: A counseling researcher finds a statistically significant difference (p < .05) between two
therapy approaches, but the effect size is Cohen's d = 0.15. What should the researcher
conclude?
A. The result is practically significant because it is statistically significant
B. The result is not practically significant despite statistical significance [CORRECT]
C. The sample size was too small to detect practical significance
D. The alpha level should be increased to .10 to achieve practical significance
Correct Answer: B
Rationale: Statistical significance (p < .05) indicates the result is unlikely due to chance, but
practical significance depends on effect size magnitude. With Cohen's d = 0.15 (below the
, "small" threshold of 0.2), the difference between therapies is negligible in real-world clinical
terms, even if statistically detectable with a large sample. Counseling researchers must
report both to avoid implementing interventions with trivial real-world impact.
Q7: Which of the following is TRUE regarding critical values and rejection regions?
A. For a two-tailed test with α = .05, the critical z-value is ±1.645
B. The rejection region represents values unlikely to occur if the null hypothesis is true
[CORRECT]
C. As sample size increases, critical t-values increase
D. The rejection region for a one-tailed test is always larger than for a two-tailed test at the
same α level
Correct Answer: B
Rationale: The rejection region contains extreme values that would be rare if the null
hypothesis were true, leading us to reject H₀. For α = .05 two-tailed, the critical z-value is
±1.96 (not 1.645, which is for one-tailed). As sample size increases, critical t-values decrease
approaching z-values. One-tailed tests concentrate all α in one tail, making the critical region
larger in that direction but nonexistent in the other.
Q8: A researcher testing a new depression intervention uses a one-tailed hypothesis
predicting improvement. The results show the intervention actually makes symptoms
significantly worse (p = .02 in the opposite direction). What should the researcher do?
A. Report the result as significant because p < .05
B. Fail to reject the null hypothesis and conclude no effect exists
C. Switch to a two-tailed test post-hoc to report the significant finding
D. Fail to reject the null hypothesis and consider the harmful effect in discussion [CORRECT]
Correct Answer: D
Rationale: With a one-tailed test predicting improvement, results in the opposite direction
cannot be declared "significant" regardless of p-value magnitude. The researcher must fail to
reject H₀ while acknowledging in the discussion that the intervention showed potential harm.
Switching to two-tailed post-hoc constitutes p-hacking, a serious ethical violation. This
