WGU C784 Applied Healthcare Statistics - Western Governors
University - Academic Year 2026/2027 - Objective Assessment
Comprehensive Examination with 100 Verified Questions and
Correct Answer Rationales
About This Exam Bank
This comprehensive 146-question exam bank is designed to prepare candidates for WGU C784 Applied Healthcare
Statistics - Western Governors University - Academic Year 2026/2027 - Objective Assessment Comprehensive
Examination with 100 Verified Questions and Correct Answer Rationales. Every question is aligned with the latest
official content outline and includes a detailed, evidence-based rationale, an explanation of why each remaining
option is incorrect, and a supporting reference.
Keywords
WGU C784 Applied Healthcare Statistics - Western Governors University - Academic Year 2026/2027 - Objective
Assessment Comprehensive Examination with 100 Verified Questions and Correct Answer Rationales, exam bank,
practice questions, verified answers, detailed rationales, test prep, study guide, review questions, certification exam,
latest update, WGU C784 Applied Healthcare Statistics - Western Governors University - Academic Year 2026/2027
- Objective Assessment Comprehensive Examination with 100 Verified Questions and Correct Answer Rationales,
exam bank, practice questions, verified answers, detailed rationales
PART 1: APPLY PROBABILITY RULES AND PROBABILITY DISTRIBUTIONS TO MODEL
CLINICAL EVENTS AND DIAGNOSTIC TEST CHARACTERISTICS
1. A continuous random variable representing patient wait times is uniformly distributed between 0 and 20 minutes.
Given that a patient has already waited 12 minutes, what is the probability they will wait at least 5 more minutes?
A) 0.15
B) 0.25
C) 0.375
D) 0.40
' Correct Answer: C
Rationale: For a uniform distribution on [0,20], the conditional probability that wait "e17 given wait "e12 is
(2017)/(2012) = 3/8 = 0.375. The memoryless-like property of the uniform distribution yields the ratio of remaining
interval lengths. Distractors reflect common errors: using unconditional probabilities or miscomputing the
conditional denominator.
2. A screening test has sensitivity 0.90 and specificity 0.95. In a population with disease prevalence 2%, what is the
approximate positive predictive value (PPV)?
A) 0.27
B) 0.45
C) 0.64
D) 0.90
' Correct Answer: A
Rationale: PPV = (sensitivity × prevalence) / [(sensitivity × prevalence) + ((1"specificity) × (1"prevalence))] =
(0.90×0.02)/[(0.90×0.02)+(0.05×0.98)] = 0.018/(0.018+0.049) 0.269. Even with high sensitivity/specificity, low
prevalence drastically reduces PPV. Distractors reflect confusion with sensitivity or ignoring prevalence.
Page 1
,3. A study reports a 95% confidence interval for the mean reduction in systolic blood pressure as (4.2, 9.8) mmHg.
Which interpretation is most appropriate?
A) 95% of patients experienced a reduction between 4.2 and 9.8 mmHg.
B) There is a 95% probability that the true mean reduction lies in this interval.
C) If the study were repeated many times, 95% of such intervals would contain the true mean reduction.
D) The sample mean reduction is between 4.2 and 9.8 mmHg with 95% confidence.
' Correct Answer: C
Rationale: The frequentist confidence interval interpretation is that 95% of intervals constructed from repeated
samples would capture the true parameter. Option B reflects a common Bayesian misinterpretation; A confuses
individual values with the mean; D is incorrect because the sample mean is a fixed point estimate, not an interval.
4. A clinical trial compares a new drug to placebo. The relative risk (RR) of adverse events is 1.8 with a 95% CI of
(1.2, 2.7). Which statement is most accurate?
A) The result is not statistically significant because the CI includes 1.0.
B) The new drug is associated with a statistically significant increased risk of adverse events.
C) The absolute risk increase is 80%.
D) The odds ratio must also be 1.8.
' Correct Answer: B
Rationale: Since the 95% CI for RR excludes 1.0 (1.2 to 2.7), the increased risk is statistically significant. Option
A is wrong because 1.0 is not in the interval; C confuses relative risk with absolute risk; D is false because OR and
RR diverge when event rates are not rare.
5. A researcher calculates Pearson's r = 0.75 between daily physical activity and BMI. Which conclusion is best
supported?
A) Increased physical activity causes lower BMI.
B) 56% of the variation in BMI is explained by physical activity.
C) There is a strong negative linear association, but causality cannot be inferred.
D) The relationship is weak because r is negative.
' Correct Answer: C
Rationale: r = "0.75 indicates a strong negative linear association, but correlation does not imply causation. Option
B misstates r² (which is 0.5625, or 56.25%, but phrased as 'explained by' without causal language is still problematic
if implying causation). Option A asserts causality; D misinterprets the sign as weakness.
6. A multiple regression model predicting hospital length of stay includes age, sex, and comorbidity index. The
coefficient for comorbidity index is 1.5 (p < 0.001). What is the correct interpretation?
A) For each one-unit increase in comorbidity index, length of stay increases by 1.5 days, holding other variables
constant.
B) Comorbidity index explains 1.5% of the variance in length of stay.
C) The odds of longer stay increase by 1.5 times per comorbidity unit.
D) The average length of stay for patients with comorbidities is 1.5 days.
' Correct Answer: A
Rationale: In multiple regression, a coefficient represents the change in the dependent variable per unit change in
the predictor, holding other predictors constant. Option B confuses coefficient with R²; C incorrectly invokes odds
ratios; D misinterprets the coefficient as a group mean.
7. A study finds that the number of nurses on a unit and patient satisfaction scores have a correlation of 0.60. Which
additional analysis would best help determine if nurse staffing predicts satisfaction while controlling for unit size?
A) Chi-square test of independence
Page 2
, B) Multiple linear regression
C) Paired t-test
D) One-way ANOVA
' Correct Answer: B
Rationale: Multiple linear regression allows assessment of the relationship between nurse staffing and satisfaction
while adjusting for potential confounders like unit size. Chi-square is for categorical association; paired t-test
compares two related means; ANOVA compares means across groups, not controlling for continuous covariates.
8. In a hypothesis test comparing two independent means, the p-value is 0.03 and the significance level is 0.05.
Which statement is most accurate?
A) There is a 3% chance the null hypothesis is true.
B) The observed difference is statistically significant at the 0.05 level.
C) The probability of a Type II error is 0.03.
D) The effect size is clinically significant.
' Correct Answer: B
Rationale: A p-value of 0.03 < 0.05 leads to rejecting the null hypothesis, indicating statistical significance. Option
A is a common misinterpretation (p-value is not the probability the null is true); C confuses p-value with Type II
error rate; D incorrectly equates statistical significance with clinical significance.
9. A researcher wants to estimate the mean HbA1c level in a diabetic population with a margin of error of 0.2% at
95% confidence. Assuming a standard deviation of 1.0%, what is the minimum required sample size?
A) 25
B) 97
C) 385
D) 1537
' Correct Answer: B
Rationale: Using n = (Z±/2 * Ã / E)² = (1.96 * 1..2)² = (9.8)² "H 96.04, round up to 97. Distractors reflect
common errors such as omitting the Z multiplier, misplacing the margin of error, or using a different confidence
level.
10. A clinical trial reports a number needed to treat (NNT) of 20 for a new therapy. Which statement best describes
this finding?
A) 20 patients must be treated for one additional patient to benefit.
B) 20% of treated patients will benefit.
C) The absolute risk reduction is 20%.
D) The therapy is ineffective in 20% of patients.
' Correct Answer: A
Rationale: NNT is the reciprocal of the absolute risk reduction (ARR); NNT = 20 means 20 patients must be
treated to prevent one additional adverse outcome. Option B confuses NNT with a percentage benefit; C misstates
ARR (which would be 1/20 = 5%); D misinterprets NNT as failure rate.
11. A screening test for a rare disease has sensitivity 0.95 and specificity 0.90. In a population where prevalence is
0.01, which statement best characterizes the clinical utility of a positive result?
A) The positive predictive value is approximately 0.95 because sensitivity is high.
B) The positive predictive value is approximately 0.09, so most positives are false positives.
C) The negative predictive value equals specificity, so a negative result reliably excludes disease.
D) Prevalence does not affect predictive values when sensitivity and specificity are fixed.
' Correct Answer: B
Page 3
, Rationale: PPV = (0.95×0.01)/[(0.95×0.01)+(0.10×0.99)] "H 0.0095/0.1085 "H 0.088, so most positives are false
positives. Sensitivity alone does not determine PPV; prevalence strongly modifies it. NPV is not equal to specificity,
and prevalence directly affects both predictive values.
12. A researcher reports that mean systolic blood pressure decreased by 8 mmHg after an intervention, with a 95%
CI of (12, 4). Which interpretation is most defensible?
A) There is a statistically significant decrease, and the true effect is plausibly between 4 and 12 mmHg.
B) The result is not statistically significant because the interval is wide.
C) The intervention caused an 8 mmHg decrease in every participant.
D) A 95% CI excluding zero proves the intervention is clinically important.
' Correct Answer: A
Rationale: A CI excluding zero indicates statistical significance, and the interval bounds the plausible magnitude of
the true mean decrease. It does not imply every participant changed equally, and statistical significance does not by
itself establish clinical importance. Interval width alone does not determine significance.
13. In a study comparing two independent group means with unequal variances and markedly unequal sample sizes,
which test is most appropriate?
A) Paired t-test
B) Welch's t-test
C) Chi-square test of independence
D) One-way ANOVA with equal-variance assumption
' Correct Answer: B
Rationale: Welch's t-test adjusts degrees of freedom for unequal variances and unequal sample sizes, making it
robust in this setting. A paired t-test requires matched data, chi-square tests categorical association, and standard
ANOVA assumes homogeneity of variance.
14. A dataset of hospital charges is strongly right-skewed with several extreme outliers. Which summary pair best
communicates central tendency and spread?
A) Mean and standard deviation
B) Median and interquartile range
C) Mode and range
D) Mean and coefficient of variation
' Correct Answer: B
Rationale: For skewed data with outliers, the median and IQR are resistant to extreme values and better represent
typical values and spread. Mean and SD are sensitive to skew and outliers, while mode and range convey limited
information about spread.
15. A clinician wants to estimate the proportion of patients readmitted within 30 days with a 95% confidence
interval no wider than ±3%. Which factor most directly determines the required sample size?
A) The population size, unless it is very small
B) The desired margin of error and assumed proportion
C) The number of hospitals in the network
D) The mean length of stay
' Correct Answer: B
Rationale: Sample size for a proportion depends primarily on the desired margin of error, confidence level, and an
assumed or estimated proportion. Population size matters only with finite population correction in small populations.
Hospital count and length of stay are not direct determinants.
Page 4
University - Academic Year 2026/2027 - Objective Assessment
Comprehensive Examination with 100 Verified Questions and
Correct Answer Rationales
About This Exam Bank
This comprehensive 146-question exam bank is designed to prepare candidates for WGU C784 Applied Healthcare
Statistics - Western Governors University - Academic Year 2026/2027 - Objective Assessment Comprehensive
Examination with 100 Verified Questions and Correct Answer Rationales. Every question is aligned with the latest
official content outline and includes a detailed, evidence-based rationale, an explanation of why each remaining
option is incorrect, and a supporting reference.
Keywords
WGU C784 Applied Healthcare Statistics - Western Governors University - Academic Year 2026/2027 - Objective
Assessment Comprehensive Examination with 100 Verified Questions and Correct Answer Rationales, exam bank,
practice questions, verified answers, detailed rationales, test prep, study guide, review questions, certification exam,
latest update, WGU C784 Applied Healthcare Statistics - Western Governors University - Academic Year 2026/2027
- Objective Assessment Comprehensive Examination with 100 Verified Questions and Correct Answer Rationales,
exam bank, practice questions, verified answers, detailed rationales
PART 1: APPLY PROBABILITY RULES AND PROBABILITY DISTRIBUTIONS TO MODEL
CLINICAL EVENTS AND DIAGNOSTIC TEST CHARACTERISTICS
1. A continuous random variable representing patient wait times is uniformly distributed between 0 and 20 minutes.
Given that a patient has already waited 12 minutes, what is the probability they will wait at least 5 more minutes?
A) 0.15
B) 0.25
C) 0.375
D) 0.40
' Correct Answer: C
Rationale: For a uniform distribution on [0,20], the conditional probability that wait "e17 given wait "e12 is
(2017)/(2012) = 3/8 = 0.375. The memoryless-like property of the uniform distribution yields the ratio of remaining
interval lengths. Distractors reflect common errors: using unconditional probabilities or miscomputing the
conditional denominator.
2. A screening test has sensitivity 0.90 and specificity 0.95. In a population with disease prevalence 2%, what is the
approximate positive predictive value (PPV)?
A) 0.27
B) 0.45
C) 0.64
D) 0.90
' Correct Answer: A
Rationale: PPV = (sensitivity × prevalence) / [(sensitivity × prevalence) + ((1"specificity) × (1"prevalence))] =
(0.90×0.02)/[(0.90×0.02)+(0.05×0.98)] = 0.018/(0.018+0.049) 0.269. Even with high sensitivity/specificity, low
prevalence drastically reduces PPV. Distractors reflect confusion with sensitivity or ignoring prevalence.
Page 1
,3. A study reports a 95% confidence interval for the mean reduction in systolic blood pressure as (4.2, 9.8) mmHg.
Which interpretation is most appropriate?
A) 95% of patients experienced a reduction between 4.2 and 9.8 mmHg.
B) There is a 95% probability that the true mean reduction lies in this interval.
C) If the study were repeated many times, 95% of such intervals would contain the true mean reduction.
D) The sample mean reduction is between 4.2 and 9.8 mmHg with 95% confidence.
' Correct Answer: C
Rationale: The frequentist confidence interval interpretation is that 95% of intervals constructed from repeated
samples would capture the true parameter. Option B reflects a common Bayesian misinterpretation; A confuses
individual values with the mean; D is incorrect because the sample mean is a fixed point estimate, not an interval.
4. A clinical trial compares a new drug to placebo. The relative risk (RR) of adverse events is 1.8 with a 95% CI of
(1.2, 2.7). Which statement is most accurate?
A) The result is not statistically significant because the CI includes 1.0.
B) The new drug is associated with a statistically significant increased risk of adverse events.
C) The absolute risk increase is 80%.
D) The odds ratio must also be 1.8.
' Correct Answer: B
Rationale: Since the 95% CI for RR excludes 1.0 (1.2 to 2.7), the increased risk is statistically significant. Option
A is wrong because 1.0 is not in the interval; C confuses relative risk with absolute risk; D is false because OR and
RR diverge when event rates are not rare.
5. A researcher calculates Pearson's r = 0.75 between daily physical activity and BMI. Which conclusion is best
supported?
A) Increased physical activity causes lower BMI.
B) 56% of the variation in BMI is explained by physical activity.
C) There is a strong negative linear association, but causality cannot be inferred.
D) The relationship is weak because r is negative.
' Correct Answer: C
Rationale: r = "0.75 indicates a strong negative linear association, but correlation does not imply causation. Option
B misstates r² (which is 0.5625, or 56.25%, but phrased as 'explained by' without causal language is still problematic
if implying causation). Option A asserts causality; D misinterprets the sign as weakness.
6. A multiple regression model predicting hospital length of stay includes age, sex, and comorbidity index. The
coefficient for comorbidity index is 1.5 (p < 0.001). What is the correct interpretation?
A) For each one-unit increase in comorbidity index, length of stay increases by 1.5 days, holding other variables
constant.
B) Comorbidity index explains 1.5% of the variance in length of stay.
C) The odds of longer stay increase by 1.5 times per comorbidity unit.
D) The average length of stay for patients with comorbidities is 1.5 days.
' Correct Answer: A
Rationale: In multiple regression, a coefficient represents the change in the dependent variable per unit change in
the predictor, holding other predictors constant. Option B confuses coefficient with R²; C incorrectly invokes odds
ratios; D misinterprets the coefficient as a group mean.
7. A study finds that the number of nurses on a unit and patient satisfaction scores have a correlation of 0.60. Which
additional analysis would best help determine if nurse staffing predicts satisfaction while controlling for unit size?
A) Chi-square test of independence
Page 2
, B) Multiple linear regression
C) Paired t-test
D) One-way ANOVA
' Correct Answer: B
Rationale: Multiple linear regression allows assessment of the relationship between nurse staffing and satisfaction
while adjusting for potential confounders like unit size. Chi-square is for categorical association; paired t-test
compares two related means; ANOVA compares means across groups, not controlling for continuous covariates.
8. In a hypothesis test comparing two independent means, the p-value is 0.03 and the significance level is 0.05.
Which statement is most accurate?
A) There is a 3% chance the null hypothesis is true.
B) The observed difference is statistically significant at the 0.05 level.
C) The probability of a Type II error is 0.03.
D) The effect size is clinically significant.
' Correct Answer: B
Rationale: A p-value of 0.03 < 0.05 leads to rejecting the null hypothesis, indicating statistical significance. Option
A is a common misinterpretation (p-value is not the probability the null is true); C confuses p-value with Type II
error rate; D incorrectly equates statistical significance with clinical significance.
9. A researcher wants to estimate the mean HbA1c level in a diabetic population with a margin of error of 0.2% at
95% confidence. Assuming a standard deviation of 1.0%, what is the minimum required sample size?
A) 25
B) 97
C) 385
D) 1537
' Correct Answer: B
Rationale: Using n = (Z±/2 * Ã / E)² = (1.96 * 1..2)² = (9.8)² "H 96.04, round up to 97. Distractors reflect
common errors such as omitting the Z multiplier, misplacing the margin of error, or using a different confidence
level.
10. A clinical trial reports a number needed to treat (NNT) of 20 for a new therapy. Which statement best describes
this finding?
A) 20 patients must be treated for one additional patient to benefit.
B) 20% of treated patients will benefit.
C) The absolute risk reduction is 20%.
D) The therapy is ineffective in 20% of patients.
' Correct Answer: A
Rationale: NNT is the reciprocal of the absolute risk reduction (ARR); NNT = 20 means 20 patients must be
treated to prevent one additional adverse outcome. Option B confuses NNT with a percentage benefit; C misstates
ARR (which would be 1/20 = 5%); D misinterprets NNT as failure rate.
11. A screening test for a rare disease has sensitivity 0.95 and specificity 0.90. In a population where prevalence is
0.01, which statement best characterizes the clinical utility of a positive result?
A) The positive predictive value is approximately 0.95 because sensitivity is high.
B) The positive predictive value is approximately 0.09, so most positives are false positives.
C) The negative predictive value equals specificity, so a negative result reliably excludes disease.
D) Prevalence does not affect predictive values when sensitivity and specificity are fixed.
' Correct Answer: B
Page 3
, Rationale: PPV = (0.95×0.01)/[(0.95×0.01)+(0.10×0.99)] "H 0.0095/0.1085 "H 0.088, so most positives are false
positives. Sensitivity alone does not determine PPV; prevalence strongly modifies it. NPV is not equal to specificity,
and prevalence directly affects both predictive values.
12. A researcher reports that mean systolic blood pressure decreased by 8 mmHg after an intervention, with a 95%
CI of (12, 4). Which interpretation is most defensible?
A) There is a statistically significant decrease, and the true effect is plausibly between 4 and 12 mmHg.
B) The result is not statistically significant because the interval is wide.
C) The intervention caused an 8 mmHg decrease in every participant.
D) A 95% CI excluding zero proves the intervention is clinically important.
' Correct Answer: A
Rationale: A CI excluding zero indicates statistical significance, and the interval bounds the plausible magnitude of
the true mean decrease. It does not imply every participant changed equally, and statistical significance does not by
itself establish clinical importance. Interval width alone does not determine significance.
13. In a study comparing two independent group means with unequal variances and markedly unequal sample sizes,
which test is most appropriate?
A) Paired t-test
B) Welch's t-test
C) Chi-square test of independence
D) One-way ANOVA with equal-variance assumption
' Correct Answer: B
Rationale: Welch's t-test adjusts degrees of freedom for unequal variances and unequal sample sizes, making it
robust in this setting. A paired t-test requires matched data, chi-square tests categorical association, and standard
ANOVA assumes homogeneity of variance.
14. A dataset of hospital charges is strongly right-skewed with several extreme outliers. Which summary pair best
communicates central tendency and spread?
A) Mean and standard deviation
B) Median and interquartile range
C) Mode and range
D) Mean and coefficient of variation
' Correct Answer: B
Rationale: For skewed data with outliers, the median and IQR are resistant to extreme values and better represent
typical values and spread. Mean and SD are sensitive to skew and outliers, while mode and range convey limited
information about spread.
15. A clinician wants to estimate the proportion of patients readmitted within 30 days with a 95% confidence
interval no wider than ±3%. Which factor most directly determines the required sample size?
A) The population size, unless it is very small
B) The desired margin of error and assumed proportion
C) The number of hospitals in the network
D) The mean length of stay
' Correct Answer: B
Rationale: Sample size for a proportion depends primarily on the desired margin of error, confidence level, and an
assumed or estimated proportion. Population size matters only with finite population correction in small populations.
Hospital count and length of stay are not direct determinants.
Page 4
