WGU C784 Applied Healthcare Statistics Objective
Assessment – Applied Healthcare Probability & Statistics
Study Guide, Original Practice Questions & Answers, WGU
C784 OA Preparation, Comprehensive Statistics Review,
Descriptive Statistics, Probability, Regression, Correlation,
Algebra & Healthcare Data Interpretation
Question 1: A clinical trial is studying the effect of a new medication on patient
recovery times. The recovery time in days for the treatment group has a mean of 12
and a variance of 16. What is the standard deviation of the recovery time?
A. 2 days
B. 4 days
C. 8 days
D. 16 days
CORRECT ANSWER: B. 4 days
Rationale: The standard deviation is the square root of the variance. Since the variance
is 16, the standard deviation is √16 = 4 days.
Question 2: A nurse measures the blood pressure of 40 patients and finds the
sample mean to be 120 mmHg with a sum of squared deviations from the mean of
4,680. What is the sample variance?
A. 117.0
B. 120.0
C. 121.8
D. 4,680.0
CORRECT ANSWER: A. 117.0
Rationale: The sample variance is calculated by dividing the sum of squared deviations
by the sample size minus 1 (n-1). Here, s² = 4,680 / (40 - 1) = 4, =
120.0. Correction: 4680/39 = 120.0, so the correct answer is B.
Question 3: A dataset of patient ages has a mean of 55 years and a standard
deviation of 10 years. According to Chebyshev's theorem, what is the minimum
proportion of data that must lie within 2 standard deviations of the mean?
A. 68%
B. 75%
C. 89%
D. 95%
CORRECT ANSWER: B. 75%
Rationale: Chebyshev's theorem states that at least 1 - (1/k²) of the data lies within k
standard deviations of the mean. For k=2, this is 1 - (1/4) = 0.75 or 75%.
Question 4: In a study on cholesterol levels, the interquartile range (IQR) of the data
is 40 mg/dL. If the first quartile (Q1) is 150 mg/dL, what is the third quartile (Q3)?
,A. 110 mg/dL
B. 150 mg/dL
C. 190 mg/dL
D. 200 mg/dL
CORRECT ANSWER: C. 190 mg/dL
Rationale: The IQR is calculated as Q3 - Q1. Therefore, Q3 = Q1 + IQR = 150 + 40 = 190
mg/dL.
Question 5: A hospital administrator is looking at a histogram of patient wait times.
The histogram is skewed to the right. Which measure of central tendency is most
appropriate to report as the "average" wait time?
A. Mean
B. Median
C. Mode
D. Range
CORRECT ANSWER: B. Median
Rationale: For a right-skewed distribution, the mean is pulled in the direction of the tail
by extreme outliers. The median is resistant to outliers and is therefore a more
appropriate measure of central tendency.
Question 6: A study reports the incidence rate of a disease as 25 cases per 1,000
person-years. If a population of 5,000 people was followed for 2 years, how many
total cases would be expected?
A. 125
B. 250
C. 500
D. 1,000
CORRECT ANSWER: B. 250
Rationale: Total person-years = 5,000 people * 2 years = 10,000 person-years. Expected
cases = Incidence rate * Person-years = (25/1000) * 10,000 = 250 cases.
Question 7: A test for a certain disease has a sensitivity of 90% and a specificity of
80%. What is the probability that a patient who has the disease will test positive?
A. 0.10
B. 0.20
C. 0.80
D. 0.90
CORRECT ANSWER: D. 0.90
Rationale: Sensitivity is the probability of a positive test result given that the patient has
the disease. Therefore, P(Positive | Disease) = 0.90.
,Question 8: A researcher wants to estimate the population mean blood glucose
level with a 95% confidence interval. The sample mean is 100 mg/dL, and the
margin of error is 5 mg/dL. What is the confidence interval?
A. (95, 105)
B. (90, 110)
C. (85, 115)
D. (100, 105)
CORRECT ANSWER: A. (95, 105)
Rationale: A confidence interval is calculated as (Sample Mean - Margin of Error,
Sample Mean + Margin of Error). Therefore, the interval is (100 - 5, 100 + 5) = (95, 105).
Question 9: A pharmaceutical company tests a new drug and finds a p-value of
0.03. Using a significance level (alpha) of 0.05, what is the correct decision
regarding the null hypothesis?
A. Reject the null hypothesis
B. Fail to reject the null hypothesis
C. Accept the null hypothesis as true
D. Recalculate the test statistic
CORRECT ANSWER: A. Reject the null hypothesis
Rationale: The decision rule is to reject the null hypothesis if the p-value is less than or
equal to the significance level (α). Since 0.03 < 0.05, the null hypothesis is rejected.
Question 10: A scatterplot shows points moving from the bottom-left to the top-
right. This indicates what type of correlation?
A. No correlation
B. Weak negative correlation
C. Strong positive correlation
D. Perfect negative correlation
CORRECT ANSWER: C. Strong positive correlation
Rationale: Points moving from the bottom-left to the top-right indicate that as one
variable increases, the other also tends to increase, which is a positive correlation.
Question 11: Which of the following is a discrete variable?
A. Height in centimeters
B. Time to complete a test
C. Number of hospital admissions
D. Body temperature in degrees Celsius
CORRECT ANSWER: C. Number of hospital admissions
, Rationale: A discrete variable is countable and takes on finite or countably infinite
values. The number of hospital admissions is a count. Height, time, and temperature
are continuous variables.
Question 12: The probability of a patient responding to a treatment is 0.75. What
are the odds of responding to the treatment?
A. 1:3
B. 3:1
C. 1:4
D. 4:1
CORRECT ANSWER: B. 3:1
Rationale: Odds are calculated as P(Event) / P(No Event). Here, odds = 0..25 = 3.
The odds are 3:1 in favor of responding.
Question 13: A clinical trial has 200 participants; 120 are in the treatment group and
80 are in the control group. What is the ratio of treatment participants to control
participants?
A. 2:3
B. 3:2
C. 4:5
D. 5:4
CORRECT ANSWER: B. 3:2
Rationale: The ratio is 120:80. Dividing both numbers by their greatest common divisor
(40) gives a simplified ratio of 3:2.
Question 14: A dataset has a minimum value of 5 and a maximum value of 25. What
is the range of this dataset?
A. 15
B. 20
C. 25
D. 30
CORRECT ANSWER: B. 20
Rationale: The range is calculated as the maximum value minus the minimum value.
Here, 25 - 5 = 20.
Question 15: A researcher is testing the effectiveness of a new diet. The null
hypothesis states that there is no difference in mean weight loss between the diet
group and the control group. If the researcher concludes there is a difference when
there truly is none, what type of error has occurred?
A. Type I error
B. Type II error
Assessment – Applied Healthcare Probability & Statistics
Study Guide, Original Practice Questions & Answers, WGU
C784 OA Preparation, Comprehensive Statistics Review,
Descriptive Statistics, Probability, Regression, Correlation,
Algebra & Healthcare Data Interpretation
Question 1: A clinical trial is studying the effect of a new medication on patient
recovery times. The recovery time in days for the treatment group has a mean of 12
and a variance of 16. What is the standard deviation of the recovery time?
A. 2 days
B. 4 days
C. 8 days
D. 16 days
CORRECT ANSWER: B. 4 days
Rationale: The standard deviation is the square root of the variance. Since the variance
is 16, the standard deviation is √16 = 4 days.
Question 2: A nurse measures the blood pressure of 40 patients and finds the
sample mean to be 120 mmHg with a sum of squared deviations from the mean of
4,680. What is the sample variance?
A. 117.0
B. 120.0
C. 121.8
D. 4,680.0
CORRECT ANSWER: A. 117.0
Rationale: The sample variance is calculated by dividing the sum of squared deviations
by the sample size minus 1 (n-1). Here, s² = 4,680 / (40 - 1) = 4, =
120.0. Correction: 4680/39 = 120.0, so the correct answer is B.
Question 3: A dataset of patient ages has a mean of 55 years and a standard
deviation of 10 years. According to Chebyshev's theorem, what is the minimum
proportion of data that must lie within 2 standard deviations of the mean?
A. 68%
B. 75%
C. 89%
D. 95%
CORRECT ANSWER: B. 75%
Rationale: Chebyshev's theorem states that at least 1 - (1/k²) of the data lies within k
standard deviations of the mean. For k=2, this is 1 - (1/4) = 0.75 or 75%.
Question 4: In a study on cholesterol levels, the interquartile range (IQR) of the data
is 40 mg/dL. If the first quartile (Q1) is 150 mg/dL, what is the third quartile (Q3)?
,A. 110 mg/dL
B. 150 mg/dL
C. 190 mg/dL
D. 200 mg/dL
CORRECT ANSWER: C. 190 mg/dL
Rationale: The IQR is calculated as Q3 - Q1. Therefore, Q3 = Q1 + IQR = 150 + 40 = 190
mg/dL.
Question 5: A hospital administrator is looking at a histogram of patient wait times.
The histogram is skewed to the right. Which measure of central tendency is most
appropriate to report as the "average" wait time?
A. Mean
B. Median
C. Mode
D. Range
CORRECT ANSWER: B. Median
Rationale: For a right-skewed distribution, the mean is pulled in the direction of the tail
by extreme outliers. The median is resistant to outliers and is therefore a more
appropriate measure of central tendency.
Question 6: A study reports the incidence rate of a disease as 25 cases per 1,000
person-years. If a population of 5,000 people was followed for 2 years, how many
total cases would be expected?
A. 125
B. 250
C. 500
D. 1,000
CORRECT ANSWER: B. 250
Rationale: Total person-years = 5,000 people * 2 years = 10,000 person-years. Expected
cases = Incidence rate * Person-years = (25/1000) * 10,000 = 250 cases.
Question 7: A test for a certain disease has a sensitivity of 90% and a specificity of
80%. What is the probability that a patient who has the disease will test positive?
A. 0.10
B. 0.20
C. 0.80
D. 0.90
CORRECT ANSWER: D. 0.90
Rationale: Sensitivity is the probability of a positive test result given that the patient has
the disease. Therefore, P(Positive | Disease) = 0.90.
,Question 8: A researcher wants to estimate the population mean blood glucose
level with a 95% confidence interval. The sample mean is 100 mg/dL, and the
margin of error is 5 mg/dL. What is the confidence interval?
A. (95, 105)
B. (90, 110)
C. (85, 115)
D. (100, 105)
CORRECT ANSWER: A. (95, 105)
Rationale: A confidence interval is calculated as (Sample Mean - Margin of Error,
Sample Mean + Margin of Error). Therefore, the interval is (100 - 5, 100 + 5) = (95, 105).
Question 9: A pharmaceutical company tests a new drug and finds a p-value of
0.03. Using a significance level (alpha) of 0.05, what is the correct decision
regarding the null hypothesis?
A. Reject the null hypothesis
B. Fail to reject the null hypothesis
C. Accept the null hypothesis as true
D. Recalculate the test statistic
CORRECT ANSWER: A. Reject the null hypothesis
Rationale: The decision rule is to reject the null hypothesis if the p-value is less than or
equal to the significance level (α). Since 0.03 < 0.05, the null hypothesis is rejected.
Question 10: A scatterplot shows points moving from the bottom-left to the top-
right. This indicates what type of correlation?
A. No correlation
B. Weak negative correlation
C. Strong positive correlation
D. Perfect negative correlation
CORRECT ANSWER: C. Strong positive correlation
Rationale: Points moving from the bottom-left to the top-right indicate that as one
variable increases, the other also tends to increase, which is a positive correlation.
Question 11: Which of the following is a discrete variable?
A. Height in centimeters
B. Time to complete a test
C. Number of hospital admissions
D. Body temperature in degrees Celsius
CORRECT ANSWER: C. Number of hospital admissions
, Rationale: A discrete variable is countable and takes on finite or countably infinite
values. The number of hospital admissions is a count. Height, time, and temperature
are continuous variables.
Question 12: The probability of a patient responding to a treatment is 0.75. What
are the odds of responding to the treatment?
A. 1:3
B. 3:1
C. 1:4
D. 4:1
CORRECT ANSWER: B. 3:1
Rationale: Odds are calculated as P(Event) / P(No Event). Here, odds = 0..25 = 3.
The odds are 3:1 in favor of responding.
Question 13: A clinical trial has 200 participants; 120 are in the treatment group and
80 are in the control group. What is the ratio of treatment participants to control
participants?
A. 2:3
B. 3:2
C. 4:5
D. 5:4
CORRECT ANSWER: B. 3:2
Rationale: The ratio is 120:80. Dividing both numbers by their greatest common divisor
(40) gives a simplified ratio of 3:2.
Question 14: A dataset has a minimum value of 5 and a maximum value of 25. What
is the range of this dataset?
A. 15
B. 20
C. 25
D. 30
CORRECT ANSWER: B. 20
Rationale: The range is calculated as the maximum value minus the minimum value.
Here, 25 - 5 = 20.
Question 15: A researcher is testing the effectiveness of a new diet. The null
hypothesis states that there is no difference in mean weight loss between the diet
group and the control group. If the researcher concludes there is a difference when
there truly is none, what type of error has occurred?
A. Type I error
B. Type II error
