, Question 1
A hospital reports that the mean length of stay (LOS) for a procedure is 5.2
days with a standard deviation of 1.3 days. Assuming a normal distribution,
what is the probability that a randomly selected patient stays more than 7.0
days?
A. 0.0823
B. 0.1587
C. 0.0418
D. 0.0918
Correct Answer: A - 0.0823
RATIONALE
Compute z = (7.0 - 5.2)/1.3 = 1.3846. The area to the right is
approximately 0.083, closest to 0.0823. Other options reflect common
z-table misreads or using the wrong tail.
Question 2
In a study examining the relationship between nurse staffing ratios and patient
fall rates, the Pearson correlation coefficient is r = -0.62. Which statement best
interprets this finding?
A. Higher staffing ratios cause lower fall rates.
B. There is a moderate negative linear association between staffing ratios
and fall rates.
C. Staffing ratios explain 62% of the variance in fall rates.
D. The relationship is not statistically significant because r is negative.
Correct Answer: B - There is a moderate negative linear
association between staffing ratios and fall rates.
Page 2
, RATIONALE
r = -0.62 indicates a moderate negative linear association. Causation
cannot be inferred from correlation, and variance explained is r² =
0.3844 (38.44%), not 62%. The sign of r does not determine
significance.
Question 3
A researcher wants to estimate the mean systolic blood pressure of a
population with a 95% confidence interval of width ±4 mmHg. Assuming a
population standard deviation of 15 mmHg, what is the minimum sample size
required?
A. 55
B. 97
C. 217
D. 385
Correct Answer: A - 55
RATIONALE
Using n = (z*/E)² with z=1.96, =15, E=4: n = (1.96*15/4)² = (7.35)²
54.02, round up to 55. Options B, C, D reflect common errors such as
using z=2.58, squaring incorrectly, or misplacing the margin of error.
Question 4
Which of the following best describes a Type I error in the context of a clinical
trial testing a new drug?
A. Concluding the drug is effective when it is not.
B. Concluding the drug is not effective when it is.
C. Failing to reject the null hypothesis when it is false.
D. Rejecting the null hypothesis when it is true.
Correct Answer: D - Rejecting the null hypothesis when it is true.
Page 3
A hospital reports that the mean length of stay (LOS) for a procedure is 5.2
days with a standard deviation of 1.3 days. Assuming a normal distribution,
what is the probability that a randomly selected patient stays more than 7.0
days?
A. 0.0823
B. 0.1587
C. 0.0418
D. 0.0918
Correct Answer: A - 0.0823
RATIONALE
Compute z = (7.0 - 5.2)/1.3 = 1.3846. The area to the right is
approximately 0.083, closest to 0.0823. Other options reflect common
z-table misreads or using the wrong tail.
Question 2
In a study examining the relationship between nurse staffing ratios and patient
fall rates, the Pearson correlation coefficient is r = -0.62. Which statement best
interprets this finding?
A. Higher staffing ratios cause lower fall rates.
B. There is a moderate negative linear association between staffing ratios
and fall rates.
C. Staffing ratios explain 62% of the variance in fall rates.
D. The relationship is not statistically significant because r is negative.
Correct Answer: B - There is a moderate negative linear
association between staffing ratios and fall rates.
Page 2
, RATIONALE
r = -0.62 indicates a moderate negative linear association. Causation
cannot be inferred from correlation, and variance explained is r² =
0.3844 (38.44%), not 62%. The sign of r does not determine
significance.
Question 3
A researcher wants to estimate the mean systolic blood pressure of a
population with a 95% confidence interval of width ±4 mmHg. Assuming a
population standard deviation of 15 mmHg, what is the minimum sample size
required?
A. 55
B. 97
C. 217
D. 385
Correct Answer: A - 55
RATIONALE
Using n = (z*/E)² with z=1.96, =15, E=4: n = (1.96*15/4)² = (7.35)²
54.02, round up to 55. Options B, C, D reflect common errors such as
using z=2.58, squaring incorrectly, or misplacing the margin of error.
Question 4
Which of the following best describes a Type I error in the context of a clinical
trial testing a new drug?
A. Concluding the drug is effective when it is not.
B. Concluding the drug is not effective when it is.
C. Failing to reject the null hypothesis when it is false.
D. Rejecting the null hypothesis when it is true.
Correct Answer: D - Rejecting the null hypothesis when it is true.
Page 3
