Mastering Biostatistics: The Ultimate Final
Exam Preparation Guide with High-Yield
Practice Questions, Formulas, and Step-by-
Step Solutions for Public Health and
Medical Students
1. A researcher wants to compare the mean systolic blood pressure of patients
who received a new drug versus a placebo. The sample size for each group is 25.
The data are approximately normally distributed, but the variances are unknown
and not assumed to be equal. Which statistical test is most appropriate?
A) Paired t-test
B) Two-sample t-test assuming equal variances
C) Wilcoxon rank-sum test
D) Welch's t-test
Answer: D) Welch's t-test
Rationale: Welch's t-test is a modification of the two-sample t-test and is specifically
designed for situations where the two samples have unequal variances and/or unequal
sample sizes. A standard two-sample t-test (Option B) assumes equal variances. A paired
t-test (Option A) is used for dependent samples. The Wilcoxon rank-sum test (Option C) is
a non-parametric alternative used when the normality assumption is violated.
2. In a study examining the association between a new biomarker (continuous)
and disease severity (ordinal, with 4 levels), which correlation coefficient is most
appropriate to measure the strength of the association?
,A) Pearson correlation coefficient
B) Spearman rank correlation coefficient
C) Point-biserial correlation coefficient
D) Phi coefficient
Answer: B) Spearman rank correlation coefficient
Rationale: The Spearman rank correlation is a non-parametric measure of rank
correlation, making it suitable for ordinal data or when the relationship between two
continuous variables is not linear. The Pearson correlation (Option A) is used for linear
relationships between two continuous variables. The point-biserial (Option C) is for one
continuous and one dichotomous variable. The Phi coefficient (Option D) is for two
dichotomous variables.
3. A clinical trial reports a risk ratio (RR) of 0.65 for a new treatment compared to
a placebo, with a 95% confidence interval of (0.45, 0.92). What is the correct
interpretation of this result?
A) The treatment is not effective because the confidence interval is wide.
B) There is a statistically significant increase in risk associated with the treatment.
C) There is a statistically significant decrease in risk associated with the treatment.
D) The result is not statistically significant because the confidence interval does not
include 1.0.
Answer: C) There is a statistically significant decrease in risk associated with the
treatment.
Rationale: A risk ratio of 0.65 indicates that the risk in the treatment group is 65% of the
risk in the placebo group, representing a 35% relative risk reduction. The 95% confidence
interval (0.45, 0.92) does not include 1.0 (the null value for a ratio), which indicates that
the result is statistically significant. Therefore, the treatment is associated with a
statistically significant decrease in risk.
,4. Which of the following measures of disease frequency is defined as the number
of new cases of a disease that occur in a population at risk during a specified
period of time?
A) Prevalence
B) Incidence
C) Attack rate
D) Mortality rate
Answer: B) Incidence
Rationale: Incidence measures the occurrence of new cases of a disease or condition in a
population at risk over a specific period. Prevalence (Option A) measures the total number
of existing cases (both new and old) in a population at a specific point in time. Attack rate
(Option C) is a type of incidence rate used in an outbreak setting. Mortality rate (Option D)
measures the number of deaths in a population.
5. A researcher calculates a p-value of 0.03. If the significance level (alpha) was set
at 0.05, what is the correct conclusion?
A) The null hypothesis is proven to be true.
B) The alternative hypothesis is proven to be false.
C) The result is not statistically significant.
D) The null hypothesis is rejected.
Answer: D) The null hypothesis is rejected.
Rationale: A p-value of 0.03 is less than the pre-set alpha level of 0.05. This means the
observed results are unlikely to have occurred by chance if the null hypothesis were true.
Therefore, we reject the null hypothesis in favor of the alternative hypothesis. It is
important to note that hypothesis testing does not "prove" anything; it only provides
evidence to reject or fail to reject the null hypothesis.
, 6. A 2x2 table is created to analyze the results of a screening test. The test
correctly identifies 90 people with the disease as positive and correctly identifies
80 people without the disease as negative. It incorrectly identifies 10 people with
the disease as negative and 20 people without the disease as positive. What is the
sensitivity of this test?
A) 90%
B) 80%
C) 81.8%
D) 88.9%
Answer: A) 90%
Rationale: Sensitivity is the ability of a test to correctly identify those with the disease (True
Positive Rate). It is calculated as: True Positives / (True Positives + False Negatives). In this
case, True Positives = 90 and False Negatives = 10. So, Sensitivity = 90 / (90 + 10) = 90 /
100 = 0.90 or 90%.
7. Which of the following is a key difference between a randomized controlled trial
(RCT) and an observational cohort study?
A) RCTs are always prospective, while cohort studies are always retrospective.
B) RCTs can establish causality more strongly because of randomization.
C) Cohort studies can only measure odds ratios, while RCTs measure risk ratios.
D) RCTs are more susceptible to confounding bias than cohort studies.
Answer: B) RCTs can establish causality more strongly because of randomization.
Rationale: Randomization in an RCT is the key feature that helps balance both known and
unknown confounding variables between the treatment groups. This allows for a stronger
causal inference than is possible in observational studies like cohort studies, where
confounding is a primary concern. Cohort studies can be prospective or retrospective
Exam Preparation Guide with High-Yield
Practice Questions, Formulas, and Step-by-
Step Solutions for Public Health and
Medical Students
1. A researcher wants to compare the mean systolic blood pressure of patients
who received a new drug versus a placebo. The sample size for each group is 25.
The data are approximately normally distributed, but the variances are unknown
and not assumed to be equal. Which statistical test is most appropriate?
A) Paired t-test
B) Two-sample t-test assuming equal variances
C) Wilcoxon rank-sum test
D) Welch's t-test
Answer: D) Welch's t-test
Rationale: Welch's t-test is a modification of the two-sample t-test and is specifically
designed for situations where the two samples have unequal variances and/or unequal
sample sizes. A standard two-sample t-test (Option B) assumes equal variances. A paired
t-test (Option A) is used for dependent samples. The Wilcoxon rank-sum test (Option C) is
a non-parametric alternative used when the normality assumption is violated.
2. In a study examining the association between a new biomarker (continuous)
and disease severity (ordinal, with 4 levels), which correlation coefficient is most
appropriate to measure the strength of the association?
,A) Pearson correlation coefficient
B) Spearman rank correlation coefficient
C) Point-biserial correlation coefficient
D) Phi coefficient
Answer: B) Spearman rank correlation coefficient
Rationale: The Spearman rank correlation is a non-parametric measure of rank
correlation, making it suitable for ordinal data or when the relationship between two
continuous variables is not linear. The Pearson correlation (Option A) is used for linear
relationships between two continuous variables. The point-biserial (Option C) is for one
continuous and one dichotomous variable. The Phi coefficient (Option D) is for two
dichotomous variables.
3. A clinical trial reports a risk ratio (RR) of 0.65 for a new treatment compared to
a placebo, with a 95% confidence interval of (0.45, 0.92). What is the correct
interpretation of this result?
A) The treatment is not effective because the confidence interval is wide.
B) There is a statistically significant increase in risk associated with the treatment.
C) There is a statistically significant decrease in risk associated with the treatment.
D) The result is not statistically significant because the confidence interval does not
include 1.0.
Answer: C) There is a statistically significant decrease in risk associated with the
treatment.
Rationale: A risk ratio of 0.65 indicates that the risk in the treatment group is 65% of the
risk in the placebo group, representing a 35% relative risk reduction. The 95% confidence
interval (0.45, 0.92) does not include 1.0 (the null value for a ratio), which indicates that
the result is statistically significant. Therefore, the treatment is associated with a
statistically significant decrease in risk.
,4. Which of the following measures of disease frequency is defined as the number
of new cases of a disease that occur in a population at risk during a specified
period of time?
A) Prevalence
B) Incidence
C) Attack rate
D) Mortality rate
Answer: B) Incidence
Rationale: Incidence measures the occurrence of new cases of a disease or condition in a
population at risk over a specific period. Prevalence (Option A) measures the total number
of existing cases (both new and old) in a population at a specific point in time. Attack rate
(Option C) is a type of incidence rate used in an outbreak setting. Mortality rate (Option D)
measures the number of deaths in a population.
5. A researcher calculates a p-value of 0.03. If the significance level (alpha) was set
at 0.05, what is the correct conclusion?
A) The null hypothesis is proven to be true.
B) The alternative hypothesis is proven to be false.
C) The result is not statistically significant.
D) The null hypothesis is rejected.
Answer: D) The null hypothesis is rejected.
Rationale: A p-value of 0.03 is less than the pre-set alpha level of 0.05. This means the
observed results are unlikely to have occurred by chance if the null hypothesis were true.
Therefore, we reject the null hypothesis in favor of the alternative hypothesis. It is
important to note that hypothesis testing does not "prove" anything; it only provides
evidence to reject or fail to reject the null hypothesis.
, 6. A 2x2 table is created to analyze the results of a screening test. The test
correctly identifies 90 people with the disease as positive and correctly identifies
80 people without the disease as negative. It incorrectly identifies 10 people with
the disease as negative and 20 people without the disease as positive. What is the
sensitivity of this test?
A) 90%
B) 80%
C) 81.8%
D) 88.9%
Answer: A) 90%
Rationale: Sensitivity is the ability of a test to correctly identify those with the disease (True
Positive Rate). It is calculated as: True Positives / (True Positives + False Negatives). In this
case, True Positives = 90 and False Negatives = 10. So, Sensitivity = 90 / (90 + 10) = 90 /
100 = 0.90 or 90%.
7. Which of the following is a key difference between a randomized controlled trial
(RCT) and an observational cohort study?
A) RCTs are always prospective, while cohort studies are always retrospective.
B) RCTs can establish causality more strongly because of randomization.
C) Cohort studies can only measure odds ratios, while RCTs measure risk ratios.
D) RCTs are more susceptible to confounding bias than cohort studies.
Answer: B) RCTs can establish causality more strongly because of randomization.
Rationale: Randomization in an RCT is the key feature that helps balance both known and
unknown confounding variables between the treatment groups. This allows for a stronger
causal inference than is possible in observational studies like cohort studies, where
confounding is a primary concern. Cohort studies can be prospective or retrospective
