Null hypothesis and P-values MCQs With Answer

Null hypothesis and P-values MCQs With Answer

This quiz set is designed for M.Pharm students to strengthen understanding of the null hypothesis and p-values in the context of research methodology and biostatistics. The questions emphasize correct interpretation of p-values, significance levels, Type I and II errors, power, multiple comparisons, and practical reporting. Each item tests conceptual depth and common misinterpretations encountered in clinical and pharmaceutical research, and includes answers to reinforce learning. Use these MCQs for self-assessment, revision before exams, or classroom practice to bridge statistical theory with application in pharmacological studies and evidence-based decision making.

Q1. What is the usual definition of a null hypothesis (H0) in inferential statistics?

• There is a specific effect or difference in the population
• There is no effect or no difference in the population
• The probability that the alternative hypothesis is true
• The observed sample mean

Correct Answer: There is no effect or no difference in the population

Q2. Which statement best defines a p-value?

• The probability that the null hypothesis is true given the observed data
• The probability of observing data as extreme as (or more extreme than) what was observed, assuming the null hypothesis is true
• The probability that results are clinically significant
• The probability that the alternative hypothesis is true

Correct Answer: The probability of observing data as extreme as (or more extreme than) what was observed, assuming the null hypothesis is true

Q3. If a computed p-value is less than the pre-specified alpha (e.g., p = 0.02, alpha = 0.05), the correct statistical decision is:

• Accept the null hypothesis
• Fail to reject the null hypothesis
• Reject the null hypothesis
• Prove the alternative hypothesis is true

Correct Answer: Reject the null hypothesis

Q4. A p-value of 0.04 means which of the following (correct interpretation)?

• There is a 4% probability that the null hypothesis is true
• There is a 96% probability that the alternative hypothesis is true
• Assuming the null hypothesis is true, there is a 4% chance of obtaining results as extreme or more extreme than observed
• There is a 4% chance the results occurred by any mechanism

Correct Answer: Assuming the null hypothesis is true, there is a 4% chance of obtaining results as extreme or more extreme than observed

Q5. What does a Type I error represent?

• Failing to detect a true effect (false negative)
• Detecting an effect when none exists (false positive)
• The probability of a correct decision
• A measurement error in the instrument

Correct Answer: Detecting an effect when none exists (false positive)

Q6. What is a Type II error (beta)?

• Rejecting a true null hypothesis
• Failing to reject a false null hypothesis
• The same as alpha
• A guaranteed error when sample size is large

Correct Answer: Failing to reject a false null hypothesis

Q7. The significance level alpha (α) is defined as:

• The probability of a Type II error
• The probability of a Type I error
• The power of a study
• The observed p-value

Correct Answer: The probability of a Type I error

Q8. Which option correctly distinguishes a two-tailed test from a one-tailed test?

• Two-tailed tests detect deviation in one specified direction only
• Two-tailed tests assess deviations in both directions from the null value
• One-tailed tests are only used for proportions, two-tailed for means
• Two-tailed tests always have higher power than one-tailed tests for the same alpha

Correct Answer: Two-tailed tests assess deviations in both directions from the null value

Q9. If a study yields p = 0.20 and alpha = 0.05, the appropriate conclusion is:

• Reject the null hypothesis
• Accept the null hypothesis as true
• Fail to reject the null hypothesis
• Prove the null hypothesis false

Correct Answer: Fail to reject the null hypothesis

Q10. How does the magnitude of the p-value generally relate to evidence against H0?

• A smaller p-value provides weaker evidence against H0
• A smaller p-value provides stronger evidence against H0
• There is no relationship between p-value magnitude and evidence against H0
• A larger p-value proves H0 is false

Correct Answer: A smaller p-value provides stronger evidence against H0

Q11. Does a p-value indicate the size or importance of an effect?

• Yes, a smaller p-value always means a larger, more important effect
• No, p-value does not measure effect size or clinical importance
• Yes, p-value equals effect size divided by sample size
• No, p-value measures only bias, not effect size

Correct Answer: No, p-value does not measure effect size or clinical importance

Q12. Conducting many hypothesis tests without correction typically leads to:

• Lower Type I error across all tests
• Increased family-wise Type I error and more false positives
• No change in overall error rates
• Guaranteed discovery of true effects

Correct Answer: Increased family-wise Type I error and more false positives

Q13. The Bonferroni correction adjusts for multiple comparisons by:

• Multiplying p-values by the number of tests and comparing to alpha
• Dividing the alpha level by the number of comparisons
• Using only the smallest p-value and ignoring others
• Changing alpha to 0.05 regardless of number of tests

Correct Answer: Dividing the alpha level by the number of comparisons

Q14. Which statement is correct regarding a non-significant p-value (p > alpha)?

• A non-significant p-value proves the null hypothesis is true
• Failure to reject the null hypothesis does not prove it is true
• A non-significant p-value indicates the study had no measurement error
• A non-significant p-value means the alternative hypothesis is impossible

Correct Answer: Failure to reject the null hypothesis does not prove it is true

Q15. How does a 95% confidence interval (CI) relate to a two-sided hypothesis test at alpha = 0.05?

• If the 95% CI includes the null value, the two-sided test typically gives p < 0.05
• If the 95% CI excludes the null value, the two-sided test typically yields p < 0.05
• Confidence intervals and p-values are unrelated
• A 95% CI excluding the null implies p > 0.05

Correct Answer: If the 95% CI excludes the null value, the two-sided test typically yields p < 0.05

Q16. When are p-values unreliable or inappropriate without modification?

• When sample size is very large and assumptions are perfectly met
• When test assumptions (normality, independence, equal variances) are violated; use nonparametric or exact tests
• When the p-value is smaller than 0.001
• When effect sizes are clinically large

Correct Answer: When test assumptions (normality, independence, equal variances) are violated; use nonparametric or exact tests

Q17. Statistical power of a test is defined as:

• The probability of making a Type I error
• The probability of making a Type II error
• The probability of correctly rejecting a false null hypothesis (1 − beta)
• The p-value threshold used in analysis

Correct Answer: The probability of correctly rejecting a false null hypothesis (1 − beta)

Q18. How does increasing sample size typically affect the p-value and power for a fixed true effect size?

• Increases p-value and decreases power
• Decreases p-value and increases power
• Has no effect on p-value or power
• Makes p-value equal to alpha

Correct Answer: Decreases p-value and increases power

Q19. Which procedure is designed to control the false discovery rate (FDR) rather than the family-wise error rate?

• Bonferroni correction
• Holm-Bonferroni method
• Benjamini-Hochberg procedure
• Sidak correction

Correct Answer: Benjamini-Hochberg procedure

Q20. Best practice for reporting a very small p-value (e.g., p = 0.0001) in a pharmacological study is to:

• Report “p = 0.0001” and avoid interpreting effect size or confidence intervals
• Report the exact p-value, provide effect size and confidence interval, and discuss clinical relevance rather than claiming absolute proof
• Only report “p < 0.05" to simplify results
• Round it to p = 0.00 and state the result is certain

Correct Answer: Report the exact p-value, provide effect size and confidence interval, and discuss clinical relevance rather than claiming absolute proof

Download