Parametric tests – t-test (sample, unpaired and paired) MCQs With Answer

Parametric tests – t-test (one-sample, unpaired and paired) MCQs With Answer

Parametric tests, especially the t-test (one-sample, unpaired and paired), are essential for B.Pharm students analyzing continuous data like drug concentrations, blood pressure, assay potency and bioassay results. These methods assume normally distributed residuals, interval/ratio measurement scale, independence and, for unpaired tests, homogeneity of variance. Mastering one-sample t-tests, independent (unpaired) t-tests and paired t-tests, plus degrees of freedom, p-values, confidence intervals and effect size (Cohen’s d), improves experimental design, data analysis and interpretation in pharmacology and pharmaceutics. Practical issues include checking normality, choosing Welch’s test if variances differ, and using nonparametric alternatives when needed. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. Which test is used to compare a sample mean to a known population mean?

• One-sample t-test
• Paired t-test
• Unpaired t-test
• Mann-Whitney U test

Correct Answer: One-sample t-test

Q2. Which of the following is NOT an assumption of the t-test?

• Data are measured on an interval or ratio scale
• Residuals are approximately normally distributed
• Observations are independent
• Data are nominal categories

Correct Answer: Data are nominal categories

Q3. When is a paired t-test appropriate?

• Comparing two independent treatment groups
• Comparing repeated measurements on the same subjects
• Comparing three or more group means
• When sample sizes are extremely large

Correct Answer: Comparing repeated measurements on the same subjects

Q4. What is the degrees of freedom for a one-sample t-test with sample size n?

• n
• n+1
• n-1
• n-2

Correct Answer: n-1

Q5. For an unpaired t-test assuming equal variances, what is the degrees of freedom?

• n1 + n2
• n1 + n2 – 1
• n1 + n2 – 2
• min(n1, n2) – 1

Correct Answer: n1 + n2 – 2

Q6. If two independent groups have unequal variances, which test is recommended?

• Pooled unpaired t-test
• Welch’s t-test
• One-sample t-test
• Chi-square test

Correct Answer: Welch’s t-test

Q7. A two-tailed t-test tests which alternative hypothesis?

• Mean1 > Mean2 only
• Mean1 < Mean2 only
• Mean1 ≠ Mean2 (difference in either direction)
• There is no difference

Correct Answer: Mean1 ≠ Mean2 (difference in either direction)

Q8. In a paired t-test the null hypothesis usually states what?

• The mean of group A is greater than group B
• The mean difference between paired observations is zero
• The variances are equal
• All observations are independent

Correct Answer: The mean difference between paired observations is zero

Q9. How does a 95% confidence interval for a mean difference relate to a two-tailed t-test at alpha = 0.05?

• If the CI includes zero, reject H0
• A CI excluding zero corresponds to rejecting H0 at alpha = 0.05
• The CI is unrelated to hypothesis testing
• The CI must include zero to show significance

Correct Answer: A CI excluding zero corresponds to rejecting H0 at alpha = 0.05

Q10. Which effect size is commonly reported with t-tests?

• Odds ratio
• Cohen’s d
• Hazard ratio
• Kendall’s tau

Correct Answer: Cohen’s d

Q11. Compared with the standard normal distribution, the t-distribution with small degrees of freedom has what characteristic?

• Thinner tails
• Heavier (fatter) tails
• Identical shape
• Lower peak but zero tails

Correct Answer: Heavier (fatter) tails

Q12. When sample size is very large, the t-distribution approximates which distribution?

• Chi-square distribution
• Uniform distribution
• Standard normal (z) distribution
• Exponential distribution

Correct Answer: Standard normal (z) distribution

Q13. The paired t-statistic is computed as t = d̄ / (sd/√n). What does d̄ represent?

• Mean of pooled variances
• Mean of differences between paired observations
• Standard deviation of original measurements
• Total sample mean across groups

Correct Answer: Mean of differences between paired observations

Q14. The pooled variance in an equal-variance unpaired t-test is best described as:

• The simple average of the two sample variances
• A weighted average of the two sample variances
• The larger of the two variances
• The variance of the combined sample means

Correct Answer: A weighted average of the two sample variances

Q15. If paired data are non-normal and sample size is small, which nonparametric alternative is appropriate?

• Mann-Whitney U test
• Wilcoxon signed-rank test
• Chi-square test
• ANOVA

Correct Answer: Wilcoxon signed-rank test

Q16. In a drug trial measuring patient blood levels before and after dosing in the same subjects, which test is most appropriate?

• One-sample t-test
• Unpaired t-test
• Paired t-test
• F-test for variances

Correct Answer: Paired t-test

Q17. The p-value is best defined as:

• The probability that the null hypothesis is true
• The probability of observing data as extreme as or more extreme than observed, assuming H0 is true
• The probability of making a type II error
• The observed effect size

Correct Answer: The probability of observing data as extreme as or more extreme than observed, assuming H0 is true

Q18. If a t-test yields p = 0.03 and alpha = 0.05, the correct decision is:

• Fail to reject H0
• Reject H0
• Increase alpha to 0.10 before deciding
• Conclude clinical importance automatically

Correct Answer: Reject H0

Q19. How do outliers typically affect t-test results?

• They reduce the sample mean but do not affect variance
• They can inflate variance and distort the t-statistic
• They always increase the chance of finding significance
• They convert a t-test into a nonparametric test

Correct Answer: They can inflate variance and distort the t-statistic

Q20. Which change will narrow a confidence interval for a mean difference?

• Smaller sample size
• Larger sample standard deviation
• Increasing sample size
• Using a higher confidence level (e.g., 99% vs 95%)

Correct Answer: Increasing sample size

Q21. For small samples, how does the critical t-value compare to the z critical value at the same alpha?

• Critical t-value is smaller than z
• Critical t-value is larger than z
• Both are identical regardless of sample size
• t-value is negative while z is positive

Correct Answer: Critical t-value is larger than z

Q22. Which R function performs t-tests (one-sample, paired, and unpaired) conveniently?

• lm()
• t.test()
• anova()
• chisq.test()

Correct Answer: t.test()

Q23. For an unpaired two-sided test, what are the null and alternative hypotheses?

• H0: μ1 ≠ μ2, H1: μ1 = μ2
• H0: μ1 = μ2, H1: μ1 ≠ μ2
• H0: μ1 > μ2, H1: μ1 < μ2
• H0: σ1 = σ2, H1: σ1 ≠ σ2

Correct Answer: H0: μ1 = μ2, H1: μ1 ≠ μ2

Q24. A one-sample t-test in pharmaceutics might be used to:

• Compare two independent drug formulations
• Compare a batch mean potency to the pharmacopoeial standard
• Test for correlation between dose and response
• Analyze categorical adverse event rates

Correct Answer: Compare a batch mean potency to the pharmacopoeial standard

Q25. Which statement about Welch’s t-test is true?

• It requires equal sample sizes only
• It assumes equal variances strictly
• It adjusts degrees of freedom when variances differ
• It is only for paired data

Correct Answer: It adjusts degrees of freedom when variances differ

Q26. Cohen’s d of 0.8 is generally interpreted as what magnitude of effect?

• Negligible effect
• Small effect
• Medium effect
• Large effect

Correct Answer: Large effect

Q27. A major advantage of paired designs is:

• They always increase bias
• They control for between-subject variability
• They eliminate the need to check assumptions
• They require larger sample sizes than unpaired designs

Correct Answer: They control for between-subject variability

Q28. If variances are equal but sample sizes are unequal, is the pooled t-test still valid?

• Yes, pooled t-test remains valid if variances are equal
• No, pooled t-test requires equal sample sizes
• Only if sample sizes differ by less than 10%
• No, use paired t-test instead

Correct Answer: Yes, pooled t-test remains valid if variances are equal

Q29. Which assumption is critical for the validity of an unpaired t-test?

• Observations within and between groups are independent
• Data must be ranked only
• Sample medians must be equal
• Both groups must have the same sample size

Correct Answer: Observations within and between groups are independent

Q30. Which statement best distinguishes statistical significance from clinical significance?

• Statistical significance guarantees clinical benefit
• A small p-value always implies a large clinical effect
• Statistical significance (small p-value) does not necessarily imply clinically meaningful effect
• Clinical significance is determined solely by p-value

Correct Answer: Statistical significance (small p-value) does not necessarily imply clinically meaningful effect

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