CRA Biostatistics & Hypothesis Testing 2 — Questions and Answers
Question 1: A clinical trial reports a p-value of 0.03 with a pre-specified alpha of 0.05. Which conclusion is most appropriate?
- Reject the null hypothesis (Correct answer)
- Fail to reject the null hypothesis
- Accept the alternative hypothesis as proven
- Increase the sample size before concluding
Correct answer: Reject the null hypothesis
Since p=0.03 < alpha=0.05, the result crosses the pre-specified threshold and the null hypothesis is rejected.
Question 2: The standard deviation of the sampling distribution of the mean is called the:
- Variance
- Standard error (Correct answer)
- Coefficient of variation
- Mean absolute deviation
Correct answer: Standard error
The standard error (SE) measures the variability of sample means around the population mean and equals σ/√n.
Question 3: A researcher uses a two-tailed test instead of a one-tailed test for the same hypothesis. How does this affect the critical region?
- It doubles the critical region size
- It splits alpha across both tails (Correct answer)
- It increases statistical power
- It reduces the chance of a Type II error
Correct answer: It splits alpha across both tails
A two-tailed test splits alpha (e.g., 0.05) equally into both tails, placing 0.025 in each tail.
Question 4: Which measure of central tendency is least affected by extreme outliers?
- Mean
- Median (Correct answer)
- Mode
- Weighted mean
Correct answer: Median
The median is resistant to outliers because it depends only on the middle value(s), not the magnitude of extreme scores.
Question 5: In a study with 80% power, what is the probability of committing a Type II error?
- 0.80
- 0.20 (Correct answer)
- 0.05
- 0.95
Correct answer: 0.20
Power = 1 − β, so if power is 0.80, the Type II error rate (β) is 1 − 0.80 = 0.20.
Question 6: A dataset has a mean of 50 and a standard deviation of 10. What is the z-score for an observation of 65?
- 0.65
- 1.0
- 1.5 (Correct answer)
- 2.0
Correct answer: 1.5
z = (65 − 50) / 10 = 1.5, indicating the observation is 1.5 standard deviations above the mean.
Question 7: When comparing means from three or more independent groups in a clinical trial, the preferred initial statistical test is:
- Paired t-test
- Chi-square test
- One-way ANOVA (Correct answer)
- McNemar's test
Correct answer: One-way ANOVA
One-way ANOVA is used to test whether at least one group mean differs among three or more independent groups while controlling the overall Type I error rate.
CRA Biostatistics & Hypothesis Testing 2
A clinical trial reports a p-value of 0.03 with a pre-specified alpha of 0.05.
Which conclusion is most appropriate?