CRA Biostatistics & Hypothesis Testing 3 — Questions and Answers
Question 1: Confidence intervals and hypothesis tests are related in that a 95% CI for a difference that does NOT include zero corresponds to:
- A non-significant result at alpha=0.05
- A significant result at alpha=0.05 (Correct answer)
- A significant result at alpha=0.01
- A non-significant result at alpha=0.10
Correct answer: A significant result at alpha=0.05
A 95% CI excluding the null value (zero for a difference) is equivalent to rejecting the null hypothesis at alpha=0.05 with a two-tailed test.
Question 2: Which distribution is used when the population standard deviation is unknown and the sample size is small?
- Normal (z) distribution
- F-distribution
- Chi-square distribution
- t-distribution (Correct answer)
Correct answer: t-distribution
The t-distribution accounts for additional uncertainty from estimating σ with s and has heavier tails than the normal distribution, particularly with small samples.
Question 3: Pearson's correlation coefficient (r) ranges from −1 to +1. A value of r = −0.85 indicates:
- A weak negative linear relationship
- A strong positive linear relationship
- A strong negative linear relationship (Correct answer)
- No linear relationship
Correct answer: A strong negative linear relationship
An r of −0.85 is close to −1, indicating a strong negative (inverse) linear association between the two variables.
Question 4: In a randomized controlled trial, the number needed to treat (NNT) is calculated as:
- Relative risk × 100
- 1 / Absolute risk reduction (Correct answer)
- Odds ratio − 1
- Absolute risk reduction × sample size
Correct answer: 1 / Absolute risk reduction
NNT = 1 / ARR, where ARR is the absolute risk reduction (control event rate minus treatment event rate).
Question 5: A study reports a relative risk (RR) of 1.0. This means:
- The exposure doubles the risk
- The exposure is perfectly protective
- The exposed and unexposed groups have equal risk (Correct answer)
- The study had no power
Correct answer: The exposed and unexposed groups have equal risk
RR = 1.0 indicates no difference in risk between the exposed and unexposed groups, implying no association.
Question 6: Which type of variable is best described as having ordered categories with unequal intervals between them?
- Nominal
- Ordinal (Correct answer)
- Ratio
- Continuous
Correct answer: Ordinal
Ordinal variables have a natural order (e.g., mild/moderate/severe) but the intervals between categories are not necessarily equal.
Question 7: A researcher increases the sample size from 100 to 400 while all other factors remain constant. The standard error of the mean will:
- Double
- Remain the same
- Decrease by half (Correct answer)
- Decrease by one-quarter
Correct answer: Decrease by half
SE = σ/√n; quadrupling n multiplies √n by 2, halving the SE.
CRA Biostatistics & Hypothesis Testing 3
Confidence intervals and hypothesis tests are related in that a 95% CI for a difference that does NOT include zero corresponds to: