FAST Confidence Intervals and Estimation 1 — Questions and Answers
Question 1: What does a 95% confidence interval mean?
- If we repeated the sampling many times, 95% of the intervals would contain the true parameter (Correct answer)
- There is a 95% probability the true value is in this specific interval
- The data is 95% accurate
- 95% of the data falls within this range
Correct answer: If we repeated the sampling many times, 95% of the intervals would contain the true parameter
A 95% confidence interval means that the procedure used will capture the true parameter 95% of the time across repeated samples.
Question 2: What happens to the confidence interval as sample size increases?
- It becomes narrower, providing a more precise estimate (Correct answer)
- It becomes wider
- It stays the same
- It shifts to the right
Correct answer: It becomes narrower, providing a more precise estimate
Larger samples reduce sampling variability, leading to narrower confidence intervals and more precise estimates.
Question 3: What is the relationship between confidence level and interval width?
- Higher confidence levels produce wider intervals (Correct answer)
- Higher confidence levels produce narrower intervals
- There is no relationship
- The relationship depends on sample size only
Correct answer: Higher confidence levels produce wider intervals
Increasing the confidence level (e.g., from 95% to 99%) requires a wider interval to maintain that higher level of certainty.
Question 4: What is the margin of error?
- Half the width of the confidence interval, representing maximum expected sampling error (Correct answer)
- The number of errors in the data
- The difference between the sample mean and zero
- The standard deviation of the sample
Correct answer: Half the width of the confidence interval, representing maximum expected sampling error
The margin of error represents the maximum expected difference between the sample statistic and the population parameter.
Question 5: When are confidence intervals more informative than p-values?
- When you need to know the magnitude and direction of an effect, not just significance (Correct answer)
- Never — p-values are always more informative
- Only in medical research
- Only when sample sizes are very small
Correct answer: When you need to know the magnitude and direction of an effect, not just significance
Confidence intervals provide both the estimated effect size and its precision, which p-values alone do not convey.
Question 6: What does it mean if a confidence interval for a difference includes zero?
- The difference is not statistically significant at that confidence level (Correct answer)
- The true difference is exactly zero
- The study had no power
- The interval is incorrectly calculated
Correct answer: The difference is not statistically significant at that confidence level
Including zero means we cannot rule out no difference, so the result is not statistically significant at the given confidence level.
FAST Confidence Intervals and Estimation 1
What does a 95% confidence interval mean?