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Nursing QUESTION #9207
Question 1
A researcher reports a confidence interval of \(95\% \text{ CI}: [2.1, 8.7]\) for a mean difference in pain scores. What is the correct interpretation?
  • There is a 95% probability that the true mean falls within this range
  • If the study were repeated 100 times, approximately 95 of the resulting CIs would contain the true population mean✔️
  • The sample mean has a 95% chance of being between 2.1 and 8.7
  • There is a 5% chance that the results are due to chance alone
Correct Answer Explanation
Correct Answer: B

The frequentist interpretation of a 95% confidence interval is:
'If this study were repeated many times, 95% of the constructed confidence intervals would contain the true population parameter.'

Common misconceptions to avoid:
  • ❌ It is NOT correct to say 'there is a 95% probability the true mean lies in this interval' — the true mean is fixed, not probabilistic
  • ❌ It does NOT mean 95% of individual values fall within the range
Clinical significance of this CI: Since the entire interval \([2.1, 8.7]\) is above zero, this suggests the difference is statistically significant at \(\alpha = 0.05\). If the CI had included zero, the result would be non-significant.