95% confidence interval

Definition

A 95% confidence interval is a range of values, derived from sample data, that is likely to contain the true population parameter with a probability of 95%. This interval gives an estimate of the uncertainty associated with a sample statistic, providing insight into how well the sample represents the population. It is a key concept in statistical inference and estimation, helping researchers to understand the reliability of their findings.

5 Must Know Facts For Your Next Test

1. The 95% confidence interval is constructed using the sample mean plus and minus a margin of error, which is determined by the standard error and critical value from the normal distribution.
2. If we were to take many samples and compute a 95% confidence interval for each sample, approximately 95% of those intervals would contain the true population parameter.
3. The width of a 95% confidence interval is influenced by the sample size; larger samples tend to yield narrower intervals, reflecting greater precision in estimates.
4. Confidence intervals can be calculated for different statistics, such as means, proportions, or differences between groups, making them versatile tools in data analysis.
5. A common misconception is that a 95% confidence interval means there is a 95% chance that the true parameter lies within that specific interval; rather, it refers to the long-run proportion of intervals that would capture the parameter if repeated samples were taken.

Review Questions

• How do you interpret a 95% confidence interval in the context of sample data?
  • A 95% confidence interval provides a range within which we expect the true population parameter to lie with 95% certainty. This means that if we repeatedly sampled from the population and constructed intervals based on those samples, about 95% of those intervals would include the actual parameter. It reflects both our estimate from the sample data and the uncertainty inherent in that estimate.
• Discuss how sample size impacts the width of a 95% confidence interval and what this means for statistical analysis.
  • Sample size has a significant impact on the width of a 95% confidence interval. Larger sample sizes typically result in narrower intervals because they provide more information about the population, reducing variability in estimates. This narrowing indicates increased precision and reliability in estimating the population parameter. Conversely, smaller samples yield wider intervals, signaling greater uncertainty in our estimates.
• Evaluate how understanding the concept of a 95% confidence interval influences decision-making in research.
  • Understanding a 95% confidence interval aids researchers and decision-makers by quantifying uncertainty around estimates. It helps in assessing the reliability of findings and informs whether results are statistically significant enough to justify action. For instance, if an intervention shows effects within this range, stakeholders can make informed choices based on how likely those effects are attributable to true differences rather than random chance.

Related terms

Point estimate: A single value that serves as an estimate of a population parameter, such as the mean or proportion.

Margin of error: The amount of random sampling error in a survey's results, often used to express the uncertainty around a point estimate.

Statistical significance: A measure of whether an observed effect or relationship in data is likely to be genuine or occurred by chance, often determined using p-values.