90% confidence interval

Definition

A 90% confidence interval is a statistical range that estimates where a population parameter, such as the mean, is likely to fall with 90% certainty based on sample data. This interval reflects the degree of uncertainty about the estimate, indicating that if many samples were taken, approximately 90% of the calculated intervals would contain the true population parameter. Understanding this interval helps in making informed decisions based on sample statistics.

5 Must Know Facts For Your Next Test

1. A 90% confidence interval indicates a balance between precision and reliability; it is wider than a 95% interval but narrower than an 80% interval.
2. In practical terms, a 90% confidence interval implies that if the same procedure were repeated many times, about 90% of those intervals would successfully contain the true parameter.
3. The width of a confidence interval is influenced by sample size: larger samples tend to produce narrower intervals, enhancing precision.
4. The confidence level chosen (like 90%) affects how much uncertainty is communicated; lower levels indicate less certainty but also result in narrower intervals.
5. When reporting a confidence interval, it's essential to also mention the point estimate and the margin of error to provide context and clarity.

Review Questions

• How does a 90% confidence interval reflect uncertainty in estimating population parameters?
  • A 90% confidence interval captures the range within which we expect the true population parameter to lie with 90% certainty. This means there is still a 10% chance that the true value falls outside this range. By providing this interval, we communicate our uncertainty and variability inherent in our sample data. It’s essential for interpreting how confident we can be about our estimates.
• Discuss how changing the confidence level from 90% to 95% affects the width and interpretation of the confidence interval.
  • Increasing the confidence level from 90% to 95% generally results in a wider confidence interval. This happens because we require more certainty that the true population parameter falls within this range, which means allowing for greater variability. Consequently, while a 95% confidence interval provides a higher assurance that it contains the true parameter, it also sacrifices some precision as it becomes broader compared to a 90% interval.
• Evaluate how sample size influences the reliability and precision of a 90% confidence interval, considering different contexts where sample size varies.
  • Sample size has a critical impact on both reliability and precision of a 90% confidence interval. As sample size increases, the variability decreases, leading to narrower intervals that are more precise estimates of the population parameter. In contexts where sample sizes are small, such as in rare disease studies, confidence intervals can be wide and less reliable, making conclusions more uncertain. Conversely, large sample sizes in common studies yield narrower intervals that more accurately reflect population characteristics, demonstrating how sample size directly affects statistical inference.

Related terms

Point Estimate:

A single value derived from sample data used to estimate a population parameter.

Margin of Error:

The amount of error allowed in the estimation process, reflecting the precision of the confidence interval.

Significance Level:

The probability of rejecting the null hypothesis when it is actually true, often represented as alpha (α), which complements the confidence level.