Confidence Interval

Definition

A confidence interval is a range of values that is likely to contain an unknown population parameter, such as a mean or proportion, with a specified level of confidence. It provides a way to quantify the uncertainty associated with estimating a parameter from a sample of data.

5 Must Know Facts For Your Next Test

1. Confidence intervals are used to assess the precision of an estimate and provide a range of plausible values for the true population parameter.
2. The level of confidence, typically 95%, represents the probability that the true parameter value falls within the calculated interval.
3. The width of the confidence interval is determined by the sample size, the variability in the data, and the desired level of confidence.
4. Confidence intervals are affected by measurement uncertainty, as they incorporate the standard error of the estimate.
5. Confidence intervals can be used to evaluate the accuracy and precision of a measurement by assessing whether the true value is likely to fall within the interval.

Review Questions

• Explain how a confidence interval is related to the concept of measurement uncertainty.
  • Measurement uncertainty is a key factor in determining the width of a confidence interval. The greater the measurement uncertainty, the wider the confidence interval will be, as it needs to account for the potential variability in the estimate. Conversely, reducing measurement uncertainty through more precise measurements can lead to a narrower confidence interval, indicating a more accurate and precise estimate of the true population parameter.
• Describe how the confidence level and margin of error are used to interpret a confidence interval.
  • The confidence level, typically 95%, represents the probability that the true parameter value falls within the calculated interval. The margin of error is the range above and below the sample statistic that defines the confidence interval. Together, the confidence level and margin of error provide information about the reliability and precision of the estimate. A higher confidence level or a smaller margin of error indicates a more precise and reliable confidence interval.
• Evaluate how the accuracy and precision of a measurement can be assessed using a confidence interval.
  • A confidence interval can be used to assess both the accuracy and precision of a measurement. If the confidence interval contains the true parameter value, it suggests the measurement is accurate. The width of the confidence interval, determined by the standard error, reflects the precision of the measurement, with a narrower interval indicating higher precision. By considering the position and width of the confidence interval, you can evaluate whether the measurement is both accurate and precise, or if there are issues with either accuracy or precision that need to be addressed.

Related terms

Margin of Error: The maximum expected difference between the true population parameter and the sample statistic, expressed as a range above and below the observed value.

Significance Level: The probability of rejecting the null hypothesis when it is true, also known as the type I error rate.

Standard Error: The standard deviation of the sampling distribution of a statistic, which is used to quantify the variability of the statistic.