Interval Estimation

Definition

Interval estimation is a statistical technique used to estimate a range of values within which a population parameter is expected to lie, based on sample data. This approach provides not just a single point estimate, but a confidence interval that reflects the uncertainty associated with the sample estimate. It allows researchers to express the precision and reliability of their estimates, which is crucial in making informed decisions based on data analysis.

5 Must Know Facts For Your Next Test

1. Interval estimation provides a range of plausible values for a population parameter, giving more context than point estimates.
2. The width of the confidence interval indicates the level of uncertainty; wider intervals suggest greater uncertainty about the parameter's true value.
3. Common confidence levels used in interval estimation include 90%, 95%, and 99%, reflecting the degree of certainty researchers want.
4. Sampling size plays a critical role in interval estimation; larger samples tend to produce narrower confidence intervals due to reduced variability.
5. In practice, interval estimation is often visualized using graphs that display the range of estimates, making it easier to interpret results.

Review Questions

• How does interval estimation differ from point estimation in terms of information provided about population parameters?
  • Interval estimation differs from point estimation by providing a range of values instead of a single value. While point estimation gives one specific estimate for a population parameter, interval estimation reflects uncertainty by indicating that the true parameter lies within a certain range, known as the confidence interval. This added layer of information helps researchers understand the precision of their estimates and make more informed decisions based on their findings.
• Discuss how changing the sample size affects the width of a confidence interval in interval estimation.
  • Changing the sample size significantly affects the width of a confidence interval. Generally, increasing the sample size leads to a narrower confidence interval because larger samples tend to reduce variability and provide more precise estimates of the population parameter. Conversely, smaller sample sizes result in wider intervals due to greater variability and uncertainty in estimating the true parameter. Thus, when planning studies, researchers must consider how their chosen sample size will impact the reliability and precision of their interval estimates.
• Evaluate the implications of selecting different confidence levels on the results obtained from interval estimation.
  • Selecting different confidence levels has substantial implications for interval estimation results. A higher confidence level, such as 99%, produces a wider confidence interval, which indicates greater certainty about containing the true population parameter but less precision. In contrast, a lower confidence level, like 90%, yields a narrower interval, reflecting more precision but less certainty. Researchers must balance these aspects based on their study goals, understanding that higher confidence may lead to less actionable insights due to broader ranges, while lower confidence may risk misrepresenting true values.

Related terms

Point Estimation:

A method of estimating a population parameter using a single value derived from sample data.

Confidence Interval:

A range of values derived from sample statistics that is likely to contain the population parameter with a specified level of confidence.

Margin of Error:

The amount of error that can be tolerated in a statistical estimate, often used in conjunction with confidence intervals to indicate the precision of the estimate.