Range of Plausible Values

Definition

The range of plausible values refers to a set of values that are consistent with the observed data and provide a reasonable estimate for a population parameter. This concept is central to interval estimation and confidence intervals, as it allows for the representation of uncertainty in statistical estimates, indicating the spectrum within which the true population parameter likely falls.

5 Must Know Facts For Your Next Test

1. The range of plausible values helps to quantify the uncertainty associated with estimating population parameters based on sample statistics.
2. This range is often represented by confidence intervals, which indicate how sure we can be about where the true parameter lies.
3. A wider interval suggests more uncertainty about the estimate, while a narrower interval indicates more precision.
4. In constructing a confidence interval, critical values are used along with standard errors derived from sample data to determine the endpoints of the range of plausible values.
5. Common confidence levels used for creating ranges of plausible values include 90%, 95%, and 99%, each affecting the width of the interval.

Review Questions

• How do ranges of plausible values contribute to our understanding of statistical estimates and their reliability?
  • Ranges of plausible values give us insight into how reliable our statistical estimates are by showing us the potential variability in the true population parameter. By presenting a set of values rather than a single estimate, they allow us to account for sampling variability and other sources of error. This helps in assessing whether our estimates can be trusted for decision-making or further analysis.
• Discuss how changing the confidence level affects the range of plausible values and what implications this has for data interpretation.
  • Adjusting the confidence level changes the width of the confidence interval, which directly impacts the range of plausible values. A higher confidence level, like 99%, results in a wider interval, reflecting greater uncertainty about where the true parameter lies but increasing our assurance that it contains that parameter. Conversely, a lower confidence level might produce a narrower interval but provides less certainty. This trade-off is crucial when interpreting data since it influences how conclusions are drawn from statistical results.
• Evaluate the importance of understanding ranges of plausible values in real-world applications such as healthcare or finance.
  • Understanding ranges of plausible values is essential in fields like healthcare and finance because it informs decision-making under uncertainty. For instance, in healthcare, knowing the range within which a patient's treatment response might fall helps doctors tailor interventions more effectively. In finance, investors use these ranges to assess risk and make informed choices about asset allocation. The ability to convey uncertainty through these ranges allows professionals to communicate risks clearly and make better strategic decisions based on statistical evidence.

Related terms

Confidence Interval: A confidence interval is a range of values derived from sample data that is likely to contain the true population parameter, expressed with a specified level of confidence.

Point Estimate: A point estimate is a single value that serves as a best guess or summary of a population parameter based on sample data.

Margin of Error: The margin of error is the range that is added to and subtracted from a point estimate to create a confidence interval, reflecting the uncertainty in the estimate.