key term - 90% Confidence Interval

Definition

A 90% confidence interval is a range of values derived from a data sample that is likely to contain the true population parameter 90% of the time. It provides an estimation of uncertainty around a sample statistic, such as the slope in a regression model. This concept allows researchers to gauge how well a sample represents a population and offers insight into the reliability of their estimates.

5 Must Know Facts For Your Next Test

1. A 90% confidence interval indicates that if we were to take many samples and build a confidence interval from each sample, approximately 90% of those intervals would contain the true population parameter.
2. The width of a confidence interval is influenced by the sample size; larger samples tend to produce narrower intervals, indicating more precise estimates.
3. In the context of regression analysis, a 90% confidence interval for the slope helps to determine whether there is a statistically significant relationship between variables.
4. If a 90% confidence interval for the slope includes zero, it suggests that there may not be a significant linear relationship between the independent and dependent variables.
5. Confidence intervals are affected by the variability in the data; greater variability leads to wider intervals, while less variability results in narrower ones.

Review Questions

• How does a 90% confidence interval help in assessing claims about the slope of a regression model?
  • A 90% confidence interval provides a range of plausible values for the slope of a regression model, allowing researchers to assess if their estimate is statistically significant. If the entire interval lies above or below zero, it indicates a significant relationship. Conversely, if zero falls within this interval, it suggests that there may be no meaningful linear relationship between the variables. Thus, understanding this interval is crucial for justifying claims about relationships in regression.
• In what way does increasing the sample size impact the width of a 90% confidence interval in regression analysis?
  • Increasing the sample size typically leads to a narrower 90% confidence interval due to reduced variability and increased precision in estimating parameters. With more data points, there's less uncertainty about the estimated slope, resulting in a tighter range around that estimate. This tighter interval allows researchers to make more confident assertions about the slope's significance and its implications for the relationship between independent and dependent variables.
• Evaluate how understanding the concept of a 90% confidence interval contributes to making informed decisions based on regression analysis results.
  • Understanding a 90% confidence interval enables researchers and decision-makers to gauge the reliability and significance of their regression analysis results. By interpreting where the true parameter may lie, they can make informed choices about actions based on statistical evidence. For instance, if policy recommendations depend on identifying effective interventions through regression analysis, knowing whether the estimated slope is significantly different from zero (indicated by its confidence interval) can significantly influence those decisions. This evaluation ensures that conclusions drawn from data are not only statistically valid but also relevant and applicable in real-world scenarios.

Related terms

Point Estimate:

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

Margin of Error:

The amount of random sampling error in a survey's results, reflecting the range within which the true population parameter is expected to fall.

Slope of Regression Line: The change in the dependent variable for every one-unit increase in the independent variable, indicating the strength and direction of a relationship between variables.