90% confidence interval

Definition

A 90% confidence interval is a statistical range, derived from a data sample, that is likely to contain the true population parameter 90% of the time. This interval is calculated using the sample mean, standard deviation, and a critical value from the normal distribution, reflecting the uncertainty in estimating the population parameter. It provides a useful way to quantify the precision of an estimate and helps in making informed decisions based on data analysis.

5 Must Know Facts For Your Next Test

1. A 90% confidence interval means there is a 10% chance that the true population parameter falls outside this range.
2. To compute a 90% confidence interval, you typically use the formula: $$ ext{CI} = ext{point estimate} \, ext{±} \, z_{0.05} imes rac{s}{ ext{√n}}$$, where $$z_{0.05}$$ is the critical value for a 90% confidence level.
3. The width of the confidence interval reflects the variability in the data; more variability leads to a wider interval.
4. As the sample size increases, the confidence interval narrows because larger samples provide more accurate estimates of the population parameter.
5. A 90% confidence interval is narrower than higher confidence levels (like 95% or 99%), meaning it provides less certainty but more precision.

Review Questions

• How does changing the confidence level affect the width of a confidence interval?
  • Increasing the confidence level results in a wider confidence interval because you need to account for more uncertainty in your estimate. For example, moving from a 90% to a 95% confidence level means you are willing to accept a smaller margin of error but want greater certainty that the true parameter lies within that range. This wider interval reflects increased caution about where the true population parameter might be located.
• What are some practical applications of using a 90% confidence interval in data analysis?
  • A 90% confidence interval can be particularly useful in fields like marketing or quality control, where businesses want to estimate customer preferences or product performance with reasonable assurance. For instance, if a company conducts a survey to gauge customer satisfaction and finds a 90% confidence interval for their satisfaction score, they can use this information to make informed decisions about product improvements and marketing strategies while being aware of the inherent uncertainty.
• Evaluate how sample size influences the reliability and accuracy of a 90% confidence interval estimation.
  • Sample size plays a crucial role in determining both the reliability and accuracy of a 90% confidence interval. A larger sample size generally leads to more reliable estimates because it reduces variability and gives a clearer picture of the population parameter. As sample size increases, the margin of error decreases, resulting in a narrower confidence interval. This allows researchers to draw more precise conclusions from their data. Thus, understanding how sample size impacts the width and precision of a confidence interval is essential for effective data interpretation.

Related terms

Margin of Error: The amount of error that is allowed in a statistical estimate, often used to calculate confidence intervals.

Point Estimate: A single value that serves as an estimate of a population parameter, such as the sample mean.

Critical Value: A factor used to compute the margin of error for a confidence interval, determined from the standard normal distribution.