90% confidence interval

Definition

A 90% confidence interval is a statistical range that estimates where a population parameter lies, based on sample data, with 90% certainty. This means if the same sampling method were repeated numerous times, approximately 90% of the calculated intervals would contain the true parameter value. It reflects both the precision of the sample estimate and the uncertainty involved in estimating population characteristics.

5 Must Know Facts For Your Next Test

1. To construct a 90% confidence interval, you typically use a sample mean and add and subtract a margin of error calculated from the standard deviation and sample size.
2. A narrower confidence interval suggests more precision in estimating the population parameter, while a wider interval indicates greater uncertainty.
3. The choice of a 90% confidence level means there’s a 10% chance that the interval does not capture the true parameter; this trade-off between confidence level and precision is crucial in statistical analysis.
4. When using a normal distribution, the z-score corresponding to a 90% confidence level is approximately 1.645, which helps in calculating the margin of error.
5. In practical terms, a 90% confidence interval can be less reliable than higher confidence levels (like 95% or 99%), but it may be used when one needs to balance precision with broader estimates.

Review Questions

• How do you calculate a 90% confidence interval for a sample mean?
  • To calculate a 90% confidence interval for a sample mean, first compute the sample mean and determine the standard deviation of your sample. Then, find the appropriate z-score for 90%, which is approximately 1.645. Multiply the standard deviation by the z-score divided by the square root of the sample size to get the margin of error. Finally, add and subtract this margin of error from the sample mean to create your confidence interval.
• Discuss how changing the confidence level from 90% to 95% affects the width of the confidence interval.
  • Increasing the confidence level from 90% to 95% results in a wider confidence interval because you are demanding more certainty that it contains the true population parameter. This increase in width occurs because the corresponding z-score for a 95% confidence level is approximately 1.96, which leads to a larger margin of error. Consequently, while you gain more assurance about capturing the true parameter, you lose precision in your estimate.
• Evaluate why someone might choose to use a 90% confidence interval instead of a higher level such as 95% or 99%.
  • Choosing a 90% confidence interval can be strategic depending on context; it offers a balance between accuracy and precision. In scenarios where quick decisions are necessary, or resources are limited for collecting data, researchers may opt for a 90% level. This allows them to generate results faster while still providing reasonable assurance about their estimates. However, it’s crucial to understand that this choice comes with increased risk of not capturing the true population parameter compared to higher levels.

Related terms

Margin of Error: The margin of error is the amount of error allowed in a statistical estimate, representing the range within which the true population parameter is expected to fall.

Point Estimate: A point estimate is a single value that serves as a best guess or approximation of a population parameter, derived from sample data.

Significance Level: The significance level, often denoted as alpha (α), is the threshold used to determine whether a statistical result is significant, typically set at values like 0.05 or 0.01.