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key term - 90% confidence level

Citation:

Definition

A 90% confidence level indicates that if you were to take many random samples from a population and construct confidence intervals for each sample, approximately 90% of those intervals would contain the true population parameter. This level reflects a moderate degree of certainty about the estimate and is often used in statistical analyses to make inferences about differences between population proportions.

5 Must Know Facts For Your Next Test

  1. A 90% confidence level means there is a 10% chance that the true population parameter is outside the calculated interval.
  2. When comparing two population proportions, if the confidence interval does not include zero, it suggests a statistically significant difference between the two groups.
  3. Increasing the confidence level above 90% will result in a wider confidence interval, while decreasing it will make the interval narrower.
  4. A sample size that is too small can lead to unreliable confidence intervals, regardless of the confidence level chosen.
  5. The choice of a 90% confidence level strikes a balance between precision and reliability, often used in exploratory research.

Review Questions

  • How does the choice of a 90% confidence level influence the interpretation of a confidence interval for differences in population proportions?
    • Choosing a 90% confidence level suggests that there is a reasonable certainty that the true difference in population proportions lies within the interval. If the interval does not include zero, we can conclude that there is a statistically significant difference between the groups with 90% confidence. This helps researchers make informed decisions based on sample data while understanding the potential for error.
  • Discuss how sample size affects the width of a confidence interval when using a 90% confidence level.
    • Sample size plays a crucial role in determining the width of a confidence interval. A larger sample size results in a narrower interval because it reduces variability and provides more accurate estimates of the population parameter. Conversely, smaller sample sizes tend to produce wider intervals due to increased uncertainty. When using a 90% confidence level, having an adequate sample size is essential to ensure that the resulting interval is both informative and reliable.
  • Evaluate how changing from a 90% to a 95% confidence level impacts statistical conclusions drawn from data regarding differences in population proportions.
    • Switching from a 90% to a 95% confidence level will result in a wider confidence interval for differences in population proportions. While this increases the certainty that the true parameter lies within this new interval, it also makes it harder to detect significant differences if they exist. Therefore, while higher confidence levels reduce the risk of Type I errors (false positives), they may also lead to more conservative conclusions, requiring stronger evidence to declare significant findings.