FAST Confidence Intervals and Estimation

Question 1

What does a 95% confidence interval mean?

Accepted Answer

If we repeated the sampling many times, 95% of the intervals would contain the true parameter

Answer

A 95% confidence interval means that the procedure used will capture the true parameter 95% of the time across repeated samples.

Question 2

What happens to the confidence interval as sample size increases?

Accepted Answer

It becomes narrower, providing a more precise estimate

Answer

Larger samples reduce sampling variability, leading to narrower confidence intervals and more precise estimates.

Question 3

What is the relationship between confidence level and interval width?

Accepted Answer

Higher confidence levels produce wider intervals

Answer

Increasing the confidence level (e.g., from 95% to 99%) requires a wider interval to maintain that higher level of certainty.

Question 4

What is the margin of error?

Accepted Answer

Half the width of the confidence interval, representing maximum expected sampling error

Answer

The margin of error represents the maximum expected difference between the sample statistic and the population parameter.

Question 5

When are confidence intervals more informative than p-values?

Accepted Answer

When you need to know the magnitude and direction of an effect, not just significance

Answer

Confidence intervals provide both the estimated effect size and its precision, which p-values alone do not convey.

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