What are some common misconceptions about confidence intervals?

What are some common misconceptions about confidence intervals?

One common misconception is that a confidence interval gives the probability that the true parameter lies within the interval.

Can you explain why that's a misconception?

Sure! A confidence interval is constructed from sample data, and it either contains the true parameter or it doesn't. The confidence level reflects the long-term proportion of intervals that would contain the true parameter if we repeated the study many times.

What about the idea that a wider interval means less precision?

That's another misconception! A wider interval indicates more uncertainty about the parameter estimate, but it doesn't necessarily mean less precision. It can also reflect a higher confidence level.

Are there any other misconceptions I should be aware of?

Yes, another misconception is that confidence intervals can be interpreted as a range of values that are likely to occur in future samples, which is not correct.