Confidence Intervals - Level of Significance

"The level of significance (
α
) is the probability of making
a Type I error [e.g., 0.05]."  
- Donnelly textbook

You're probably wondering what a Type I error is.
Actually, Type I and Type II errors will be discussed in detail during the next lecture.

Suffice it to say at this point:
1. A Type I error is when we reject a null hypothesis
when in fact it is true.
2. The probability of a Type I error =
α.
3. For 95% confidence intervals,
α = 0.05 and 1 - α = 0.95.



DON'T CONFUSE
LEVEL OF SIGNIFICANCE (e.g., 0.05)
WITH
CONFIDENCE LEVEL (e.g., 95%).
Although they are mathematically related, they are different.

In 1925 R.A. Fisher recommended using the 5% (0.05) level of significance.  Unless you have very good reason to use a different value for
α, it is wise to stick with 0.05.

Distribution of Means
s