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.
LEVEL OF SIGNIFICANCE (e.g., 0.05)
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