Confidence Interval (CI)
Idea:
If
P
(
L
< θ <
U
) = 1
−
α
, then,
(
L
,
U
) is a 100(1
−
α
)%
CI for the parameter
θ
.
▶
(
L
,
U
): Lower and Upper bounds (random intervals)
▶
1
−
α
: Confidence level,
▶
α
: level
▶
Interpretation: For instance a 95% CI indicates that we would expect 19
out of 20 samples (95 out of 100) from the same population to produce
confidence intervals that contain the population parameter of interest, on
average.
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