Ch. 2. Bridge between Two Worlds
I. Sampling Distribution
A. Definition: A theoretical distribution of a statistic
computed across all possible samples (usually
infinite) of a given size (n) drawn from a given
population (e.g.)
1. Theoretical, probability distribution
2. Can have a sampling distribution for each
statistic and for each sample size (
X
, s², s*²)
B. Notation
1. Population distribution: μ , σ² (parameter)
2. Sample distribution:
X
, s², s*² (statistic)
3. Sampling distribution:
2
,
xx
σµ
22 ,
ss
σµ
C. Sampling distribution of sample means
1. Definition: a particular sampling distribution
consisted of all possible values of sample means
with a given sample size.
2. A theoretical and probability distribution.
3. Central Limit Theorem: For a population of Xi
with a finite mean (=μ) and variance (=σ²), the
sampling distribution of sample means is normally
distributed with the mean (=μ) and variance
(=σ²/n) if the sample size (n) approaches
infinity. Practically n > 30.
II. Other sampling distributions
A. z-distribution
B. t-distribution
C. χ²-distribution
D. F-distribution
III. Unbiasedness: If the mean of a sampling distribution of a
statistic is equal to the parameter estimated, the statistic is
called an unbiased statistic
Docsity.com
