• Sample Distritubion
The sample distribution of a statistic is the probability
distribution that specifies probabilities for the possible values
the statistic can take.
• Mean and Standard Deviation of the Sample Distribution of a
Proportion
For a random sample of size n from a population with
proportion p of outcomes in a particular category, the
sampling distribution of the proportion of the sample in that
category has
r
p(1 − p)
.
mean = p and standard deviation =
n
We call the standard deviation of a sampling distribution a
standard error.
• Population distribution
• Data distribution
• Sampling distribution
Mean and Standard Error of Sampling Distribution of Sample
Mean x̄
For a random sample of size n from a population having mean µ
and standard deviation σ, the sampling distribution of the
sample mean x̄ has
center described by the smaple mean which equals µ (the
population mean)
√
spread described by the standard, which equals σ/ n (the
population standard deviation divided by the square root of
the sample size).
Central Limit Theorem (Approximately Normal Sampling
Distribution for Sample Mean x̄)
For random sampling with a large sample size n, the sampling
distribution of the sample mean x̄ is approximately a normal
distribution.