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Chapter 9
Sampling Distribution
Good Day!!
Chapter 9 Sampling Distributions
• Parameter – is a number that describes
the population, like µ and σ
• Statistic – is a number that can be
computed from sample data without
making use of any unknown parameters,
like or s, x-bar.
• Sampling Variability – how the value of a statistic
varies in repeated random sampling.
– Statisticians always ask: “What would happen if I took
many samples of the same size from
the same population?”
Law of Large Numbers – Draw observations from any
population with a finite mean, µ. As the number of
observations drawn increases, the mean x-bar, of
the observed values gets closer and closer to µ.
• Unbiased Estimator – when a statistic is
used to estimate a parameter, it is
unbiased if the mean of its sampling
distribution is equal to the true value of the
parameter being estimated.
Sampling Distribution – is the
distribution of values taken by the
statistic in all possible samples of the
same size from the same population.
-For example: the distribution of x-bar for
each 100 samples taken from a particular
-Even if the parent population is skewed
or not normal, its sampling distribution
will approach normal when n, the
sample size is large.
• Central Limit Theorem – Draw an
SRS of size n from any population
whatsoever, with mean µ, and standard
deviation σ. When n is large, the sampling
distribution of the sample mean x-bar, is
close to a normal distribution, N(µ,σ/√n)
• Homework p. 457 #s1-4
p. 468 # 9
» p. 485 & 486 #s 26 & 28
» p. 491 & 492 #s 31 – 34
Lets do #30 together in class p.491