Section 3.3 Toward Statistical Inference
Parameter
 is a number that describes the population.
Statistic
 is a number the describes a sample
Sampling
Distribution
 is the distribution of values taken by the statistic in all possible samples of the same size from the same
population
Bias
 concerns the center of the sampling distribution.
The reduce bias use random sampling.
Variability
 describes the spread of the sampling distribution
To reduce variability use a larger sample
Population
Size doesn’t matter: The variability of a statistic from a random sample does not depend on the size of the population
as long as the population is at least 100 times larger than the sample
4.1 Randomness
*chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run
Probability only describes what happens in the long run
Probability is empirical in that it is based on observation rather than theorizing
Random
 only random is the outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a larger number
of repetitions
4.4 The sampling distribution of a sample mean
Law
of
Large
Numbers
: Draw independent observations at random from any population with finite mean u. As the number of
observations drawn increases, the mean (X bar) of the observed values gets closer and closer to the mean u of the population
Mean
of
sample
mean
 the mean of the sampling distribution of xbar is u. (When we want information about the population
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 Spring '07
 Gemberling
 Statistics, Normal Distribution, Statistical hypothesis testing, o.

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