Chapter 9 (14)

Most questions that we ask about large populations are translated into
questions about specific summary characteristics of the group

Parameter:
a number that is a summary characteristic of a population, a
random situation, or a comparison of populations
o
“Population parameter”
is a phrase used to make it clear that a
parameter is associated with a population instead of a sample
o
Examples the proportion of adults in the world who are lefthanded
o
Parameters have fixed, unchanging values
o
Usually, the value of a parameter is not known to us, and will not be
known to us because we will not be able to measure every unit in
the population
o
Although we will not have the information necessary to find the
numerical value of a population parameter, we will be able to use
statistical methods to make a good guess

Statistic/sample statistic:
a number that is computed from a sample of
values taken from a larger population
o
Summary characteristic of the sample data
o
The sample data may be collected in a sample survey, an
observational survey, or an experiment

Sample estimate/estimate:
a sample statistic when the statistic is used
to estimate the unknown value of a population parameter

Possible values of sample statistics are variable

If two different samples are taken from the same population, it is likely that
the sample statistics will be different for those two samples

The value of a sample statistic may change from sample to sample, and
we will know the value once we have measured a sample

Statistical inference:
when information from a sample is used to make
generalizations about a larger population. Sample statistics are used to
make conclusions about population parameters. Confidence intervals and
hypothesis tests are two common statistical inference techniques

Confidence interval:
an interval of values that the researcher is fairly
sure will cover the true, unknown value of the population parameter
o
We use a confidence interval to estimate the value of a population
parameter

Hypothesis testing/significance testing:
uses sample data to attempt to
reject a hypothesis about the population
o
Usually, researchers want to reject the notion that chance alone can
explain the sample results
o
In most research settings, the desired conclusion is that the
variables under scrutiny are related
o
Hypothesis testing is applied to population parameters by
specifying a
null value
for the parameter – a value that would
indicate that nothing of interest is happening
o
Hypothesis testing proceeds by obtaining a sample, computing a
sample statistic, and assessing how unlikely the sample statistic
would be if the null parameter value were correct
o
In most cases, the researchers are trying to show that the null value
is not correct
o
Achieving
statistical significance
is equivalent to rejecting the
idea that the observed results are plausible if the null value is
correct

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 Fall '10
 Gunderson
 Statistics, Normal Distribution, Standard Deviation, Probability theory, population parameter