Inferential Statistics

1
Inferential Statistics Use sample information to
make estimates of (infer) something about a
population -sample must be a probability sample
(i.e., representative) Sample information is
called a statistic (e.g., sample mean) Population
information is called a parameter (e.g.,
population mean) Use value of sample mean to
estimate (or make inferences about) the
population mean Example Have a sample of those
who received job training and and their mean
earnings is 10,000--use this, along with other
sample information (standard deviation and sample
size) to make inferences about mean earnings for
the population of all trainees
2
How are the sample mean and population mean
related? Repeated samples of a given size will
give different values of the mean. Thus the
sample mean is a random variable that has some
distribution of its own (i.e., the sampling
distribution of the sample mean). With a simple
random sample, the sample mean is distributed as
a normal random variable with a mean equal to the
population mean and a standard deviation equal to
the population standard deviation divided by the
square root of the sample size A normal random
variable has a known distribution, so it is
possible to make statements about the value of
the population mean given the value of the sample
mean (and s.d. and size).