Sampling distributions
sample vs. population
parameter - measure used to describe characteristic of
a population (e.g., mu, population mean)
statistic - measure used to describe characteristic of
a sample (e.g., X bar, sample mean)
inferential statistics - how to use sample statistics
to make inferences about population parameters
-
apply (usually) just to studies involving probability
sampling
sampling error - difference between sample statistic value
and population parameter value
sampling distribution - theoretical distribution of all
possible sample statistic values
sampling distribution of mean - theoretical distribution
of all possible sample means
Rule for Sample Means (Central Limit theorem)
-
sampling distribution of the mean = normal if sample size
is large enough, regardless of underlying population distribution
-
mean of sampling distribution = population mean (in long
run for large sample sizes)
-
standard error of the mean - standard deviation of the
sampling distribution of mean
-
in practice, sample sd used in place of pop sd
-
standard error influenced by sample size
-
standard error unrelated to population size
Rule for sample proportions
sampling distribution of proportions also distributed
normally if sample size sufficiently large
standard error for proportions (sd of sampling distribution
of a proportion)
-
SQRT (pop proportion x (1 - pop proportion)) / sample
size)
applying Empirical rule to sample statistics and standard
errors
Summary:
parameter, statistic
sampling error
sampling distributions of mean and proportion are approximately
normal
standard error
increasing sample size decreases standard error