Chapter 7: sampling and sampling distribution
chapter 7 provides the basis for determining
how large that error might be
systematic sampling
if a sample size of n desired from a population containing N elements, we might sample one element for every n/N elements in the population. +EASIER
A point estimator is consistent
if the values of the point estimator tend to become closer to the population parameter as the sample size becomes larger.
examples of on-going process with infinite populations:
-parts being manufactured on a production line -transactions occurring at the bank -telephone calls arriving at a technical help desk -customers entering a store
sampling from an infinite population
-populations are often generated by an on going process where there is no upper limit on the number of units that cab be generated
sampling from a finite population :
-sampling without replacement is the procedure used most often
A random sample from an infinite population is a sample selected such that the following conditions are satisfied (characteristics):
-each element selected comes from the population of interest -each element is selected INDEPENDENTLY.
Finite populations are often defined by a list such as
-organization membership roster -credit card account numbers -inventory product numbers
Central limit theorem:
In selecting random samples of size n from a population, the sampling distribution of the sample mean xbar can be approximated by a normal distribution as the sample size becomes larger
step 4:
find the area under the curve to the left of the lower end point
a sample mean provides
an estimate of population mean, and a sample proportion provides an estimate of population proportion
*we want to make sure that target population & sampled population
are in agreement.*
Judgment sampling
baed on judgment of a researcher
step 5:
calculate the area under the curve btw the lower and upper end points of the interval. subtract upper Z value - lower Z value results
step 1:
calculate the z value upper point
step 3:
calculate the z-value at the lower end point of the interval
With the estimates we can assume,
estimation error can be expected.
step 2:
find area under the curve to the left of the upper end point
population
is a collection of all the elements of interest
point estimator
is a form is a form of statistical inferences
frame
is a list of the elements that the sample will be selected from
sample
is a subset of the population
element
is the entity on which data are collected
sampled population
is the population from which the sample is actually taken
sampled population
is the population from which the sample is drawn
target population
is the population we want to make inferences about
sampling distribution of x bar
is the probability distribution of all possible values of the sample mean x bar.
sampling distribution of P bar:
is the probability distribution of all possible values of the sample proportion P bar.
convenience sampling
it is a non probability sampling technique, Items are included in the sample without known probabilities =it is not random it is convenient
at the sample size INCREASES
it is getting closer to the population (mean), so standard deviation would be smaller.
higher sample size will give a standard deviation that is
lower
normal distribution is
n> 30
used finite population formula when
np≤5
use infinite population formula when
np≥5
X bar
point estimator of mean µ.
P bar
point estimator of the population proportion p
S is the point estimator of the
population standard deviation (standard error)
in point estimator we use the data from the sample to compute the value of a
sample statistic that serves as an estimate of population parameter.
In cases where population is highly skewed or outliers are present,
samples of size 50 may be needed
It is best recommend that probability sampling methods such as .. be used
simple random, stratified, cluster, systematic
given the choice of two unbiased estimators of the same population parameter, we would prefer to use the point estimator with the
smallest standard deviation, since it tends to provide estimates closer to the population parameter
cluster sampling
the population is first divided into operate groups of elements called clusters -different characteristics have to belong to only one cluster +good representative
when the population has a normal distribution
the sampling distribution of x bar is normally distributed for any sample size.
if the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to be an
unbiased estimator of the population parameter
sample results provide only *ESTIMATES* of the
values of the population characteristics.
when the expected value of the point estimator equals the population parameter
we say the point estimator is unbiased (going to very close to population mean)
stratified random sampling
when the population is first divided into groups of elements called strata. -each element of population belongs to only one stratum