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