chapter 7 Flashcards
Describe sample results
- provides only estimates
- contains only a portion of the population
- some sampling errors are to be expected
Describe a sample population
- population from which the sample is drawn
Frame
a list of elements that the sample will be selected from
Simple Random sampling
- can be used to select a sample from a finite pop
- and describes how a random sample can be taken from an infinite pop that is generated by an ongoing process
Element
entity on which data is collected
Population
collection of all elements of interest
sample
subset of the pop
Parameters
numerical characteristics of a population
Pop Parameter for mean
M = pop mean
pop parameter for SD
Q = pop SD
Pop parameter for Proportion
P= Pop proportion
Selecting a sample - FInite Pop
- use a table of random #s to choose the elements for the sample one at a time in such a way that, at each step, each element remaining has the same prob of being selected
Sampling without replacement
it is possible that a random # used previously may appear again
- any prevously used #s are ignored
- used most often in practice
Sampling with Replacement
- not used as often
- still a valid method
Sampling from an Infinite population - Simple Random sample
- a random sample of size n from an infinite pop is a sample selected such that the following conditions are met
- each element selected comes form the same pop
- each element is selected independently - to prevent selection bias
care must be taken, each case may require a different selection procedure
when is the population considered infinite
when we cannot develop a list of all the elements that could be produced
Process for selecting an sample from an infinite pop and provide some examples
- usually associated with a process that operates over time
ex - parts being manufactured - repeated experimental trials in a lab
- transactions occurring at a bank
- telephone calls coming into a call center
- customers entering a store
What is a sample statistic
- a sample characteristic
- ie. sample mean xbar, sample SD, sample proportion etc.
Numerical values obtained for each sample statistic is called
a point estimate
by making calculations, we are calculating
point estimators
Target Pop
pop we want to make inferences about
Describe the sampling distribution of x bar
- various possible values of x bar are the result of different simple random samples
the prob distribution of x is called the
sampling distribution of x bar
What does the sampling distribution of x bar allow us to do
- make prob statements about how close the sample x bar mean is to the pop mean
- can generate a variety of values of x bar and phat
but in practice we only use one
WHat is the sampling distribution of x bar
the prob distribution of all possible values of the sample mean x bar
What is the expected value of x bar
- b/c many different values of x bar are possible, we are often interested in the mean of all possible x bars that can be generated
What is another name for the expected value of x bar
mean
if x bar = the mean then
pop parameter is said to be unbiased
what is the name of the sd of x bar
standard error
what is N-n / N-1 called
the finite pop correction factor
What are the two rules for using Q/Square root of n
- pop is infinite
2. pop is finite and sample size is LESS THAN OR EQUAL TO 5% of the pop size
when n increase the standard error does what
decreases
- when this happens there is less variation or it is closer to the sample mean
What can the shape or form of x bar be
- pop normal distributed - any sample size will be normally disribuited
- Pop does not have a normal distribution
- use central limit theorem
- when sample size gets bigger, the shape becomes normally distributed (use size of 30 or more) or 50 if highly skewed or has outliers
When the pop is discrete what is the form of the sample size
sample size depends on pop proportion
n/N is less than 0.05
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What is the sampling distribution of p hat formula
p hat = x/n = sample proportion
What is the sampling distribution of p hat formula
p hat = x/n = sample proportion
what is the expected value of p hat
= the population proportion
if you are using a finite pop for the sampling distribution of p hat, when can you use the infinite formula
use sample rule
n/N is less than or equal to 0.05
if the sample size increases, what happens to the standard error of p hat?
it goes down which means it is less variable
when using a binomial random variable for sampling, what are the conditons in order to use the normal distribution
np is greater than 5 and
n(1-p) is is greater than 5
What are the 3 properties of point estimates
- unbiased
- efficiency
- consistency
describe unbiased
M=x bar
describe efficiency
- point estimator with smaller sd is preferred
- b/c it tends to provide estimates closer to the pop parameter
point estimators with smaller se is said to have what
greater efficiency than the other one
describe consistency
- if the value of the point estimator tends to become closer to the pop parameter as the sample size increases
- larger sample size tends to provide a better point estimate than a smaller one
What are the other 5 sampling methods
- stratified random sampling
- cluster sampling
- systematic sampling
- convenience sampling
- judgmental
Describe random sampling
the pop is 1st divided into strata (or groups of the same)ie pink dresses, blue dress and purple dresses and a simple random sample is taken form each strata
Describe cluster sampling
- pop is 1st divided into clusters (ie all people on one street, all people on next etc)
- then a simple random sample of the cluster is taken
ie everyone on main street is interviewed
Describe Systematic Sampling
we randomly select 1 of the 1st k elements and then select every kth element there after
Describe Systematic Sampling
we randomly select 1 of the 1st k elements and then select every kth element there after
Describe convenience sampling
non prob method
- elements are selected based on convenience
Describe judgement sampling
non prob method
- selected based on the judgement of the person sampling
the sampling distribution of x bar is the
probability distribution of the sample mean
Parameters are
numerical characteristics of a population
The prob distribution of all possible values of the sample proportion p hat is the
sampling distribution of p hat
in computing the standard error of the mean, the finite pop correction factor is used when
n/N > 0.05
Stratified random sampling is a method of selecting a sample in which the
population is first divided into strata, and then random samples are drawn from each stratum
The closer the sample mean is to the population mean,
the smaller the sampling error
since the smaples size is always smaller than the size of the population, the sample mean
can be smaller, larger or equal to the pop mean
as the sample size increases, the standard error of the mean
decreases
a simple random sample form an infinite pop is a sample selected such that each element is selected
independently and from the same pop
in point estimation, the data from the sample is used to
estimate the population parameter
the sample statistic s is the point estimator of
S
The sample mean is the point estimator of
m
if we condsier the simple random sampling process as an experiment, the sample mean is
a random variable
the prob distribution of the sample mean is called the
sampling distribution of the mean
the standard deviation of all possible x bar values is called the
standard error of the mean
As the sample size becomes larger, the sampling distribution of the sample mean approaches a
normal distribution
The sampling error is the
difference between the value of the sample mean and the value of the pop mean
a prob distribution for all possible values of a sample statistic is known as
a sampling distribution
a pop characteristic, such as a pop mean, is called
a parameter
a sample statistic such as a sample mean, is known as
a statistic
a single numerical value used as an estimate of pop parameter is known as
a point estimate
the sampling statistic, such as x bar, s, or p hat, that provides the point estimate for the pop parameter is known as
a point estimator
THe purpose of statistical inference is to provide information about the
sample based upon information contained in the population
