ISDS ch 7 and 9
a sample can provide results more quickly and for a lower cost. In some cases taking the population is not a viable option, so decision makers can only rely on info obtained from sample. If a sample is selected properly, a sample can provide more reliable results than taking a census.
why do we take a sample instead of a census
to make conclusions about the population based upon a single sample Ex: political pollsters: the sample proportion is used to estimate the actual proportion of the votes that each candidate will get from the population of voters
main goal of inferential statistics
random variable
a statistic is a ______whose value depends on these chosen random samples
selected bias
a systematic under representation of certain groups from consideration for the sample
not equal to, > , <
alternative hypothesis uses what signs regarding population parameters
census and survey
are used to represent a population and sample
simple random sample most statistical methods presume
basic type of sample that can be used to draw statistically sound conclusion about non population is
if i'm pulling a sample from a population that is unknown distribution, then the sample will be normally distributed if it is sufficiently large n> or = 30
central limit theory says what about a sample mean
- a control chart plots the sample estimates - all sample estimates are plotted with reference to a center line -have upper and lower control limit which indicate excessive deviation above or below expected value
characteristics of all charts
c chart
chart that monitors the count of defects per item, such as the number of blemishes on a piece of furniture
r chart and s chart
chart that monitors the variability of production process
statistical quality control
involved statistical techniques used to develop and maintain a firm's ability to produce high quality goods and services.
parameter
is a constant even though its value maybe unknown
what is simple sample random
is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.
p chart
is a useful chart to asses a population based on a sample
sample distribution
is the probability distribution of the sample mean x
survey data
is used to analyze government and business activities
reject the null or do not reject the null
We either ____ or _____ the null hypothesis
the sample distribution is normal if the sample size is sufficiently large np> 5 and n>(1-p)
central limit theorem for sample proportion says:
x chart
chart that monitors central tendency of a production process
the sampling distribution of the relevant estimator is normal
control chart is only valid if
three standard deviations
control limits are _____ from the centerline
non response error
error incurred when some subjects refuse to respond to a survey
what is a sample and what is it used for
it is a subset of the population. A sample statistic is used to make inferences about the unknown population parameter
identical
no two products are
coverage error
occurs when certain items are excluded from the sampling frame
x, r,s chart
quantitative control charts
bias
refers to the tendency of a sample stat to systematically over or underestimate a population parameter, often caused by samples that are not representative of the population
detection approach
the preferred method of quality control. Inspects the production process and determines whether production process should be continued or adjusted before a large number of defects are produced
the standard error of the sample mean
the standard deviation of the sample mean is called
standard error of the sample proportion
the standard deviation of the sample proportion is called
stratified random sampling
type of sample where population is divided into mutually exclusive and collectively exhaustive groups called strata. It includes randomly selected observations per stratum. The number of observations per stratum is proportional to the stratum's size in the population. the data from each stratum are eventually pooled.
assignable variation
type of variation caused by specific events or factors that can usually be identified and eliminated
as the sample size increases
when will a sample size that is not normally distributed begin to look normal
making statistical inferences
****probability sample is necessary when
probability sample Ex: simple random sample
sample in which items are selected based upon known probabilities
null hypothesis
Ho=
Type II error, where the probability of making a Type II error is denoted by β.
If we accept the null hypothesis when in reality the null hypothesis is false, we commit a
Type I error, where the probability of making a Type I error is denoted by α.
If we reject the null hypothesis when in reality the null hypothesis is true, we commit a
one tailed
____ is used when we can reject the null hypothesis only on one side of the hypothesized value of population parameter
two tailed
_____ is used when we can reject the null hypothesis on either side of the hypothesized value of population parameters
estimate
a particular value of a statistic is
non probability sample Ex: Convenience sample
a sample in which the items have unknown probabilities of being selected
always less than one; when N is large relative to n the finite correction factor is close to one and the correction factor isn't negligible
correction factor is
non sampling error (bias)
error that results in a distortion of conclusions
non response error
estimating percentage of car crashes that involve alcohol. Drunk drivers usually refuse the BAC test. What type of error
used to reduce the sampling variation of the sample mean. n> .05 N
finite population correction for sample mean says
the population from which the sample is drawn is normally distributed
for any sample size, the sample distribution is normal if
adjustment of production process is likely necessary
if calculated stats reveal an undesirable trend, then
controlled
if the calculated statistics a fall in an expected range, the product process is
standard error
sample size and ____ have an inverse relationship
statistical inference
where we examine the problem of estimating population parameters or testing hypothesis about such parameters
=,> =,<=
a null hypothesis uses what signs regarding population parameters
alternative hypothesis
Ha=
p chart
chart that monitors proportion of defectives in production process
chance and assignable
two types of variation
measurement error
CDC Hepatitis survey, teacher evaluation requiring you to fill in your name, order of survey questions. What type of error
type 1: the medical test says they have a disease, but they really don't (false positive) type 2: the medical test shows they don't have the disease, but they actually do. (false positive)
H0: A person is free of a particular disease Ha: A person has a particular disease explain type 1 and type 2
type 1: verdict found guilty, but really innocent type 2: verdict found them innocent, but are actually guilty
H0: An accused person is innocent Ha: An accused person is guilty what is type 1 and type 2 error?
reduce non response rate
most effective way to deal with non responsive bias is to
no statistical inference would be needed
population consist of all items of interest in a statistical problem. If we had access to data that encompasses the entire population then the values of the parameters would be known and
p and c chart
qualitative control charts
sample
since it is generally not feasible to gather info on the whole population,_______is used to to make a statistical inference
stratified consists of observations from each group and is preferred when objective is to increase precision. cluster consists of observations from the selected groups and is preferred when the objective is to reduce cost
stratified vs. cluster
non response bias
systematic difference in preferences between respondents and non respondents to a survey or a poll
of the sample its based on
the credibility of a statistic depends on the quality of
sample error (as soon as you look at anything less than the entire population, you are not going to report 100 percent accuracy characteristic if the population)
the error incurred by taking a sample instead of a census
the population mean this means the sample mean is an unbiased estimator of the population mean
the expected value of the sample mean equals
equal to the population proportion
the expected value of the sample proportion is
many possible samples of a given size can be drawn from the population
there is only one population ,but
non response, coverage error, measurement error
three types of non sampling error
control chart commonly used in quality control
tool used to monitor the behavior of the production process
accepting sampling and detection approach
two approaches are used for quality control
accepting sampling
type of quality control used if it produces a product and at the completion of the production process, firm inspects a portion of the products. If it doesn't conform to specifications it is discarded or repaired, Problem is not all products are detected
cluster sample
type of sampling where population is divided into clusters (such as geographic areas). It includes observations from randomly selected clusters
chance variation
type of variation caused by number of randomly occurring events that are part of the production process. Not under the control of the individual worker or machine
estimator
when a statistic is used to estimate a parameter it is called
measurement error
when data collected do not reflect the true measurements
bias
when the info of a sample is not typical of info of population in a systematically way we say that a _____ has occured