OBA 311 Final (Fang Yin)
central limit theorem
1) If the sample size is large enough, then the sampling distribution of the mean is approximately normally distributed regardless of the distribution of the population and has a mean equal to the population mean 2) If the population is normally distributed, then the sampling distribution is also normally distributed for any sample size
margin of error (for t)
=CONFIDENCE.T(alpha, standard_deviation, size)
Data>Data Analysis>Sampling
How do you do simple random sampling in excel?
sampling plan
a description of the approach that is used to obtain samples from a population prior to any data collection activity
the t-distribution
a family of probability distributions with a shape similar to the standard normal distribution
confidence interval
a range of values between which the value of the population parameter is believed to be, along with a probability that the interval correctly estimates the true (unknown) population parameter
point estimate
a single number derived from sample data that is used to estimate the value of a population parameter
random variate
a value randomly generated from a specified probability distribution
100(1-alpha)% probability interval
any interval [A, B] such that the probability of falling between A and B is 1-alpha
increases
as sample size decreases, the sampling error ________
decreases
as sample size increases, the sampling error _____________
decreases
as the size of the sample increases, the standard error ______
estimation
assessing the value of an unknown population parameter using sample
one-way data table
evaluate an output variable over a range of value for a single input variable
two-way data tables
evaluate an output variable over a range of values for two different input variables
=NORM.S.INV(1-alpha/2)
excel formula for upper tail area of alpha/2
=T.INV(1-alpha/2, n-1)
excel function for t values
=RAND()
excel function that finds a random value between 0 and 1
=VLOOKUP
excel function that finds a random value in a table
unbiased
if the expected value of an estimator equals the population parameter it is intended to estimate, the estimator is said to be ____________.
standard error; standard deviation
if the measurement relates to the mean of a sample, use ___________________, NOT __________________
subjective sampling methods
judgement sampling and convenience sampling
=CONFIDENCE.NORM(alpha, standard_dev, size)
margin of error excel formula
confidence interval with unknown population standard deviation
mean +/- t sub (alpha/2, n -1) (stdev/sqrt(n))
estimators
measures used to estimate population parameters (e.g. sample mean, sample variance, sample proportion)
sample size for the proportion
n >= (zsub(alpha/2))^2*((pi(1-pi))/E^2)
sample size for the mean:
n >= (zsub(alpha/2))^2*(stdev^2/E^2)
sampling (statistical) error
occurs because samples are only a subset of the total population and is inherent in any sampling process and can be minimized but not totally avoided
nonsampling error
occurs when the sample does not represent the target population adequately; usually is the result of poor sample design or inadequate data reliability
confidence interval for a proportion
p hat +/- zsub(alpha/2)*sqrt((phat(1-phat))/n)
level of confidence
probability of the confidence interval being correct
monte carlo simulation
process of generating random values for uncertain inputs in a model, computing the output, and repeating this process to understand the distribution of the output results
interval estimate
provides a range for a population characteristic based on a sample
confidence interval formula
sample mean +/- margin of error
simple random sampling
sampling from a population where every subset of a given size has an equal chance of being selected
convenience sampling
sampling of all customers who happened to visit this month
random sample
sampling that selects a simple random sample
periodic sampling
sampling that selects every nth number
judgement sampling
sampling that surveys the best customers
stratified sampling
sampling where populations are divided into sub-groups (strata) based on a particular characteristic. A random sample is then taken from each of these strata proportional to its size.
cluster sampling
sampling where you divide a population into subgroups and sample a set of those subgroups
continuous process sampling
sampling where you select a time at random and select the next n items produced after that time
risk analysis
seeks to examine the impact of uncertain inputs on various outputs
systematic (periodic) sampling
selects every nth item from the population; might induce bias if there is underlying pattern in the population
principles of a good spreadsheet design
separating the data, model calculations, and model output are
probabilistic sampling
simple random sampling is what kind of sampling method
standard error of the mean formula
stdev/sqrt(n)
data tables
summarizes the impact of one or two inputs on a specified output
sampling distribution of the mean
the distribution of the means of all possible samples of a fixed size n from some population
degrees of freedom
the higher the __________ of ____________, the closer to the standard normal distribution the distribution is
risk
the likelihood of an undesirable outcome
standard error of the mean
the standard deviation of the sampling distribution of the mean
z sub alpha/2
the value of the standard normal random variable for an upper tail area of alpha/2
n-1
what is the degrees of freedom formula
π
what is the sample proportion denoted as in sampling?
0.5
what should π (the proportion) be set equal to for a conservative estimate for precision?
probabilistic sampling
which of the following types of sampling involves using random procedures to select a sample? •probabilistic sampling •convenience sampling •judgement sampling •subjective sampling
margin of error
z(a/2)*standard error