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