Week 10 PT 1
Week 10 PT 1
Week 10 PT 1
5/13/17
Inferential Methods:
Confidence Interval
Estimation
Week 10 Part 1
Discrete w/ Probability Single variable with probability distribution; E(X), V(X)
Distribution
Linear Combinations Multiple variables with known expected values E(aX + bY), V(aX +
bY)
Bernoulli Single trial resulting in one of two mutually exclusive and collectively
exhaustive outcomes.
One parameter, E(X)=, V(X) = (1-)
Students t: t(df)
known
To
estimate
Populatio
n Mean
To
when is
estimate
unknown
Populatio
n
Proportio
n when
n*>5 &
n*(1-) >
5
Parameters are important!
We never know parameters,
but, we WANT to know parameters!
About the closest we are going to get is to
make educated guesses about parameter
values.
Ourfirst inferential task is to figure
out how to estimate parameters.
Wewill focus on estimating the population
mean, , and the population proportion, .
Estimators
Wehave options when we choose
point estimators, so criteria have
been developed for selecting the best
point estimator.
Thebest estimators are unbiased; they
are close to the parameter they estimate.
An estimator is unbiased if its expected value is
equal to the parameter being estimated.
Thebest unbiased estimators are those
that vary the least.
An efficient estimator is one that has the
smallest variance of all estimators.
Anatomy
of a Confidence Interval
=ABS(NORM.S.INV(/
2))
= NORM.S.INV(1- /2)
=ABS(T.INV(/2, n-1))
=T.INV(1- /2, n-1)
=ABS(NORM.S.INV(/
2))
= NORM.S.INV(1- /2)
Margins of Error