Quantitative Business Methods for Decision Making. Estimation and Testing of Hypotheses. Lecture Outlines. Estimation Confidence interval for estimating means Confidence interval for predicting a new observation Confidence interval for estimating proportions. Lecture Outlines (con’t).
Estimation and Testing of Hypotheses
will decrease as n gets large.
With a 95% degree of confidence is estimated within ( )
written as Or more accurately
Use instead of ,
remember , and
“t” is 95th% percentile of the t
distribution with (n-1) degrees of freedom.
Suppose n= 26. Then degrees of freedom
(d.f.) = n-1 = 25.
A two-sided degree of C.I. is computed
But, for a one-sided 95% C.I. , t = 1.711 instead
The population should be normally (at least
close to) distributed. If skew, then median is
an appropriate measure of the center than the
To estimate mean with a specified margin of
error (m.e.), take a random sample of size n
Prediction Interval for a new observation is given by
Let denote the proportion of items in a
population having a certain property
An estimate of is the binomial
proportion: , What is ?
For a C.I. for , use
For estimating ,“t” is the percentile of the
t-distribution with (equivalently,
percentile of the standard normal
distribution), and s.e. of p is
framed as alternative hypotheses.
alternative hypothesis is called null
Ha: Researcher’s belief that are to be tested (alternate hypothesis)
H0: Complement of Ha (Null hypothesis)
Depending upon what an investigator
believes a priori, an alternative hypothesis
is formulated to be one of the followings:
Regardless of what an alternative hypothesis
about the mean is formulated, the decision
rule is defined by a t- statistic:
The reference number is a specified amount for comparing the
difference between two means. There are two distinct practical
situations resulting in samples on X and Y.
example, males salary X and females
Use p value to reach a decision
To estimate in a 95% C.I.,