Chapter 12: Hypothesis Testing (12.4)
Since Chapter 9 was not covered in STAT 420, Section 12.3:
Losses & Risk, will be skipped.
RECAP:
Two types of ERRORS [Definition 12.2]
Type I-error [Reject the Null Hypothesis, when it is
True]
Type II-error [Do
Section 12.4: Neyman-Pearson Lemma
RECAP:
In this section, we only consider Simple Null Hypothesis
against Simple Alternative Hypothesis testing based on
a random Sample of n observations from the population
with X f ( x; ).
H 0 : 0 against H1 : 1 .
D
Section 12.5 Power Function of a Test
Given the MP Critical Region for a simple against simple hypothesis,
we can find the power (to reject the false Null) of the test (= 1 ) by
calculating the P (Reject H 0 | =) = X CR | =).
1 P(
1
For example, in the n
Chapter 13: Tests of Hypothesis
Section 13.1 Introduction
RECAP: Chapter 12 discussed the Likelihood Ratio Method as a general
approach to find good test procedures.
Testing for the Normal Mean Example, discussed in Section 12.6.
Example: Sample of size
Section 13.4 Tests Concerning Variances
Why do we need to test hypothesis about population
variance?
o We need to certify that the variability in our
product is below a certain level (Consistency in
quality)
o For warrantee purposes, we need to make sure
Section 13.5 Test of Hypothesis for Population
Proportion
As discussed in Section 11.4-11.5, inference about the
probability of success in independent Bernoulli trials is
same as the mean of independent observations on binary
outcomes.
If we assume that
Interval Estimation Section 11.1-11.2
The interval (1 , 2 ) varies from
Stat 421-SP2012
sample to sample.
For a given random sample, the
statement (1 , 2 ) , i.e., the
We now understand (Chapter 10) how to find point
estimators of an unknown parameter .
Section 11.3 Estimation of the Difference of Two population means
Example: Two different manufacturers of long life bulbs:
o Life times are Normal with (unknown) means i , i 1, 2
2
and variances 12 2500,2 3600.
o Want to estimate the difference in their e
Section 11.5 Estimation of difference of two proportions
As seen in estimation of difference of two means for nonnormal population based on large sample sizes, one can use
CLT in the approximation of the distribution of sample mean.
Therefore, an approxim
Stat 421-SP 2012
Point Estimation-I Section 10.1-10.3
Outline:
A Random Sample (RS) of size n - Observed values of n independent and
identically distributed (iid) random variables X1, X 2 , , X n from an infinite
population, with common probability distr
April 3, 2012
Note: Highlighted parts show the differences from 4/1 version, and
underlined phrases were emphasized in the class.
Point Estimation-II (Complete)
Sections 10.4-10.6 - Consistency, Sufficiency and Robustness
Section 10.4 Consistency Property
Point Estimation-III:
General Methods for Obtaining Estimators
RECAP 10.1-10.6
Data: Random Sample from a Population of interest
o Real valued measurements:
o Assumption (Hopefully Reasonable)
o Model: Specified Probability Distribution
f (x | )
o Involv
Tests for MeansExamples using MINITAB SOFTWARE
One-Sample T: Exercise 13.30 TarCont,
Exercise 13.31 TarConAlt
Esercise 13.33
Test of mu = 14 vs not = 14
Variable
TarCont
TarConAlt
N
5
5
Mean
14.4000
14.700
StDev
0.1581
0.742
SE Mean
0.0707
0.332
95% CI
(1
Chapter 12: Hypothesis Testing
Chapter 11-Constructed Estimates of Parameter of Interest
With a statement of underlying uncertainty
Confidence Intervals with a level of confidence
Interval Estimation
Instead of estimating the unknown parameter, one m