Chapter 1 Quality Control in the Modern Business
Environment
1.1 The Meaning of Quality and Quality
Improvement
" SpeciÞcations
◦For manufactured product, the speciÞcations
are designed measurements for quality
characteristics of components and
subassemblies that make up he product, as well
as the designed value for quality characteristics
in Þnal products
◦Lower speciÞcation limit (LSL): smallest
allowable value for a quality characteristic
◦Upper speciÞcation limit (USL): largest allowable
value for a quality characteristic
◦Target/ nominal value: a value of a measurement
that corresponds to the desired value for that
quality characteristic
" Defective or nonconforming product/ defect or
nonconformity
◦Nonconforming products are those that fail to
meet one or more of their speciÞcations
◦A speciÞc type of failure is called a
nonconformity
◦A nonconforming product is considered
defective if it has one or more defects
◦Defects are nonconformities that are serious
enough to signiÞcantly aûect the safe or
eûective use of products
1.1.1 Eight Dimensions of Quality
◦Performance (Will the product do the intended
job?)
◦Reliability (How often does the product fail?)
◦Durability (How long does the product last?)
◦Serviceability (How easy is it to repair the
product?)
◦Aesthetics (What does the product look like?)
◦Features (What does the product look like?)
◦Perceived Quality (What does the product look
like?)
◦Conformance in Standards (What does the
product look like?)
" DeÞnition of Quality
◦Traditional deÞnition: Þtness for use
# Two general aspects:
" Quality of design: variations in grades
or levels of quality are intentional
" Quality of conformance: how well
product conforms to speciÞcations
required by the design
◦Modern deÞnition: Quality is inversely proportional
1.3 Statistical Methods for Quality Control and
to variability in the important characteristics of a
Improvement
product (implies: ³variability, ±quality)
" Fig1.1 warranty costs
quality; Fig1.2
distribution
variability
" Japanese-produced transmissions having much
lower costs (Japan: higher quality)
" US: ~75% width of speciÞcations; Japan: ~25%
width of speciÞcations (Japan: lower variability)
" Japan: Less variability in the important
characteristics
lower costs (better quality)
" US: higher variability, lower cost (lower quality)
³variability, ³costs (±quality)
" (Modern) deÞnition of quality improvement: reduction
of variability in processes and products
◦Equivalent deÞnition: elimination of waste
1.1.2 Quality Engineering Terminology
" Quality characteristics: parameters
" Critical-to-quality (CTQ) characteristics:
◦Physical: length, weight, voltage, viscosity
◦Sensory: taste, appearance, color
◦Time orientation: reliability, durability,
serviceability
" Variability Ð statistical terms: classify data on quality
characteristics as either attributes or variable data
◦Variable data: continuous measurements (ex.
Length, voltage, or viscosity)
◦Attribute data: discrete data (often taking form of
counts)
" Fig 1.3: a process as a system with a set of inputs and
an output
" In a manufacturing process, controllable input factors
x1, x2, É, xp are process variables such as
temperature, pressures, and feed rates; the input
factors z1, z2, É, zq are uncontrollable (or diûcult to
control inputs such as environmental factors or
properties of raw materials provided by an external
supplier
" The production process transforms the input raw
materials, component parts, and subassemblies into a
Þnished product that has several quality
characteristics
" The output variable y is quality characteristic Ð that is,
a measure of process and product quality
" Statistical and engineering technology useful in quality
improvement. SpeciÞcally three major areas:
◦Statistical process control
◦Design of experiments
◦Acceptance sampling
" Statistical process control (SPC):
◦Control chart: one of the primary techniques of
SPC
◦Useful in monitoring processes, reducing
variability through elimination of assignable
◦Plots averages of measurements of a quality
characteristic in sample taken from process vs.
time (or sample number)
# Upper control limit (UCL)
# Center line (CL)
# Lower control limit (LCL)
◦Center line: represents where this process
characteristic should fall if there are no unusual
sources of variability present
" Designed experiment:
◦Extremely helpful in discovering the key variables
inßuencing the quality characteristics of interest
in the process
◦An approach to systematically varying the
controllable input factors in the process and
determining the eûect these factors have on the
output product parameters
◦Invaluable in reducing the variability in the quality
characteristics and in determining the levels of
the controllable variables that optimize process
performance
◦Factorial design: One major type of designed
experiment
# factors are varied together in such a way
that all possible combinations of factor
levels are tested
◦Fig 1.5a: two factors, each two levels, low and
high four possible test combinations
◦Fig 1.5b: three factors, each two levels, low
and high
eight possible test combinations
# Eg. d measure x1 from low to high
increase average level of process
output/ shift oû target (T); e when x2
and x3 high levels process variability
seem to be substantially reduced
" Acceptance Sampling
◦DeÞnition: inspection and classiÞcation of a
sample of units selected at random from a
larger batch or lot and the ultimate decision
about disposition of the lot, usually occurs at
two points: incoming raw materials or
components, or Þnal production
◦Closely connected with inspection and testing
of product
◦One of the earliest aspects of quality control
◦Outgoing inspection & incoming inspection
◦Fig 1.6a: outgoing inspection
# Inspection operation is performed
immediately following production, before the
product is shipped to the customer
◦Fig 1.6b: incoming inspection
# A situation in which lots of batches of
products are sampled as they are received
from the supplier
◦Fig 1.6c: disposition of lots
# Sampled lots may either be accepted or
rejected
# If accepted: ship to customers
# If rejected:
" scrapped/recycled
" rework
" replaced with good units rectifying
inspection
1.4 Management Aspects of Quality Improvement
" Six sigma: eûective quality management system
" Logic of six sigma (textbook page 28-32)
" Main idea: reduce variability (Ã: standard deviation) in
critical-to-quality (CTQ) variables to level at which
failure or defects are extremely unlikely
" Recall: CTQ variables for a product are parameters/
elements that jointly describe what users/consumers
think of as quality
◦Smallest/largest value for CTQ variables: lower/
upper speciÞcation limits (LSL/USL)
" Formal description: reduce à so that LSL/USL are at
least 6Ã from the mean
◦Fig 1.12a: shows a normal probability distribution as
a model for a quality characteristic with speciÞcation
limits at three standard deviation (Ã) on either side of
mean.
◦The probability of producing a product within these
speciÞcations is 0.9973, 2700 parts per million
(ppm) defective
# Òthree sigma quality performanceÓ
If a product consists of 100 independent
components, then the probability that any
speciÞc unit of product is non-defective is
(0.9973)^100 = 0.7631
# 23.7% products defective Ð not acceptable
" The Motorola Six Sigma concept is
to reduce the variability in the
process so that the speciÞcation
limits are at least six standard
deviations from the mean.
◦The probability of producing a
component within L/USL is
0.999999998 Ð one
component
◦Probability that any speciÞc
unit of product is nondefective
is (0.999999998)^100 or 0.2
ppm (100 independent
components in a product)
◦The process mean was still
subject to disturbances that
could cause it to shift by as
much as 1.5 standard
deviations oû target
◦Under this scenario, a Six
Sigma process would produce
about 3.4 ppm defective
" Why ÒQuality ImprovementÓ is important: A simple
example
" A visit of a fast-food restaurant: Hamburger (bun,
meat, special sauce, cheese, pickle, onion, lettuce,
and tomato), fries, and a soft drink
# This product has ten components
◦Is 99% good quality satisfactory?
◦If we assume that all ten components are
independent, the probability of a good meal is:
P{Single meal good} = (0.99)^10 = 0.9044
◦Suppose family of 4, once a month:
# P{All meals good} = (0.9044)^4 = 0.6690
# P{All visits during the year good} =
(0.6690)^12 = 0.0080
# Unacceptable!
◦What if 99.9% good quality? Is it satisfactory?
# P{Single meal good} = (0.999)^10 = 0.9900
# P{All meals good} = (0.9900)^4 = 0.9607
# P{All visits during the year good} =
(0.9607)^12 = 0.6186
Chapter 2 The DMAIC Process
2.1 Overview of DMAIC
" DMAIC is a structured problem-solving procedure
widely used in quality and process improvement.
◦Consisting of the following steps:
# DeÞne
# Measure
# Analyze
# Improve
# Control
◦It is usually associated with six sigma, but I can
be used with any business or process
improvement eûort
" Tollgates:
◦Tollgates between each of major steps
◦Project is reviewed to ensure that this is on
track, evaluate whether team can successfully
complete project on schedule
◦Tollgates also present an opportunity to
provide guidance regarding the use of speciÞc
technical tools and other information about the
problem
◦Tollgates are critical to the overall problemsolving process; It is important that these
reviews be conducted very soon after the team
completes each step.
" Projects:
◦Essential part of DMAIC (quality and process
improvement)
◦Breakthrough opportunity
◦Financial systems integration
◦Value opportunity of a project must be very
clear
◦Project selection
# Completed within a reasonable time
frame
# Real impact on key business metrics
# Understand interrelationships and
develop appropriate performance
measures
" What should be considered when evaluating
proposed project?
◦Suppose a company is operating at the 4Ã
level (6210 ppm defective, assuming the 1.5Ã
shift in the mean that is customary with Six
Sigma applications)
◦Objective: achieve the 6Ã performance level
(3.4 ppm)
◦Suppose that the criterion is a 25% annual
improvement in quality level.
◦Then to reach the Six Sigma performance
level, it will take x years, where x is the
solution to this: 3.4=6210(1-0.25)^x x is
about 26 years
# Not going to work!
◦Annual improvement
# 50%
x=11 years
# 75%
x=5 years
2.2 The DeÞne Step
2.3 The Measure Step
" Objective:
" Purpose: evaluate and determine present process state
◦identify project opportunity
(evaluate and understand the current state of process)
◦verify or validate it represents legitimate
◦Identify key process input variables (KPIV) and
◦must be important to customers (voice of the
key process output variables (KPOV)
customer) and important to the business
◦Data: from historical records; from sampling; from
" project charter: a short document; a description of
observational studies
project and it scope & others
◦Histograms, box plots, scatter diagrams, stem◦a description of the project and its scope, the start
leaf diagrams
and the anticipated completion dates, an initial
◦In transaction and service business, measurement
description of both primary and secondary metrics
system
that will be used to measure success and how
# the capability of the measurement system
those metrics align with business unit and
should be evaluated. (capacity/uniformity
corporate goals, the potential beneÞts to the
±, ó)
customer, the potential Þnancial beneÞts to the
" The Measure Tollgate
organization, milestones that should be
◦Comprehensive process ßow chart or value
accomplished during the project, the team
stream map
members and their roles, and any additional
◦KPIVs and KPOVs
resources that are likely to be needed to complete
◦Measurement system capability documented
the project.
◦Assumption noted
◦Respond to requests
2.4 The Analyze Step
" Graphic aids:
◦process map and ßow charts
◦value stream maps
◦SIPOC diagram (a high level map of process)
# Suppliers
# Input
# Process
# Output
# Customer
" The DeÞne Tollgate
◦Symptoms (focus) not on possible
causes or solutions
◦Stakeholders
◦Value opportunity
◦Scope neither too small nor too large
◦SIPOC diagram
◦Obvious barriers or obstacles
◦Action plan
" Purpose: use data from the Measure step to determine
Òcause-and-eûectÓ relationships in the process
" Sources of variability:
◦Common cause: embedded in system or process
itself
◦Assignable cause: arise from an external source
" Tools:
◦control charts
# separate common cause variability from
assignable cause variability
◦hypothesis testing and conÞdence intervals
# hypothesis testing: determine if diûerent
conditions of operations process statistically
signiÞcantly diûerent results
# CIs: provide information about the accuracy
with which parameters of interest have been
estimated
◦regression models
# allows models relating outcome (eûect)
variables of interest to independent input
(cause) variables to be built
" The Analyze Tollgate
◦Opportunity targeted in the Improve step
◦Data and analysis
◦Other opportunities
◦Track
2.5 The Improve Step
" Tools:
◦Process redesign to improve work ßow and to
reduce bottlenecks
◦Mistake-prooÞng
◦Statistical tools: particularly designed
experiments are probably most important
statistical tools in the Improve step
# Physical process or a computer model of
process
" Pilot test: a form of conformation experiment
◦Evaluates and documents solution and conÞrms
solution attains the project goals
◦Iterative activity
" The Improve tollgate
◦How problem solution was obtained
◦Alternative solutions
◦Pilot test
◦Plans to implement pilot test results
◦Any risks of implementing solution
2.6 The Control Step
" Objectives:
◦Complete all remaining work on project
◦Provide the process owner with a process control
plan
" The process owner should be provided with before and
after data on key process metrics, operations and
training documents, and updated current process
maps.
" The process control plan should be a system for
monitoring the solution that has been implemented,
including methods and metrics for periodic auditing.
" Control charts are an important statistical tool used in
the Control step of DMAIC; many process control plans
involve control charts on critical process metrics.
◦Control charts: an important statistical tool in
control step
" Transition plan: new process weight include a validation
step (The transition plan for the process owner should
include a validation check several months after project
completion.)
" The Control tollgate
◦Data (before and after) available
◦Process control plan & control charts
◦Documentation
◦Summary of lessons
◦Opportunities not pursued in project
◦Opportunities use results of project in other parts
of business
Chapter 3 Modeling Process Quality
3.1 Describing Variation
" Stem-and-Leaf Plot
◦Data: x1, x2, É, xn; each number xi consist of at
least two digits, divide x1 into two parts
# A stem: one or more leading digits
# A leaf: two remaining digits
◦For example, data from 10 to 100, number 76
divide value 76 into stem 7 and leaf 6
◦Percentiles of data:
# the 100 kth percentile is a value such that
at least 100 k% of the data values are at or
below this value and at least 100 (1 2 k)%
of the data values are at or above this
value
# The Þftieth percentile of the data distribution is
called the sample median x-bar
" First, sort the observations in ascending
order (or rank the data from smallest
observation to largest observation).
" Then the median will be the observation in
rank position [(n 2 1)/2 + 1] on this list. If n is
even, the median is the average of the (n/2)st
and (n/2 + 1)st ranked observations.
◦Eg. n =11 x6; n=40 average of x20
and x21
# The tenth percentile is the observation with rank
(0.1)(40) + 0.5 = 4.5 (halfway between the fourth
and Þfth observations)
# The Þrst quartile is the observation with rank (0.25)
(40) + 0.5 = 10.5 (halfway between the tenth and
eleventh observation)
# the third quartile is the observation with rank (0.75)
(40) + 0.5 = 30.5 (halfway between the thirtieth and
thirty-Þrst observation)
# the interquartile range: IQR = Q3 2 Q1
" occasionally used as a measure of variability
Procedure:
" plot of data in time order
" take time order of observations into account
" important factors to variability in quality improvement
" plot data value versus time
" time is an important source of variability in this process
" processing cycle time for Þrst 20 claims is substantially
longer than processing cycle time for second 20 claims
" Histogram
◦A more compact summary of data
◦To construct a histogram for continuous data:
# Divide range of data into intervals called bins
# Sort data into bins, count number of obs. in
each bin
# Use horizontal axis to represent
measurement scale vertical scale to
represent counts or frequency or relative
frequencies (frequencies in each bin divided
by total number of observations (n)
◦Example 3.2 Metal Thickness in silicon wafers
◦Gives a visual impression of shape of the
distribution of measurement and inherent
variability in data
◦Shows reasonably symmetric or bell-shaped
distribution of metal thickness data
◦Histogram relatively sensitive to choice of number
and width of bin for small data sets
◦Histogram suited for larger data sets, 75 to 100 or
more observations
◦Box plot Ð hole diameter distribution is not exactly
symmetric Ð left/right boxes around median not same
" Comparative box plots Ð useful in graphical
comparisons among data sets
◦Too much variability at plant2
◦Plant 2 and 3 need to raise their quality index
performance
◦Height of each bin represents number of
observations less than or equal to upper limits of
bin
# Eg. about 75 of 100 wafer less than 460 Å
◦To construct a histogram for discrete or count
data (sample space is countable)
# Determine frequency (r relative frequency)
" Probability distributions
for each value of x, each x value
◦Sample: a collection of measurements selected
corresponds a bin
from some larger score or population
# Plot frequency (or relative frequency) on
# Eg. analyze sample layer thickness data
vertical scale and values of x on horizontal
◦
Probability
distribution: mathematical model
scale
relates value of variable with probability of
◦Example 3.3: defects in automobile hoods
occurrence of that value in the population
# Eg. layer thickness Ð a random variable
# Probability of occurrence of any value of
layer thickness in population
" DeÞnition
◦Continuous distributions
# When the variable being measured is
" Numerical summary of data
expressed on a continuous scale, its
probability distribution is called a
continuous distribution.
# The probability distribution of metal layer
thickness is continuous
◦Discrete distributions
# When the parameter being measured can
only take on certain values, such as the
integers 0, 1, 2, . . . , the probability
distribution is called a discrete distribution.
# For example, the distribution of the number
of nonconformities or defects in printed
circuit boards would be a discrete
distribution.
" Box plot
◦A graphic display; important features of the
data, such as location or central tendency,
spread or variability, departure from symmetry,
and identiÞcation of observations that lie
unusually far from the bulk of the data (these
observations are often called ÒoutliersÓ).
◦Display three quartiles, minimum and maximum
of data on a rectangular box
" Probability mass function (discrete variable)
" Scatter, spread, or variability in a distribution
◦Variance
" Probability density function (continuous variable)
◦standard deviation à Рsquare root of variance
# a measure of spread or scatter in
population express in original data
" Expected value/ mean ¿ of a probability distribution is
a measure of central tendency in the distribution, or
its location
Chapter 4 Inferences About Process Quality
4.1 Statistics and Sampling Distributions
" Statistical inference: draw conclusions about
populations (or process) based on sample data from
that system
" Random sample: a sample selected so that
observations are independent Ð same probability of
selection
" Statistics: any function of observations in sample
◦Eg: sample mean, sample variance, sample
standard deviation
" Sampling distributions
◦Statistic Ð a random variable; probability
distribution
◦Sampling distribution Ð probability distribution of
a statistics
◦Question: let x1, x2, É, xn be a random sample
size n from a distribution (population) with mean ¿
and variance Ã^2. What is the mean (expected
value) and variance of sample mean x-bar?
" Three important and useful sampling distributions
based on normal distribution
◦Chi-square distribution
If x1, x2, É, xn are normally and independently distributed
random variable with mean 0 and variance 1, then random
variable
is distributed as chi-square with n degrees of freedom
◦t distribution
if x is standard normal random variable and if y is a chisquare random variable with k degrees of freedom, and if
x and y are independent, then random variable:
is distributed as t with k d.f.
◦F distribution
if w and y are two independent chi-square random
variable with u and v degrees of freedom, then
is distributed as F with u: numerator df and v:
denominator df
4.2 Point Estimation of Process Parameters
4.3.1 Inference on mean of a population, variance known
" Distributions described by their parameters
" Parameters unknown, must be estimated
" Estimator: deÞne an estimator of an unknown
parameter as statistic that corresponds to parameter
" Point estimator: a statistic that produce a single
numerical value as ÒestimateÓ of parameter
" Example: consider random variable x~N(¿,Ã^2)
mean and variance both known
" If a random sample of n observations, then sample
mean x-bar and sample variance S^2 are point
estimators of population mean ¿ and population
variance
◦Suppose random variable x inside diameter
n=20 bearings. Sample mean x-bar = 1.495;
sample variance S^2 = 0.001
4.3 Statistical Inference for a single sample
" Three components of statistical inference
◦Point estimation
◦Hypothesis testing
# Null hypothesis vs.. alternative hypothesis
# Statistical hypothesis: a statement about
values of parameter of a probability
distribution
# Two-sided alternative hypothesis vs. onesided alternative hypothesis
◦ConÞdence intervals
# Refers to the probability that a population
parameter will fall between pair of values
around mean
# Measure two degree of uncertainty in a
sampling method
# Constructed by conÞdence levels of 95%
or 99%
" To test a hypothesis
◦Take a random sample from population
◦Compute an appropriate test statistic
◦Either reject or fail to reject the null hypothesis
◦Òcritical regionÓ or Òrejection regionÓ: set of
values of test statistic leading to rejection of H0
" Two kinds of error when testing hypothesis
◦Type I error: if null hypothesis is rejected when it
is true
◦Type II error: if null hypothesis is not rejected
when it is false
◦Power of a statistical test
" In quality control work:
◦³: producerÕs risk (probability that a good lot will
be rejected)
◦´: consumerÕs risk (probability of accepting a lot
of poor quality)
" ConÞdence interval
◦An interval estimate of a parameter is interval
between two statistics that include true value of
parameter with some probability
◦For example, construct an interval estimator of
mean ¿, must Þnd two statistics L and u such that
P{L <= ¿ <= U} = 1-³
◦Interval L <= ¿ <= U is called 100(1-³)%
conÞdence interval for unknown mean ¿
◦L and U Ð lower and upper conÞdence limits
◦1-³: conÞdence coeûcient
" Interpretation of CI:
◦If a large number of such intervals are
constructed, each resulting from a random
sample, then (1-³)% of these intervals will
contain true value of ¿
◦One-sided lower 100(1-³)% conÞdence bound
on ¿
L <= ¿
# L: lower conÞdence bound so that P{L<=¿}
=1-³
◦One-sided upper 100(1-³)% conÞdence bound
on ¿
¿ <= U
# U: upper conÞdence bound so that
P{¿<=U}=1-³
" Normal distribution, compute p value
" ConÞdence interval on mean with variance known
◦Consider random variable x, with unknown
mean ¿ and known variance. Suppose a
random sample of n observations x1, x2, É ,xn.
◦Then the 100(1-³)% two-sided CI on ¿ is:
4.3.3 Inference on Mean of a Normal Distribution,
Variance Unknown
" Hypothesis testing: x normal random variable with
unknown mean and unknown variance
4.3.2 The Use of P-Values for Hypothesis Testing
" P-value is the probability that test statistic will take
on a value that is at least as extreme as observed
value of statistic when null hypothesis is true
◦The p-value is smallest level of signiÞcance that
would lead to rejection of null hypothesis
" ConÞdence interval on mean of a normal distribution
with variance unknown
4.4 Statistical Inference for Two Samples
4.4.1 Inference on diûerence in mean, variance known
4.3.5 Inference on a Population Proportion
" Hypothesis testing: suppose test proportion p of a
population equals to a standard value,
Ònormal approximation to binomialÓ
" Suppose a random sample of n observations from
population
◦X items in sample Ð class associated with p
4.4.4 Inference on two proportions
4.4.2 Inference on diûerence in means of two normal
distribution, variance unknown
Review STAT 513 Midterm Spring 2022
Zhongyuan Chen
[Detailed instruction will be uploaded on Brightspace before the exam.]
Please do not distribute this exam.
This exam has the format: calculations (most) and short answer questions
(minor).
There are 100 points on this exam. Please show your work on each problem
on this exam, in which case liberal partial credit will be awarded.
This exam is open book and open notes.
Exam open window: March 29 (Tuesday) 9:00 a.m. EST - March 30
(Wednesday), 2022 8:59 a.m EST
Please print the exam (If you do not have a printer available, you can please
use your own paper to work the exam. Please organize your work in numerical
order.), work on the papers, scan your materials (a single PDF file, better to
use a scanner or application program, such as CamScanner, on a smart phone
or ipad), and upload it on Brightspace.
Exam time limit: 120 min
Please bring a calculator.
Chapter1: Quality improvement in the modern business environment
¯ Definitions of quality (modern definition) and quality improvement
¯ Terminology: quality characteristics, critical-to-quality (CTQ)
characteristics, specifications (lower specification limit, upper specification
limit, target or nominal values), defective or nonconforming product,
defect or nonconformity
¯ Statistical methods: statistical process control (SPC), designed
experiments, acceptance sampling.
¯ Six sigma: calculation (example: hw2.12)
1
Chapter2: The DMAIC process
¯ DMAIC: define, measure, analyze, improve, and control
¯ Tollgates
Chapter3: Modeling process quality
¯ Describing variation: histogram, boxplot, numerical summary of data
(sample mean, sample variance, sample standard deviation), probability
distribution (discrete variable: probability mass function; continuous
variable: probability density function), mathematics definition of mean
and variance.
¯ Discrete distribution: hypergeometric distribution, binomial distribution
(bernoulli trials), poisson distribution, negative binomial
distribution,geometric distribution (calculation: example: hw3.29)
¯ Continuous distribution: normal distribution (central limit theorem),
lognormal distribution, exponential distribution, gamma distribution,
weibull distribution (calculation: example: Example3.8)
Chapter4: Inference about process quality
¯ Statistics and sampling distributions: statistical inference, random sample,
statistic, sampling distribution (sampling from a normal distribution),
three important sampling distribution (chi-square distribution, t
distribution, F distribution)
¯ Point estimation of process parameter: point estimator (properties),
estimate.
2
¯ Statistical inference for a single sample: hypothesis testing, confidence
intervals.
Hypothesis testing: null hypothesis (H0), alternative hypothesis (H1),
standard procedure--- random sample---compute test statistic--- compare
with critical value--- either reject null or fail to reject null hypothesis.
Two kinds of errors:
\alpha = P(type I error)=P(reject H0 | H0 is true)
\beta = P( typeII error)=P(fail to reject H0 | H0 is false)
Power = 1 - \beta = P(reject H0 | H0 is false)
Inference on the mean of a population (variance known (z test statistic:
population variance), variance unknown (t test statistic: use sample variance
to estimate)): hypothesis testing, confidence interval
Inference on a population proportion: hypothesis testing, confidence
interval
Calculation example: Example4.3; Example4.4
(Note: population variance sigma square unknown, use sample variance
as estimate for calculation, use t test statistic)
¯ Statistical inference for two samples: hypothesis testing, confidence
intervals.
Inference on the difference in means (variance known, variance unknown
(equal/unequal variance)): hypothesis testing, confidence interval.
Inference on the difference in two proportions: hypothesis testing,
confidence interval
Calculation example: Example4.8
(Note: population variance sigma square known, use z test statistic)
3