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Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.

Copyright (c) 2009 John Wiley & Sons, Inc.

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Learning Objectives



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• Statistical inference is concerned with drawin

conclusions about populations (or processes) basedon sample data from that system

• – observations are independent – a random sample has

the property that it has the same probability of.

• Statistic – any function of the observations in asample that doesn't contain unknown parameters

• The sample mean, the sample variance, and thesample standard deviation are all statistics



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Observations in a sam le are used to draw

conclusions about the population



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• ,

different sample with produce a different

• Every statistic has a probability distribution• T e pro a ty str ut on o a stat st c s

called a sampling distribution



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Sampling from a Normal Distribution



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Sampling from a Bernoulli Distribution



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Sampling from a Poisson Distribution



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•

• Parameters are generally unknown and must be

es ma e

• Point estimator – a statistic that a singlenumer ca va ue t at s t e est mate o t e

parameter

• Examples, page 110 & 111



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Properties of Point Estimators



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• =

• Hypothesis testing

– u ypot es s, 0

– Alternative hypothesis, H1• Confidence intervals

• These two techniques are closely related



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4.3.1 Inference on the Mean of a Population, Variance Known



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Minitab

output



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Upper and

lower

confidence

bounds



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-. .



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4.3.3 Inference on the Mean of a Normal



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Checking the normality assumption – we will see how to do this in

Example 4.3



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4.3.4 Inference on the Variance of a Normal Distribution



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Upper and

lower

con ence

bounds



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4.3.5 Inference on a Population Proportion

Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

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Minitab can perform sample size and power calculations. From

Example 4.7:

From Example 4.3:


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Comparing means, comparing variances, comparing proportions


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4 4 1 I f h Diff i M V i K

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4.4.1 Inference on the Difference in Means, Variances Known


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This is a two-sided CI. The one-sided confidence

limits in Equation (4.49) with α/2 replaced by α.


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4 4 2 I f th Diff i M f

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4.4.2 Inference on the Difference in Means of

wo orma str ut ons, ar ances n nown


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C fid I t l C 1

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Confidence Intervals – Case 1:

Case 2:


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Paired Data:

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Chapter 4 Introduction to Statistical Quality Control, 6th

Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

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4 4 3 Inference on the Variances of Two Normal Distributions

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4.4.3 Inference on the Variances of Two Normal Distributions



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The two-sided CI is:

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4.4.4 Inference on Two Proportions

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4.5 What if There Are More Than Two Populations?

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e na ys s o ar ance

the mean tensile strength of paper?



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Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc. 69

The Analysis of Variance (ANOVA)

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The ANOVA is based on the following partitioning of the total sum of

squares (which measures the total variability in the sample data):



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Chapter 4 Introduction to Statistical Quality Control, 6

th


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The ANOVA test statistic is:

0 α,a-1, a(n-1)

hypothesis of equal treatment means is rejected. A P-valueapproach can also be used. The P-value would be the probability


th


a- , a n- .

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th


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th


Graphical comparison of individual means

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20% hardwood produces higher mean strength than the

others; 5% hardwood produces lower strength; 10% and

15% hardwood don’t differ but give lower strength than 20%.



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.ˆ

i i i i ie y y y y



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es ua o s:



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4.6 Linear Regression Models

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regression techniques, so long as they are linear in the parameters.

Important cases include models with interaction terms and

po ynom a s.



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The method of least squares:

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Least

squares

norma

equations



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The test procedure is to calculate the test statistic



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The regression sum of squares is

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See Table 4.12

s e or e -tests on the

individual

regressors in the

consumer nance

model – both

variables are

significant



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•

• R-student – an outlier diagnostic• T e PRESS stat st c

• R2 for prediction based on PRESS – a measure

of how well the model will predict new data

• Measure of levera e – hat dia onals

• Cook’s distance – a measure of influence



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Learnin Ob ectives

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