Engineering Management 385 Statistical Process Control Stephen A. Raper, Ph.D., Associate Professor Chapter 3 – Inferences About Process Quality Continued – Single Sample Case

Objectives Continue illustration of Statistical Inferences for Single Sample Cases Illustrate case of Inference on the mean of a normal distribution, variance unknown Illustrate case of Inference on the Variance of a Normal Distribution Inference on Population Proportion Work Example Problems

Continue illustration of Statistical Inferences for Single Sample Cases

Illustrate case of Inference on the mean of a normal distribution, variance unknown

Illustrate case of Inference on the Variance of a Normal Distribution

Inference on Population Proportion

Work Example Problems

These PowerPoint slides are the author/text provided slides. Slight modifications may have occurred and the background used is that required by UMR. The slides generally follow the order in each chapter.

These PowerPoint slides are the author/text provided slides. Slight modifications may have occurred and the background used is that required by UMR. The slides generally follow the order in each chapter.

3-3.4 Inference on the Variance of a Normal Distribution Hypothesis Testing Hypotheses: H 0 : H 1 : Test Statistic: Significance Level,  Rejection Region:

Hypothesis Testing

Hypotheses: H 0 : H 1 :

Test Statistic:

Significance Level, 

Rejection Region:

3-3.4 Inference on the Variance of a Normal Distribution Confidence Interval on the Variance Two-Sided: See the text for the one-sided confidence intervals.

Confidence Interval on the Variance

Two-Sided:

See the text for the one-sided confidence intervals.

3-3.5 Inference on a Population Proportion Hypothesis Testing Hypotheses: H 0 : p = p 0 H 1 : p  p 0 Test Statistic: Significance Level,  Rejection Region:

Hypothesis Testing

Hypotheses: H 0 : p = p 0 H 1 : p  p 0

Test Statistic:

Significance Level, 

Rejection Region:

3-3.5 Inference on a Population Proportion Confidence Interval on the Population Proportion Two-Sided: See the text for the one-sided confidence intervals.

Confidence Interval on the Population Proportion

Two-Sided:

See the text for the one-sided confidence intervals.

3-3.6 The Probability of Type II Error Calculation of P(Type II Error) Assume the test of interest is H 0 : H 1 : P(Type II Error) is found to be The Power of the test is then 1 - 

Calculation of P(Type II Error)

Assume the test of interest is H 0 : H 1 :

P(Type II Error) is found to be

The Power of the test is then 1 - 

3-3.6 The Probability of Type II Error Operating Characteristic (OC) Curves Operating Characteristic (OC) curve is a graph representing the relationship between  ,  ,  and n . OC curves are useful in determining how large a sample is required to detect a specified difference with a particular probability.

Operating Characteristic (OC) Curves

Operating Characteristic (OC) curve is a graph representing the relationship between  ,  ,  and n .

OC curves are useful in determining how large a sample is required to detect a specified difference with a particular probability.

3-3.6 The Probability of Type II Error Operating Characteristic (OC) Curves

Operating Characteristic (OC) Curves

3-3.7 Probability Plotting Probability plotting is a graphical method for determining whether sample data conform to a hypothesized distribution based on a subjective visual examination of the data. Probability plotting uses special graph paper known as probability paper . Probability paper is available for the normal, lognormal, and Weibull distributions among others. Can also use the computer.

Probability plotting is a graphical method for determining whether sample data conform to a hypothesized distribution based on a subjective visual examination of the data.

Probability plotting uses special graph paper known as probability paper . Probability paper is available for the normal, lognormal, and Weibull distributions among others.

Can also use the computer.

3-3.7 Probability Plotting Example 3-8

Example 3-8

Program Completed © 2003 Curators of University of Missouri University of Missouri-Rolla