Statistical Process Control

Slides:

Advertisements

Similar presentations

Lecture 14 chi-square test, P-value Measurement error (review from lecture 13) Null hypothesis; alternative hypothesis Evidence against null hypothesis.

Advertisements

Chapter 9: Simple Regression Continued

Inference about Means/Averages Chapter 23 Looking at means rather than percentages.

Distributions of sampling statistics Chapter 6 Sample mean & sample variance.

Estimating a Population Variance

1 1 Slide © 2003 South-Western /Thomson Learning™ Slides Prepared by JOHN S. LOUCKS St. Edward’s University.

1 1 Slide IS 310 – Business Statistics IS 310 Business Statistics CSU Long Beach.

1 1 Slide Slides Prepared by JOHN S. LOUCKS St. Edward’s University © 2002 South-Western/Thomson Learning 

Econ 3790: Business and Economic Statistics

1 1 Slide © 2005 Thomson/South-Western Slides Prepared by JOHN S. LOUCKS St. Edward’s University Slides Prepared by JOHN S. LOUCKS St. Edward’s University.

Chi square.  Non-parametric test that’s useful when your sample violates the assumptions about normality required by other tests ◦ All other tests we’ve.

Confidence intervals. Population mean Assumption: sample from normal distribution.

DATA ANALYSIS I MKT525. Plan of analysis What decision must be made? What are research objectives? What do you have to know to reach those objectives?

Useful Statistical Distributions for Econometrics Econometrics is usually concerned with the estimation of equations of the form: The normal distribution.

1 Inference About a Population Variance Sometimes we are interested in making inference about the variability of processes. Examples: –Investors use variance.

1 Confidence Intervals for Means. 2 When the sample size n< 30 case1-1. the underlying distribution is normal with known variance case1-2. the underlying.

SECTION 6.4 Confidence Intervals for Variance and Standard Deviation Larson/Farber 4th ed 1.

Estimating a Population Variance

1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 11 Inferences About Population Variances n Inference about a Population Variance n.

Statistics for the Behavioral Sciences Second Edition Chapter 11: The Independent-Samples t Test iClicker Questions Copyright © 2012 by Worth Publishers.

Measures of Variability Objective: Students should know what a variance and standard deviation are and for what type of data they typically used.

1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Slides by JOHN LOUCKS St. Edward’s University.

Chapter 13 – Difference Between Two Parameters Math 22 Introductory Statistics.

Estimating a Population Standard Deviation. Chi-Square Distribution.

Normal Distribution.

Analysis of Variance. What is Variance? Think….think…

7.5 Hypothesis Testing for Variance and Standard Deviation Key Concepts: –The Chi-Square Distribution –Critical Values and Rejection Regions –Chi-Square.

Section 6.4 Inferences for Variances. Chi-square probability densities.

1 1 Slide The Simple Linear Regression Model n Simple Linear Regression Model y =  0 +  1 x +  n Simple Linear Regression Equation E( y ) =  0 + 

Chapter 9 Inferences Based on Two Samples: Confidence Intervals and Tests of Hypothesis.

Estimating a Population Variance

Chapter 4 Exploring Chemical Analysis, Harris

Chi Square Test for Goodness of Fit Determining if our sample fits the way it should be.

Unit 7 Section : Confidence Intervals for Variances and Standard Deviations  In 7-2 to 7-4 we determined confidence intervals for means and proportions.

Section 7-5 Estimating a Population Variance. MAIN OBJECTIIVES 1.Given sample values, estimate the population standard deviation σ or the population variance.

Measures of Variation. Range, Variance, & Standard Deviation.

1 1 Slide IS 310 – Business Statistics IS 310 Business Statistics CSU Long Beach.

Histograms and Distributions Experiment: Do athletes have faster reflexes than non-athletes? Questions: - You go out and 1st collect the reaction time.

Cross Tabulation with Chi Square

Statistical Inferences for Population Variances

統計學 Spring 2004 授課教師：統計系余清祥日期：2004年3月16日第五週：比較變異數.

Sampling distribution of

Inference concerning two population variances

Lecture Slides Elementary Statistics Twelfth Edition

Other confidence intervals

Chapter 4. Inference about Process Quality

Variance and Standard Deviation Confidence Intervals

Math 4030 – 10b Inferences Concerning Variances: Hypothesis Testing

Confidence Intervals and Hypothesis Tests for Variances for One Sample

Part Three. Data Analysis

Statistics in Applied Science and Technology

Review of Chapter 11 Comparison of Two Populations

Inference on Mean, Var Unknown

Section 6-4 – Confidence Intervals for the Population Variance and Standard Deviation Estimating Population Parameters.

2) Using the data in the table above, compute the sample mean.

Since everything is a reflection of our minds,

Chapter 11 Inferences About Population Variances

Chapter 12 Inference on the Least-squares Regression Line; ANOVA

F - Ratio Table Degrees of Freedom for the Factor

STATISTICS INTERVAL ESTIMATION

Confidence Intervals for a Standard Deviation

Department of Computer Science

Summary of Tests Confidence Limits

Chapter 7 Lecture 3 Section: 7.5.

6.3 Sampling Distributions

Chapter 6 Confidence Intervals.

One Way ANOVA test Determine whether there are any statistically significant differences between the means of three or more independent groups.

Statistical Inference for the Mean: t-test

Testing a Claim About a Standard Deviation or Variance

Estimating a Population Variance

Presentation transcript:

Statistical Process Control Ratio of Variances Review of the F distribution

Derivation of Sampling Distributions A sum of m standard normals squared is a chi-square with m degrees of freedom Chi-square with m degrees of freedom plus a chi-square with n degrees of freedom is a chi-square with m+n degrees of freedom A standard normal divided by the square root of a chi-square with n degrees of freedom is a t-distribution with n degrees of freedom

Derivation of the F A chi-square with m degrees of freedom divided by a chi-square with n degrees of freedom is an F-distribution with m and n degrees of freedom

F Confidence Interval

F Confidence Interval

Hypothesis Test