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| Introduction | |
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| Describing Data Graphically and Numerically | |
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| Getting Started With Statistics | |
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| What is Statistics? | |
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| Population and Sample in a Statistical Study | |
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| Classification of Various Types of Data | |
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| Frequency Distribution Tables for Qualitative and Quantitative Data | |
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| Graphical Description of Qualitative and Quantitative Data | |
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| Dot Plot | |
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| Pie Chart | |
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| Bar Chart | |
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| Histograms | |
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| Line Graph | |
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| Stem-and-Leaf Plot | |
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| Numerical Measures of Quantitative Data | |
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| Measures of Centrality | |
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| Measures of Dispersion | |
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| Numerical Measures of Grouped Data | |
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| Measures of Relative Position | |
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| Box-Whisker Plot | |
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| Measures of Association | |
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| Case Studies | |
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| Using JMP | |
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| Review Practice Problems | |
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| Elements of Probability | |
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| Random Experiments, Sample Spaces, and Events | |
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| Concepts of Probability | |
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| Techniques of Counting Sample Points | |
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| Tree Diagrams | |
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| Permutations | |
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| Combinations | |
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| Arrangements of n Objects Involving Several Kinds of Objects | |
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| Application of Combinations to Probability Problems | |
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| Conditional Probability | |
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| Bayes' Theorem | |
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| Introducing Random Variables | |
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| Review Practice Problems | |
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| Discrete Random Variables and Some Important Discrete Probability Distributions | |
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| Graphical Descriptions of Discrete Distributions | |
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| Mean and Variance of a Discrete Random Variable | |
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| The Moment-Generating Function Expectation of a Special Function | |
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| The Discrete Uniform Distribution | |
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| The Hypergeometric Distribution | |
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| The Bernoulli Distribution | |
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| The Binomial Distribution | |
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| The Multinomial Distribution | |
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| The Poisson Distribution | |
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| Poisson Distribution as a Limiting Form of the Binomial | |
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| The Negative Binomial Distribution | |
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| Some Derivations and Proofs (Optional) | |
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| Proof that the Probability Function of the Hypergeometric Distribution Sums to | |
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| Mean and the Variance of the Hypergeometric Distribution | |
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| Mean and the Variance of the Binomial Distribution | |
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| Mean and the Variance of the Poisson Distribution | |
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| Derivation of the Poisson Distribution | |
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| A Case Study | |
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| Using JMP | |
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| Review Practice Problems | |
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| Continuous Random Variables and Some Important Continuous Probability Distributions | |
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| Continuous Random Variables | |
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| Mean and Variance of Continuous Random Variables | |
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| The Moment-Generating Function - Expectation of a Special Function | |
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| Chebychev's Inequality | |
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| The Uniform Distribution | |
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| The Normal Distribution | |
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| Definition and Properties | |
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| The Standard Normal Distribution | |
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| The Moment-Generating Function of the Normal Distribution | |
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| Distribution of Linear Combinations of Independent Normal Variables | |
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| Approximation of the Binomial Distribution by the Normal Distribution | |
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| A Test of Normality | |
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| The Lognormal Distribution | |
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| The Exponential Distribution | |
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| The Gamma Distribution | |
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| The Weibull Distribution | |
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| A Case Study | |
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| Using JMP | |
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| Review Practice Problems | |
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| Distribution Functions of Random Variables | |
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| Distribution Functions of Two Random Variables | |
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| Case of Two Discrete Random Variables | |
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| Case of Two Continuous Random Variables | |
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| The Mean Value and Variance of Functions of Two Random Variables | |
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| Conditional Distributions | |
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| Correlation Between Two Random Variables | |
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| Bivariate Normal Distribution | |
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| Extension to Several Random Variables | |
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| The Moment-Generating Function Revisited | |
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| Review Practice Problems | |
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| Sampling Distribution | |
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| Random Sampling | |
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| Random Sampling from an Infinite Population | |
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| Random Sampling from a Finite Population | |
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| The Sampling Distribution of the Mean | |
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| The Central Limit Theorem | |
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| Sampling from a Normal Population | |
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| The Chi-Square Distribution | |
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| The Student t Distribution | |
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| Snedecor's F Distribution | |
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| Order Statistics | |
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| Distribution of the Largest Element in a Sample | |
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| Distribution of the Smallest Element in a Sample | |
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| Distribution of the Median of a Sample and of the kth-Order Statistic | |
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| The Range as an Estimate of in Normal Samples | |
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| Using JMP | |
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| Review Practice Problems | |
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| Estimation of Population Parameters | |
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| Introduction | |
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| Point Estimators for the Population Mean and Variance | |
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| Properties of Point Estimators | |
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| Methods of Finding Point Estimators | |
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| Interval Estimators for the Mean of a Normal Population | |
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| Known | |
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| Unknown | |
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| Sample Size is Large | |
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| Interval Estimators for the Difference of Means of Two Normal Populations | |
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| Variances are Known | |
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| Variances are Unknown | |
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| Interval Estimators for the Variance of a Normal Population | |
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| Interval Estimators for the Ratio of Variances of Two Normal Populations | |
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| Point and Interval Estimators for the Parameters of Binomial Populations | |
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| One Binomial Population | |
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| Two Binomial Populations | |
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| Determination of Sample Size | |
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| Some Supplemental Information (Optional) | |
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| Proof of | |
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| Predicting an Arbitrary Observation | |
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| A Case Study | |
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| Using JMP | |
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| Review Practice Problems | |
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| Hypothesis Testing | |
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| Introduction | |
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| Basic Concepts of Testing a Statistical Hypothesis | |
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| Tests Concerning the Mean of a Normal Distribution Having Known Variance | |
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| Tests Concerning the Mean of a Normal Population Having Unknown Variance | |
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| Large Sample Theory | |
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| Tests Concerning the Difference of Means of Two Populations Having Distributions with Known Variances | |
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| Tests Concerning the Difference of Means of Two Populations Having Distributions with Unknown Variances | |
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| Two Population Variances Are Equal | |
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| Two Population Variances Are Not Equal | |
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| The Paired t-Test | |
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| Testing Population Proportions | |
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| Testing Concerning the One Population Proportion | |
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| Testing Concerning the Difference Between Two Population Proportions | |
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| Tests Concerning the Variance of a Normal Distribution | |
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| Tests Concerning the Ratio of Variances of Two Normal Populations | |
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| An Alternative Technique for Testing of Statistical Hypotheses: Using Confidence Intervals | |
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| Sequential Tests of Hypotheses (Optional) | |
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| A One-Sided Sequential Testing Procedure | |
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| A Two-Sided Sequential Testing Procedure | |
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| Case Studies | |
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| Using JMP | |
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| Review Practice Problems | |
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| Elements of Reliability Theory | |
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| The Reliability Function | |
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| The Hazard Rate | |
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| Employing the Hazard Function | |
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| Estimation: Exponential Distribution | |
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| Hypothesis Testing: Exponential Distribution | |
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| Estimation: Weibull Distribution | |
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| Case Studies | |
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| Using JMP | |
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| Review Practice Problems | |
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| Statistical Quality Control and Phase I Control Charts | |
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| Basic Concepts of Quality and Its Benefits | |
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| What Is a Process? | |
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| Common and Assignable Causes | |
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| Control Charts | |
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| Control Charts for Variables | |
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| Shewhart and R Control Chart | |
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| Shewhart and R Control Chart When Process Mean and Process Standard Deviation Are Known | |
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| The Shewhart and S Control Chart | |
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| Control Charts for Attributes | |
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| The p Chart: Control Chart for the Fraction of Nonconforming Units | |
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| The p Chart: Control Chart for the Fraction of Nonconforming units with Variable Sample Sizes | |
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| The np Control Chart: Control Chart for Number of Nonconforming Units | |
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| The C Control Chart | |
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| The U Control Chart | |
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| Process Capability | |
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| Case Studies | |
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| Using JMP | |
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| Review Practice Problems | |
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| Statistical Quality Control and Phase II Control Charts | |
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| Basic Concepts of CUSUM Control Chart | |
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| Designing a CUSUM Control Chart | |
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| Two-Sided CUSUM Control Chart Using a Numerical Procedure | |
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| The Fast Initial Response (FIR) Feature for the CUSUM Control Chart | |
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| The Combined Shewhart-CUSUM Control Chart | |
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| The CUSUM Control Chart for Controlling Process Variability | |
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| The Moving Average (MA) Control Chart | |
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| The Exponentially Weighted Moving Average (EWMA) Control Chart | |
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| Case Studies | |
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| Using JMP | |
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| Review Practice Problems | |
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| Analysis of Categorical Data | |
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| Introduction | |
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| The Chi-Square Goodness of Fit Test | |
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| Contingency Tables | |
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| The 2 2 Case Parameters Known | |
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| The Case Parameters Unknown | |
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| The Contingency Table | |
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| Chi-Square Test for Homogeneity | |
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| Comments on the Distribution of the Lack-of-Fit Statistic (optional) | |
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| Case Studies | |
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| Using JMP | |
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| Review Practice Problems | |
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| Nonparametric Tests | |
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| Introduction | |
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| The Sign Test | |
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| One-Sample Test | |
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| The Wilcoxon Signed-Rank Test | |
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| Two-sample Test | |
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| The Mann-Whitney (Wilcoxon) W Test for Two Samples | |
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| Run Tests | |
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| Runs Above and Below the Median | |
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| The Wald-Wolfowitz Run Test | |
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| Spearman Rank Correlation | |
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| Using JMP | |
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| Review Practice Problems | |
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| Simple Linear Regression Analysis | |
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| Introduction | |
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| Fitting the Simple Linear Regression Model | |
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| Simple Linear Regression Model | |
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| Fitting a Straight Line by Least Squares | |
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| Sampling Distributions of the Estimators of Regression Coefficients | |
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| Unbiased Estimator of | |
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| Further Inferences Concerning Regression Coefficients and | |
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| Confidence Interval for with Confidence Coefficient | |
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| Confidence Interval for with Confidence Coefficient | |
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| Confidence Interval for with Confidence Coefficient | |
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| Prediction Interval for a Future Observation with Confidence Coefficient | |
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| Test of Hypotheses for | |
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| Analysis of Variance Approach to Simple Regression Analysis | |
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| Residual Analysis | |
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| Transformations | |
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| Inference About | |
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| A Case Study | |
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| Using JMP | |
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| Review Practice Problems | |
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| Multiple Linear Regression Analysis | |
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| Introduction | |
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| The Multiple Linear Regression Model | |
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| Estimation of Regression Coefficients | |
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| Estimation of Regression Coefficients Using Matrix Notation | |
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| Properties of the Least-Squares Estimators | |
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| The Analysis of Variance Table | |
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| More Inferences About Regression Parameters | |
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| The Multiple Linear Regression Model Using Qualitative or Categorical Predictor Variables | |
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| Standardized Regression Coefficients | |
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| Building Regression Type Prediction Models | |
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| Residual Analysis | |
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| Certain Criteria for Model Selection | |