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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 | |